1、HandbookDesign of experiments in protein production and purification ContentsIntroduction 4Symbols used in this handbook 5Traditional experimental design versus DoE 6DoE nomenclature 8DoE at a glance 8History of DoE 10 Industrial applications 11DoE in protein production and purification 12Upstream p

2、rocess development 14A strategy for protein purification 15The individual purification steps 15Principles of combining purification steps 16Principles of selection of chromatography media 17Factors and responses when optimizing protein 18 purification Responses 18 Capture 19 Intermediate purificatio

3、n 19 Polishing 20 Chromatography step optimization 20Process development and characterization 21Quality by design(QbD)22Protein purification tools for DoE 23 Process development tools 23 Other tools for parallel protein purification 25Design of experiments,step-by-step 26Gather information before st

4、arting 27Step 1.Define objective,factors,and ranges 28 Objectives 29 Screening 29 Optimization 30 Robustness testing 30 Design considerations 30 Factors and factor ranges 30 Quantitative and qualitative factors 32 Controllable and uncontrollable factors 32 Structured approach to selecting factors 32

5、 Independent measurements of factor effects 33Step 2.Define responses and measurement systems 34 Quantitative and qualitative responses 34 Measurement system requirements 35Step 3.Create the design 36 Design resolution 38 Number of experiments needed 38 Systematic bias 39 Order of experiments 39 Rep

6、lication of experiments 40 Arranging experiments into blocks 40 Experimental design center points 41 Evaluation of design quality(condition number)42Step 4.Perform experiments 43 DoE with UNICORN software and KTA systems 43Configuration of KTA systems 44Step 5.Create model 44 Signal and noise 46 Mod

7、el details 47Step 6.Evaluation of data 50 Our questions(hypotheses)about the process 53 Analyzing model quality 54 P-values 54 Lack of fit 55 Confidence level how sure can we be?56 Alpha-risk and confidence level 56 Outliers in the data 57 Confounding failing to see the difference 58Visualization of

8、 results 59 Replicate plot 61 Normal probability plot of residuals 62 Summary-of-fit plot 63 Coefficient plot 65 Main-effects plot 66 Interaction plot 66 Residuals-vs-variable plot 67 Observed-vs-predicted plot 68 Residuals-vs-run order plot 68 ANOVA table 69 Response-surface plot 70 Sweet-spot plot

9、 70Practical use of the obtained model 71 Predict outcome for additional factor values 71 (prediction list)Optimize results 71Application examples 725.1 Study of culture conditions for optimized 73 Chinese hamster ovary(CHO)cell productivity Case background 73 Methodology 73 Results 74 Conclusions 7

10、45.2 Rapid development of a capture step for purifying 75 recombinant S-transaminase from E.coli Case background 75 Methodology 75 Results 76 Conclusion 7801020305042Principles and methodology handbooks from CytivaCytiva offers a wide range of handbooks that provides practical tips and in-depth info

11、rmation about common methodologies used in the lab.Visit to view the complete list and download your copies today.5.3 Optimization of conditions for immobilization 79 of transaminase on NHS-activated Sepharose chromatography medium Case background 79 Methodology 79 Results 80 Conclusion 815.4 Optimi

12、zation of dynamic binding capacity of 82 Capto S chromatography medium Case background 82 Methodology 83 Results 84 Conclusions 845.5 Purification of an antibody fragment using Capto L 85 chromatography medium Case background 85 Methodology 86 Results 86 Conclusions 875.6 Optimization of elution con

13、ditions for a human IgG 88 using Protein A Mag Sepharose Xtra magnetic beads Case background 88 Methodology 89 Results 90 Conclusions 915.7 Optimization of the multimodal polishing step 92 of a MAb purification process Case background 92 Methodology 92 Results 93 Conclusions 93Appendix 94Appendix I

14、95Parameter interactions 95Monte Carlo simulation 96Design considerations 97Design descriptions 99 Full factorial design 101 Fractional factorial design 102 Rechtschaffner screening design 103 L-designs 103 Composite factorial design for optimization and 104 response surface modeling(RSM)Box-Behnken

15、 RSM design 105 Three-level full RSM design 105 Rechtschaffner RSM design 105 Doehlert RSM design 106 Mixture design 106 D-optimal design 107Calculating coefficients 108Data transformation 110Blocking RSM designs 111Appendix II 112Terminology 112 Six Sigma terminology and selected formulas 112 Chrom

16、atography terminology 120Literature list 124Ordering information 125063Introduction014Design of experiments(DoE)is a technique for planning experiments and analyzing the information obtained.The technique allows us to use a minimum number of experiments,in which we systematically vary several experi

17、mental parameters simultaneously to obtain sufficient information.Based on the obtained data,a mathematical model of the studied process(e.g.,a protein purification protocol or a chromatography step)is created.The model can be used to understand the influence of the experimental parameters on the ou

18、tcome and to find an optimum for the process.Modern software is used to create the experimental designs,to obtain a model,and to visualize the generated information.In a protein research lab or during process development,a DoE approach can greatly improve the efficiency in screening for suitable exp

19、erimental conditions,for example,for cell culture,protein separation,study of protein stability,optimization of a process,or robustness testing.This handbook provides an introduction and an overview of DoE,followed by a step-by-step procedure that targets both newcomers and those with previous exper

20、ience in DoE.The focus is on DoE for protein production and purification but the theory can be applied in many other applications.General advice WarningsSymbols used in this handbook5Traditional experimental design versus DoEDoE is not an alternative approach for experimental research.DoE is rather

21、a methodology that provides stringency to the classical approach for performing research.How DoE can contribute to the statistical part of the research process is briefly illustrated in Figure 1.1.Before describing the individual components of a DoE methodology,it is worthwhile to briefly consider t

22、he shortcomings of the traditional one-factor-at-a-time optimization approach.In the simplest traditional approach to optimize experiments,one parameter is varied while all others are fixed.In Figure 1.2,the traditional approach is exemplified with the optimization of yield in a purification step.It

23、 can wrongly be assumed that the optimum levels for the factors(pH and conductivity in Fig 1.2)can simply be found by using the optimum levels of the factors obtained in the two series of experiments.As this setup only covers a limited part of the experimental space,this assumption is often incorrec

24、t.The reason is that experiments performed in the traditional way could be positioned out of scope,leading to no conclusions or sometimes even worse,the wrong conclusions.Further,the traditional setup does not take into account that experimental parameters can be dependent of each other(parameter in

25、teraction).In ion exchange chromatography,for example,the pH optimum will change when conductivity is changed.Thus,with the one-factor-at-a-time experimental setup,there is a great risk that the true optimum for the studied process is not identified.Ultimately,a study with the wrong setup cannot be

26、saved or evaluated by even the most advanced statistical software programs.Current knowledge Formulate a hypothesisInterpret and use resultsPlan experimentsDesign and perform experimentsVisualize and analyze results and statisticsFig 1.1.Schematic overview of the statistical contribution of DoE(the

27、green oval)to the iterative research process.Yield(%)pHpH range 58pH 6.570Yield(%)ConductivityConductivity range 1070 mS/cm40 mS/cm70(A)(B)Fig 1.2.The traditional one-factor-at-a-time approach used for optimization of a protein purification step with respect to pH and conductivity.(A)A first series

28、of experiments varying pH.(B)A second series of experiments varying conductivity at the pH value(pH 6.5)giving the highest response in(A).The experiments indicate that highest yield is obtained by using pH 6.5 and a conductivity of 40 mS/cm.HighYieldLowYield(%)ConductivityConductivity range 1070 mS/

29、cm40 mS/cm706In the DoE approach,on the contrary,process parameters are allowed to vary simultaneously,which allows the effect of each parameter,individually as well as combined to be studied.As shown in Figure 1.3,each parameter can have an optimum,but when combined,values might be found to give a

30、different optimum.When studying the effect of two or more factors on a process,the controlled arrangement of the DoE experimental setup allows collection of sufficient information with fewer experiments,compared to the traditional approach(Fig 1.4).Fig 1.3.(A)The traditional one-parameter-at-a-time

31、optimization approach versus(B)the DoE approach.With the DoE approach,the chances of finding the optimal conditions(in dark orange)for the studied process increase.In addition,the combined effect of parameter 1 and 2(interaction)on the response can be identified and evaluated.Although more experimen

32、ts were performed than with the DoE approach,the traditional experimental setup failed to identify the optimum.Individual experiments are depicted with the filled black circles.Color scale:blue indicates a low response value and dark orange a high response value,here the desired response(optimum).In

33、formation(%)Number of experiments64128HighLow100Traditional one-factor-at-a-time approach DoE approach Required level Fig 1.4.A schematic comparison of the number of experiments required to reach an acceptable level of information in an experimental study.Traditional approachOptimumParameter 1Parame

34、ter 2(A)(B)DoE approachOptimumParameter 2Parameter 27DoE nomenclatureLike all scientific disciplines,DoE has its own nomenclature.The nomenclature differs between the fields to which DoE is applied.Hence,there can be several terms for a particular phenomenon.For example,the model is also called the

35、transfer function,the cause-and-effect relationship,or simply the relationship between our factors and the responses.In this handbook,we use the basic DoE terms introduced in Figure 1.5.Other terms are defined as they are introduced in the text.For some terms that are firmly established in protein r

36、esearch and in process development,we use that term and the corresponding DoE term alternately.In cases of uncertainty,please consult Appendix 2,Terminology.DoE at a glanceDoE can be defined as a systematic way of changing experimental parameters(factors)to create results that can be methodically an

37、alyzed and that provide useful information about the process studied.Figure 1.5 provides an overview of the various steps of the DoE workflow.The different steps of the DoE workflow are described in more detail in Chapter 3.The first step involves defining the objective of the study and the factors

38、that should be systematically varied.In the example in Figure 1.2,these factors are pH and conductivity.The range of variation(the upper and lower value of each factor)is also defined in this step.The second step involves defining relevant responses(type of analytical methods and data).Chapter 2 cov

39、ers a comprehensive discussion on factors and responses that are relevant for DoE in protein production and purification.Define the objective of the study,critical experimental parameters,and their rangesDefine what should be analyzed and decide which analysis method to be used Create an experimenta

40、l designPerform the experimentsEnter response data for a mathematical model of the studied processEvaluate the mathematical model 1.Define objective,factors,and their ranges2.Define responses and measurement system 3.Create the design4.Perform the experiments5.Create model6.Evaluate the model(A)(B)F

41、ig 1.5.The DoE workflow summarized using both(A)the terminology used in protein purification and in(B)the corresponding DoE terminology used throughout this handbook.Predominately software-supported steps are indicated.8A DoE experiment is set up in a rational way to cover the intended experimental

42、space.As shown in Figure 1.6,the design can be visualized by a cube that represents the experimental space to be explored.The different factors are represented by the axes of the cube(x1,x2,and x3 represent three different factors,e.g.,pH,conductivity,and temperature).Using DoE,multiple factors hand

43、led in a single series of experiments can be viewed in arrangements called hypercubes as the setup becomes multidimensional.Depending on the study to be performed,different types of designs are available(see Chapters 3 and 6).After performing the experiments according to the selected design,step 5 i

44、n the workflow(Fig 1.5)involves the use of DoE software for obtaining a mathematical model that describes the investigated process or system.A relevant model tells us,for example,which factors have a significant impact on the response and which factors do not.It is important to evaluate the model to

45、 determine its relevance,again using DoE software(step 6,Fig 1.5).The model is often visualized as a response surface plot and is used for evaluation of other parameter settings or process outputs within the experimental space(Fig 1.3 and Chapter 4).When performing a DoE study,it should always be ca

46、refully verified that the model is relevant.Verification of the model is preferably done through verification experiments within the experimental space.One important requirement for the model to be relevant is that there actually is a relationship between a factor and the response.UNICORN software,u

47、sed together with the KTA systems,provides support for the entire DoE workflow.x1x3x2(A)(B)Fig 1.6.(A)A cube and(B)a hypercube representing the experimental space in a DoE setup.The cube represents an experimental design with three factors(x1,x2,and x3),where the blue spheres correspond to experimen

48、ts in which low and high settings for each factor are combined and the yellow spheres represents the replicated center point,that is,the midpoint setting for each factor.If more than three factors(e.g.,four as in B)are studied,a hypercube can represent the set of experiments with combinations of all

49、 the factors.A center point(yellow),the mid value between the low and high setting for each factor,is replicated to estimate the experimental error and also to detect nonlinear relationships(see Chapter 3).9History of DoEDoE methodology was proposed by Sir Ronald A.Fisher,a British statistician,as e

50、arly as 1926.The pioneering work dealt with statistical methods applied to agriculture and the concepts and procedures are still in use today.In particular,Fisher and coworkers found that experimental design requires multiple measurements(i.e.,replicates)to estimate the degree of variation in the me

51、asurements.During World War II,DoE expanded beyond its roots in agricultural experiment as the procedure became a method for assessing and improving the performance of weapons systems.Immediately following World War II,the first industrial era marked a boom in the use of DoE.Total quality management

52、(TQM)and continuous quality improvement(CQI)are management techniques that were later used also by the US armaments industry.Some efficient designs for estimating several main effects simultaneously were developed by Bose and Kishen in 1940,but remained rather unknown until the Plackett-Burman desig

53、ns were presented in 1946.About that time,Rao introduced 1910R.A.Fisher revolutionizes modern statistics.He pioneered DoE,introduced the use of p-values for deciding which experiments are significant and which are not,and Analysis of Variance(ANOVA),etc.Confidence intervals are introduced by Jerzy N

54、eyman leading to modern scientific samplingBox and Wilson introduceresponse surfaces for applications in the chemical and process industriesIndustrial(automobile and electronics)quality improvement initativesTaguchi statistical methods and robust parameter designsEconomic competitiveness and globali

55、zation Statistical programming Big data0001950Agricultural originsIndustrial useIndustrial developmentModern timesFig 1.7.A summary of the history of DoE.the concepts of orthogonal arrays as experimental designs.This concept played a central role in the methods devel

56、oped by Taguchi in the early 50s.In 1950,Cox and Cochran published the book Experimental Designs that became the major reference work for statisticians for years afterwards.The development of the theory of linear models was considered and the concerns of the early authors were addressed.Today,the th

57、eory rests on advanced topics in linear algebra and combinatorics.The history of DoE is briefly outlined in Figure 1.7.10Industrial applicationsThe Taguchi methods were successfully applied and adopted by Japanese industries to improve quality and cost efficiency.In the 1960s,the quality of Japanese

58、 products started to improve radically as the Japanese car industry adopted statistical quality control procedures and conducted experiments that started a new era.Total quality management(TQM)and continuous quality improvement(CQI)are management techniques that were subsequently also embraced by US

59、 industry and are referred to as fractional factorial designs.In the 1960s,randomized experiments became the standard for approval of new medications and medical procedures.Medical advances were previously based on anecdotal data,drawing conclusions from poor experimental setups and limited number o

60、f trials.The implementation of statistical procedures during this period was a move toward making the randomized,double-blind,clinical trial a standard method for approval of any new pharmaceutical product,medical equipment or procedure.Since its beginnings in agriculture,DoE has been applied across

61、 many sectors of the industry.Around 1990,Six Sigma,a new way of representing CQI,became popular.Six Sigma is a technique that uses various tools,including DoE,to drive statistics-based quality improvements.Today,Six Sigma has been adopted by many of the large manufacturing companies including Cytiv

62、a.11DoE in protein production and purification0212Optimization of protein purification is a multifactorial exercise,where factors such as sample composition,concentration and volume,purification technique,chromatography media(resins),binding,wash,and elution conditions(including pH,ionic strength,te

63、mperature,and additives)all might play a role.DoE is an excellent tool for identifying which factors are important and for finding an optimum for the process.The selection of factors and responses to explore in DoE for different protein purification situations is discussed in this chapter.A descript

64、ion of useful laboratory tools for performing DoE in the development of a protein purification process is also included.For a thorough description of protein purification strategies,please refer to the handbook Strategies for Protein Purification(28-9833-31).For academic laboratories,the terminology

65、 used in the industry might sometimes be confusing.For example,the word“process”can refer to a method or protocol,but also to a complex workflow of different techniques and operations for a complete production and purification procedure.“Upstream”refers to the production part,for example,of cells or

66、 proteins in cell culture processes,whereas“downstream”involves processing of the material from the upstream process into a final product.Biopharmaceutical protein production and purification differs from protein production and purification in the research laboratory,both in scale and in regulatory

67、and industrial demands.The basic production,purification strategy,and technologies used,however,are the same.Therefore,the DoE approach in terms of selecting relevant factors and responses is similar in both the research and the industrial setting.An example from one area is generally applicable als

68、o to other areas.The main difference from a DoE perspective is that the industrial production setting requires stringent optimization to reach the most economical process.A comprehensive DoE effort is often a must in current process development.In research,good-enough purification schemes are often

69、sought.In such case,a more limited DoE effort can be sufficient,comprising less coverage of the experimental space and thus requiring fewer experiments.13Upstream process developmentIn the biopharmaceutical industry,the production process for a target molecule is divided into upstream processing,inc

70、luding production of the target protein in a cell culture or fermentation process,as well as filtration steps;downstream processing,comprising yield of the target protein in a pure form;and final processing to gain product integrity and safety using techniques such as sterile filtration.The upstream

71、 process has a profound effect on the downstream process.Optimized upstream and downstream processes are essential for fast production of highly pure proteins.Despite the long experience and widespread use of recombinant technology,many challenges remain when generating recombinant variants of nativ

72、e proteins.Critical cultivation conditions,such as temperature,pH,induction conditions,and medium composition,are carefully selected during process development to improve expression performance of the host cells.Because of the high number of impacting parameters and potential interaction between the

73、m,process optimization can be a tedious procedure.By applying a traditional trial-and-error approach,including changing one parameter at a time,the parameter responsible for the outcome can be identified.However,this approach requires numerous cultivations and is time-consuming.As parameters interac

74、t,the identification of impacting factors is suboptimal and does not allow for detection of significant contributors to response changes.Using DoE helps to reduce necessary experimental burden,as settings of several parameters can be changed simultaneously.In addition,individual parameter effects as

75、 well as interactions and nonlinear effects can be identified and quantitated during data evaluation.As an example of use in an upstream process,a DoE for optimization of monoclonal antibody(MAb)production was set up.Cultivation temperature and pH were selected as factors(Chapter 5.1).The responses

76、were MAb monomer content,as monitored by gel filtration(size exclusion chromatography),and target protein concentration.For this MAb,a maximum for monomer content was found by cultivation at 32C,at pH 6.8.14A strategy for protein purificationA protein purification process can be structured into diff

77、erent steps(Fig 2.1).In the capture,intermediate purification,and polishing(CIPP)model,sample preparation is followed by isolation and concentration of the target protein in the initial capture stage.During intermediate purification,bulk contaminants are removed.In the final polishing step,the most

78、difficult impurities,such as aggregates of the target protein,are removed.In a research setting,the purity requirements are often modest and,in such cases,only a capture step may be required.Also in cases where purity demands are higher,the capture step can be sufficiently efficient to be immediatel

79、y followed by the polishing step.The number of purification steps will depend on the desired outcome of the overall purification process and on how efficient the individual steps are.Even in the simplest case,where our aim is a single purification step,a DoE approach can be beneficial.Increasing the

80、 number of purification steps will decrease the overall protein yield.Additional purification steps also means a longer purification time,which can be detrimental to the activity of the product.Thus,addition of purification steps will increase purity at the cost of decreased yield of active protein.

81、The individual purification stepsThe target protein is separated from other sample components by its unique properties such as size,charge,hydrophobicity,isoelectric point(Ip),metal ion-binding property,and recognition of specific ligands(Table 2.1).The careful selection and combination of purificat

82、ion techniques is crucial for an efficient purification process.Irrespective of technique,each purification step is a combination of several operations such as sample loading,wash,and elution.The experimental conditions for all of these operations are essential for achieving the desired purification

83、 goals.DoE for experimental planning,tools for modern high-throughput screening and optimization,and the automation capabilities of modern chromatography systems play a central role for simplification in resolving which conditions to be used in individual operations and in each purification step.Wit

84、h these tools and technologies,we can study essentially any key parameter in a multivariate automated approach.StepPurityCaptureIntermediate purificationPolishingPreparation,extraction,clarificationAchieve final high-level purityRemove bulk impuritiesIsolate,concentrate,and stabilizeFig 2.1.The diff

85、erent steps of a protein purification process.This way of structuring the protein purification process is referred to as the CIPP strategy.The goal of each step of the purification is indicated.Table 2.1.Protein properties used during purificationProtein property TechniqueSpecific ligand recognition

86、Affinity chromatography(AC)Metal ion bindingImmobilized metal ion affinity chromatography(IMAC)Charge Ion exchange chromatography(IEX)SizeGel filtration(GF)HydrophobicityHydrophobic interaction chromatography(HIC)Reversed phase chromatography(RPC)Size,charge,and hydrophobicityMultimodal chromatograp

87、hy(MMC)Isoelectric pointChromatofocusing(CF)15Principles of combining purification steps Often,the most efficient improvement in an overall protein purification strategy is to add a second purification step instead of optimizing a single-step protocol.Each purification technique has inherent charact

88、eristics,which determine its suitability for the different purification steps.As a rule of thumb,two simple principles are applied:Combine techniques that apply different separation mechanisms.Minimize sample handling between purification steps by combining techniques that omit the need for sample c

89、onditioning before the next step.Table 2.2.Suitability of purification techniques in a CIPP modelTypical characteristicsPurification phaseConditionsSelectivityCapacityCaptureIntermediatePolishingSample start conditionsSample end conditionsMultimodal chromatography(MMC)+The pH depends on protein and

90、type of ligand,salt tolerance of the binding can in some cases be expectedThe pH and ionic strength depend on protein and ligand type Affinity chromatography(AC)+Various binding conditionsSpecific elution conditionsImmobilized metal ion affinity chromatography(IMAC)+Low concentration of imidazole an

91、d high concentration of NaClIntermediate to high concentration of imidazole,pH 7,500 mM NaClGel filtration(GF)+Most conditions acceptable,limited sample volumeBuffer exchange possible,diluted sample Ion exchange(IEX)+Low ionic strength,pH depends on protein and IEX typeHigh ionic strength and/or pH

92、changedHydrophobic interaction chromatography(HIC)+High ionic strength;addition of salt requiredLow ionic strengthReversed phase chromatography(RPC)+(+)+(+)+Ion-pair reagents and organic modifiers might be requiredOrganic solvents(risk of loss of biological activity)Chromatofocusing(CF)+Low ionic st

93、rengthPolybuffer,low ionic strength16The strategy for combining purification techniques works well in both small laboratory-and large production-scale applications.Table 2.2 provides a brief overview of where different purification techniques are most suitable in a purification scheme.Applying these

94、 guidelines,Fig 2.2 shows some suitable and commonly used combinations of purification techniques for research applications.Keep in mind the interplay between purity and yield.Every added purification step will increase purity at the expense of overall process yield.Principles of selection of chroma

95、tography mediaThe purification efficiency is also highly dependent of the chromatography medium selected for each technique.The efficiency,flow resistance,selectivity,and binding capacity differ between media.The particle size of the medium strongly affects efficiency and flow resistance.A medium wi

96、th large beads gives chromatography columns with low resolution(broad peaks)but generates low backpressure,whereas small beads give higher resolution(narrow peaks)but also generates higher backpressure.Figure 2.3 shows the general principle of choosing chromatography media with larger bead size for

97、early purification steps,and smaller bead size for later steps,where demand on purity is increased.Inserted chromatograms show the separation results of applying a small,complex sample to columns with IEX media of different bead size.The importance of bead size is greater in large-scale purification

98、s,where high flow rates are required for cost-efficient processing.At lab scale,intermediate-sized beads are commonly used for the initial capture step.CapturePolishingIEXHICGFHICGFIEXHICGFHICGFIEXIntermediateGFGFACIEXACAC(NH4)2SO4 precipitationFig 2.2.Example of suitable combinations of chromatogra

99、phic techniques.90 m34 m30 m15 m10 mQ Sepharose FF 16 50 mmQ Sepharose HP 16 50 mmSOURCE Q16 50 mmRESOURCE Q 1 mLMono Q 5/50 GLResolutionPurification stageFig 2.3.Principle for chromatography medium bead size selection.Large beads are primarily suitable for capture,while small beads offer the high r

100、esolution required for polishing.17Factors and responses when optimizing protein purificationResponsesThe output of a protein purification scheme is traditionally described in terms of purity,homogeneity,and yield.Economy is an overall concern and some aspect of it is always targeted during optimiza

101、tion(Fig 2.4).These output parameters can be translated into a number of different responses and measurement systems for a DoE setup.Protein purity can be analyzed by measurement systems,such as electrophoresis or high-performance liquid chromatography(HPLC),and specified as the target protein-to-to

102、tal protein(response)ratio.As a complement,host cell proteins(HCP),host cell DNA(hcDNA),and other impurities,can be monitored.Target protein homogeneity can be specified as monomer to aggregate content as analyzed by GF,or as correctly folded to incorrectly folded target protein as analyzed by HIC o

103、r RPC.Yield can be measured using a quantitative assay such as enzyme-linked immunosorbent assay(ELISA),or using an activity assay for the target protein,or both.Overall economy depends on a number of parameters such as process time,buffer consumption,buffer additives,binding capacity and lifetime o

104、f the included chromatography media,the requirement for additional formulation steps(e.g.,concentration and buffer exchange),as well as purchase cost for the components used.We also have to consider how much work(i.e.,the number of experiments and responses)that can be conducted in the given time fr

105、ame.Usually,all of these parameters need to be considered when planning a chromatographic purification.The importance of each parameter will vary depending on whether a purification step is used for capture,intermediate purification,or polishing.Often,optimization of one of the output parameters can

106、 only be achieved at the expense of the other output parameters,and each purification step will therefore be a compromise.Purification techniques should be selected and optimized to meet the objectives for each purification step.PurityRecoveryHomogeneityEconomyFig 2.4.Common output parameters for a

107、protein purification process.18CaptureIn the capture step,the objectives are to rapidly isolate,concentrate,and transfer the target protein to an environment that will conserve its activity.A capture step is often a separation based on functional groups using,for example,IEX or AC,with step elution.

108、Ideally,removal of critical impurities and contaminants is also achieved.With modern affinity chromatography media,it is often possible to achieve a very high level of purity during capture,for example,by using highly selective ligands for antibody purification such as protein A or protein L.In Chap

109、ter 5.5,the optimization of a capture step for an antibody fragment using Capto L is shown.Sample application and wash conditions(conductivity and pH)were varied and the effect on purity(measured as the reduction of HCP)and yield was estimated.An optimum was identified,at which HCP was reduced 25 00

110、0-fold at a high yield of the target protein(96%).Key optimization parameters and responses for the capture step are outlined in Figure 2.5.Use a high-capacity,concentrating technique to reduce sample volume,enable faster purification and to allow the use of smaller columns.Focus on robustness and s

111、implicity in the first purification step.Do not try to solve all problems in one step when handling crude material.For the capture step,select the technique that binds the target protein,while binding as few impurities as possible,that is,the technique that exhibits the highest selectivity and/or ca

112、pacity for the target protein.Changing a protocol from gradient elution to step elution will increase speed at the expense of selectivity.Step elution will also increase the concentration of the target protein.Intermediate purificationDuring the intermediate purification step,the key objective is to

113、 remove most of the bulk impurities,such as additional proteins,nucleic acids,endotoxins,and viruses.If the capture step is efficient,the intermediate purification step is often omitted in favor of one or more polishing steps.The ability to chromatographically resolve similar components is of increa

114、sed importance at this stage(Fig 2.6).For a maintained recovery,the capacity is still important in the intermediate purification step,as there might still be significant amounts of impurities in the sample.Speed is often less critical in the intermediate purification step as the sample volume is red

115、uced and the impurities,causing proteolysis or other destructive effects,preferably have been removed in the capture step.The optimal balance between capacity and resolution should be defined for each case.In Chapter 5.4,the optimization of an intermediate purification step for a MAb using a cation

116、exchanger is shown.The effect of pH and conductivity during sample loading was studied using dynamic binding capacity(DBC)of the chromatography medium as a response,and a global maximum was identified.Key factors:Sample loadConductivitypHBuffer volumesAdditivesResidence timeMedium characteristicsCap

117、ture:Key responses:RecoveryDynamic binding capacitySpeedTarget protein concentrationFig 2.5.Initial purification of the target molecule from the source material is performed in the capture step,with the goals being rapid isolation,stabilization,and concentration of the target protein.Key factors:Sam

118、ple loadConductivitypHBuffer volumesAdditivesGradient concentrations and volumeFlow rateMedium characteristicsIntermediate purification:Key responses:RecoveryPuritySpeedTarget protein concentrationFig 2.6.The intermediate purification step is characterized by the removal of bulk impurities,with the

119、goals being purification and concentration.19PolishingIn the polishing step,most impurities have already been removed.At this stage,only trace amounts of impurities remain,although these often consist of proteins closely related to the target protein,like fragments or aggregates of the target protei

120、n.To achieve high purity and homogeneity,the focus is on chromatographic resolution in the polishing step(Fig 2.7).The technique chosen should discriminate between the target protein and any remaining impurities.To achieve sufficient resolution,it might be necessary to sacrifice sample load(overload

121、 might decrease purity)and yield by narrow-peak fractionation.On the other hand,product losses at this stage are more costly than at earlier stages.Preferably,the product should be recovered in buffer conditions suitable for the next procedure.In Chapter 5.7,a polishing step for a MAb was optimized.

122、A key purpose of this step was to remove aggregates of IgG.Monomer content and purity were studied as a function of aggregate content in the starting sample,elution pH,and elution conductivity,and a sweet spot was identified.Chromatography step optimizationEach chromatographic step in a protocol can

123、 be split into several phases(Fig 2.8).Each phase can involve different factors(such as pH,conductivity,additives,flow rate),of which all can have a profound effect on the outcome of the chromatographic step.Because of the large number of tentative factors that can affect the outcome,a DoE approach

124、is well-suited for screening and optimization of chromatographic purification steps.This symbol indicates general advice This symbolKey factors:Sample loadConductivitypHBuffer volumesAdditivesResidence timeMedium characteristicsPolishing:Key responses:RecoveryPurityLevel of key contaminantsHomogenei

125、ty(monomer,correct conformation,nontruncated,correct isoform)Fig 2.7.Polishing involves removal of trace impurities and variants of the target protein as well as adjustment to conditions for final use or storage.The goals are high purity and homogeneity of the final product.Method SettingsEquilibrat

126、ionCleaning in Place(CIP)ElutionWashSample ApplicationFig 2.8.Typical phases of a chromatographic purification step.20Process development and characterizationDuring process development,where the aim is set at process optimization,the general strategy is to use initial screening designs,explore the c

127、ause-and-effect relationship,include additional factors,and explore wider ranges of factor settings.Usually,these initial DoE studies are performed in small scale.This initial screening could also give information about other process characteristics.For example,a lack of fit(model error),indicated i

128、n the model evaluation,can be due to a nonlinear relationship between factors and the responses(curvature effect)in the system(see Chapter 3 for more details).In Chapter 3,a number of useful tools for process optimization are described,for example,fishbone diagrams,gage repeatability and reproducibi

129、lity(gage R&R),and fractional factorial screening designs.When focusing on the detected critical factors,we use optimization type of designs comprising less factors,higher order models(including interaction and quadratic terms),and exploration of narrower ranges within the design space.The goal of p

130、rocess development is the specification of final operational parameter ranges in order to meet the quality criteria for the process or product.In this step,we try to reach both optimal settings for our parameters as well as process robustness.For example,we often try to reach the maximal product yie

131、ld with minimal variation in product quality.The tools we choose often focus on accurate determination of curvature effects(i.e.,response surface modeling(RSM)designs,see Chapter 3).Process optimization is usually followed by verification of the process(robustness testing),at both small and large sc

132、ale,using reduced designs(fewer studies of the important factors)in a range equal to an estimated factor variation.In this design space,we are looking at critical process parameters versus process/equipment capabilities.21Quality by design(QbD)DoE provides a method for linking critical material attr

133、ibutes and process parameters to critical quality attributes of the product.As stated in the FDA-issued guidelines for process validation and QbD(January 2011),the underlying principle of quality assurance is that a therapeutic product should be produced in a way so that it fits the intended use.Thi

134、s principle incorporates the understanding that quality,safety,and efficacy are designed or built into the product rather than obtained by inspection or testing.The guidance divides process validation into three stages:design,qualification,and continued verification.The QbD concept is described in F

135、igure 2.9.DoE is an integral part of the QbD concept.It is used,for example,for determination of the process design space and process parameters that are crucial for achieving the critical quality attributes for the final product.DoE also involves mapping of how the effects of process parameters dep

136、end on each other(interactions).The output of DoE for determination of design space forms a basis for setting acceptable and realistic variability ranges for the control space.A structure for defining the process design space in QbD is outlined in Fig 2.10.Block and Fishbone diagrams Which factors c

137、ould potentially affect our process?Failure mode and effects analysis(FMEA)Which parameters should be investigated in detail?Screening extended space in many parameters Detailed quantitation of cause and effect relationships How does variation in critical process parameters(CPP)translate into variat

138、ion in critical quality attributes(CQA)and other process attributes?Process mappingRisk analysisDesign of experimentsMonte Carlo simulationFig 2.10.An example workflow for definition of a process design space.Characterized spaceDesign space Operating spaceOperating range:Acceptable range:Characteriz

139、ation range:Acceptable variability in key and criticalquality attributesProcesscharacterizationstudiesCombination of parametersIndividual parametersFig 2.9.The concept of QbD.Process development aims at defining the design space(the experimental space that yields results within the set of responses

140、specified for the process).An operating space is selected with conditions for operating the process in an optimal way.Data is collected while running the process.If the responses are found to be changed,or for any reason needs to be further optimized,changes of the running conditions can be made wit

141、hin the design space without revalidation of the process.22Protein purification tools for DoEProcess development toolsEfficient development of the manufacturing process is a requirement in the biopharmaceutical industry as well as in other industries.A steadily increasing demand from regulatory auth

142、orities for a better understanding and control of manufacturing processes puts even more pressure on the development work.In high-throughput process development(HTPD),the initial evaluation of chromatographic conditions is performed in parallel,often using a 96-well plate format.Further verification

143、 and fine-tuning is typically performed using small columns before moving up to pilot and production scale.This approach to process development,using DoE,is illustrated in Figure 2.11.PreDictor 96-well filter plates are prefilled with chromatography media.These plates can be used for the initial scr

144、eening of process conditions,or for a more thorough investigation of a defined space as a basis for detailed process understanding and/or robustness studies.When using PreDictor plates,the fundamental interactions between the chromatography medium and the target molecule are the same as in chromatog

145、raphy columns.Basic concepts,such as mass balance,rate of uptake(at defined conditions),and adsorption isotherms,are the same in PreDictor plates as in chromatography columns.The Assist software helps chromatography process developers design and evaluate PreDictor plate experiments.The software prov

146、ides guidance to experimental design and to handling experimental data,and also provides tools for data analysis.PreDictor RoboColumn units are prepacked,miniaturized columns that support HTPD using a robotic liquid handling workstation,such as the Freedom Evo platform from Tecan,for fully automated

147、,parallel chromatographic separations.PreDictor RoboColumn units are available prepacked with a range of Cytiva chromatography media(Fig.2.12).(A)(B)Total characterization spaceDetailed studies to define design spaceArea for further optimizationPreDictor prefilled 96-well filter plates,Assist softwa

148、re,and PreDictor RoboColumn units for screening of conditionsKTA avant,KTA pure,UNICORN 6,HiScreen and HiTrap columns for optimization ReadyToProcess platform and AxiChrom columns for scale-up and productionFig 2.11.Conceptual workflow for process development using DoE.Fig 2.12.(A)PreDictor RoboColu

149、mn units are prepacked,miniaturized columns.(B)PreDictor 96-well filter plates prefilled with chromatography media.23After scouting and screening in a multiwell plate format such as PreDictor plates,verification and fine-tuning are performed in column format using KTA systems such as KTA avant or KT

150、A pure(Fig 2.13)with UNICORN 6 software.UNICORN 6 software has integrated DoE functionality.As DoE is seamlessly integrated into UNICORN 6,methods are automatically generated from DoE schemes,allowing for fast and efficient process development.UNICORN 6 supports a number of different fractional fact

151、orial designs,full factorial designs,and response surface modeling(RSM)designs.Chapter 3 provides a comprehensive description of design types.Figure 2.14 illustrates a workflow for process development using Cytiva products.Fig 2.13.KTA avant and KTA pure are high-performance chromatography systems d

152、esigned for automated protein purification and process development.Prepacked columns,such as HiScreen 10 cm bed height columns,can be used with these systems.Operating range:Acceptable range:Characterization range:Individual parametersFig 2.14.Process development workflow using Cytiva products for e

153、fficient applications of DoE under the QbD paradigm.24Other tools for parallel protein purificationDoE greatly improves efficiency in method development and optimization.Laboratory tools,enabling experiments to be performed in parallel,contribute to the efficiency gain.MultiTrap 96-well filter plate

154、s are prefilled with chromatographic media and are designed for efficient,parallel initial screening of chromatographic conditions(Fig 2.15).MultiTrap plates can be operated manually(using a centrifuge or a vacuum chamber to drive liquid through the wells)or in an automated fashion using a laborator

155、y robot.Conditions defined in a screening study using MultiTrap plates can be verified and optimized using prepacked chromatography columns such as HiTrap or HiScreen columns.Magnetic beads offer another possibility for small-scale,parallel protein purification,for example,for screening purposes(Fig

156、 2.15).Mag Sepharose beads(substituted with protein A,protein G,and other affinity ligands)can either be operated manually or automated.An example of a DoE study for optimization of IgG purification on Protein A Mag Sepharose Xtra is given in Chapter 5.6.(B)Fig 2.15.(A)MultiTrap filter plates prefil

157、led with chromatography media and(B)and Mag Sepharose beads.(A)25Design of experiments,step-by-step0326The individual DoE steps were briefly defined in Chapter 1.This chapter gives a step-by-step reference to performing DoE.Visualization of DoE results is described in Chapter 4.Application examples

158、are given in Chapter 5 and additional information is found in Chapter 6.Performing a DoE study is typically an iterative process.For example,an initial DoE could be set up for screening of process conditions(e.g.,to identify relevant factors)before a more targeted DoE is conducted for careful optimi

159、zation of the process.In this chapter,DoE is described in a step-by-step fashion for clarity,but the iterative nature of the methodology should be kept in mind.Also,it should be understood that each of the individual steps described here typically have an impact on,or are impacted by,how later steps

160、 will be carried out.The design type,for example,should be briefly considered(create design,Step 3)while defining the objectives(Step 1)for the extent of the study to become realistic from a resource-availability perspective.Similarly,the response and measurement systems(Step 2)need to be considered

161、 when setting the objectives.For these reasons,each individual step described in this chapter will contain references to both the previous steps and also to the later steps.Gather information before startingFor a DoE setup,some basic information regarding the process to be studied must be available.

162、As a wealth of information is often available,both general(e.g.,an ion exchange separation is always impacted by the ionic strength and pH of the solutions used)and specific(the size and sequence characteristics of a recombinant protein to be purified),having an idea of which factors could possibly

163、impact the process is typically not an issue.A good starting point for a DoE setup is to collect all available information.If there are obvious gaps,initial experiments should be performed,for example,chromatographic runs using small column formats for indications on factor(starting)levels.27Step 1.

164、Define objective,factors,and rangesStep 1 contains the following elements:Define the overall project goal(s)and the study objective Define process requirements(measurable)or issues that are not strictly part of the DoE study but that need to be fulfilled Define the size of the study Identify all par

165、ameters that have an effect on the end result and exclude irrelevant ones Pool all available information about the factors and responses Perform test experiments if necessary Define factors and their levelsThe initial DoE step is critical.It lays the foundation for a good,conclusive experimental stu

166、dy.Most DoE failures can be traced to incomplete and/or incorrect identification of parameters(both input and output)and,hence,to an incorrect setup of the study.It could be tempting to move quickly to optimization(if that is the purpose)of a few parameters,but one has to be sure that the selected f

167、actors are the relevant ones.A screening DoE is a great tool for rapid identification of relevant factors and for screening of factor levels.The first DoE step covers exactly the same elements as any experimental planning,irrespective of experimental design.The underlying logics will easily be recog

168、nized.During the first step,basic questions,such as study purpose,factors to include,and achievability within the given resource frame,are posed.28ObjectivesThe starting point for any DoE work is to state the objective,define the questions about the process to be answered,and choose the relevant fac

169、tors and ranges.The objective describes the purpose of the study.For a screening study,the objective could be to identify key parameters that impact purity and yield in an affinity chromatography capture step.Another objective could be to identify the most suitable chromatography medium for achievin

170、g high target protein homogeneity in a polishing step.These screening studies could subsequently be followed by optimization studies,again using DoE,with objectives such as maximizing purity and yield in antibody capture using a protein A medium or maximizing aggregate removal through a multimodal i

171、on exchange purification step.It is important to define the requirements in detail and to make sure that they can be measured.For example,maximizing aggregate removal is linked to additional requirements such as the maximum allowed separation time or the minimum allowed yield of target protein.It is

172、 useful to start by listing a brief,overall study objective and the additional requirements.When this is listed,focus should be on how these requirements can be measured.At a detailed level,there are as many study objectives as there are different studies.But at a higher level,there are three differ

173、ent categories of studies for which DoE is typically used.These are screening studies,optimization studies,and robustness testing.These studies differ not only in their objectives but also in the number of factors used,and the number of experiments involved(Fig 3.1).For future reference,a study prot

174、ocol is useful for documentation of the experimental rationale,as well as the objectives,methods,and more.ScreeningScreening DoE explores the effects of a large number of factors in order to identify the ones that have significant effect on the response of a process or system and to determine which

175、factors need to be further characterized or optimized.The law of the vital few(Pareto principle)states that for many events,roughly 80%of the effects come from 20%of the causes.By screening,we ensure that all critically important variables are considered before reducing number of variables.Screening

176、 DoE is also used when screening for conditions such as factor levels or ranges.Number of experimentsNumber of factorsOptimizationResponse surface modelingTrying to find optimum conditionsNumber of experimentsNumber of factorsScreening Screen parametersand conditionsNumber of experimentsNumber of fa

177、ctorsRobustnessSimilar designsDoes small variationin factors affectthe process?Fig 3.1.Common overall objectives for different types of DoE studies and some of their characteristics.The arrows indicate the number of experiments and the number of factors for these objectives.A screening DoE is used f

178、or obtaining information about factors and for selecting significant factors and their settings.Optimization is used for finding the optimal levels of a few relevant factors,and for obtaining a useful process model for future predictions.Robustness testing is used for verifying that the optimized co

179、nditions will give the expected response,with a variance that is sufficiently small.The different DoE objectives can be used sequentially to develop a process.29OptimizationOptimization is used for determination of optimal factor settings for a process or a system.The relationship between a selected

180、 response and the significant factors is determined in order to create a model.Several responses may be optimized simultaneously,but the final factor settings might be a compromise between the responses.Additional designs may be applied when the studied region does not contain the optimum.When addit

181、ional factor ranges are required,this should be guided by the results from the previous design.The settings are varied to allow crawling across the experimental region towards optimum conditions.When the optimum has been identified,the chosen conditions should be verified.Robustness testingRobustnes

182、s testing is used for determination of process robustness and is conducted by performing experiments based on a design,with only minor adjustments of the factor levels.The variation of the obtained responses should be within set specification limits.If the responses do not vary significantly when th

183、e factor levels are changed,the process is considered to be robust.Design considerationsAlthough creation of the design is described in a later step,it is worthwhile to already at this point consider design selection,as the study objective will have an impact on which type of design is required.Ther

184、e is a balance between the amount of information needed and the number of experiments required(Fig 3.2).This balance is the initial,and one of the most important,considerations to be highlighted before conducting experiments.We should also keep in mind that the experimental process can be iterated a

185、nd the initial screening results from the first DoE step can be used as input for the next DoE step.Factors and factor rangesFactors are the input parameters or conditions that we wish to control and vary for a process.We expect that a selected factor has an impact on the response that we intend to

186、measure.Already when we decide what factors to control (see example in Fig 3.2),we also assume that other factors will not significantly affect the response and will be constant or left uncontrolled during the experiments.Constant variables are,if possible,fixed,measured,and recorded during the expe

187、riments.One common example of a constant variable in protein chromatography is temperature.Fig 3.2.Factors and factor ranges are entered into the UNICORN software,for automated chromatography runs.30The factor range(i.e.,the levels that are possible to set)depends on the experimental objective and t

188、he experimental noise(nonsystematic variability)for easier readability.In screening studies,the range should be large enough to increase the possibility of covering the optimum and to obtain effects above the noise.A broad range can also make the model more stable.In optimization DoE,the range shoul

189、d,and can usually be reduced as there is more information available at this stage.Determination of appropriate factor starting values(e.g.,pH and conductivity in IEX)could include performing separate gradient runs(one for pH and one for conductivity)to find an approximate factor range for elution of

190、 the target.Setting of factor values and ranges requires attention to avoid exceeding physical/chemical restrictions such as recommended maximum flow rate for a chromatography column.DoE studies most often use two numerical levels for each factor.For each factor,a high and a low value are selected f

191、or the settings to cover the operating range for each variable.As an example,for optimization of an affinity chromatography separation,one selected factor can be flow rate during sample load.The range for this factor is selected from 1 to 5 mL/min.The low value is 1 mL/min and the high value is 5 mL

192、/min.The design will thus cover experiments within these two factor levels.For the DoE model to be reliable(Step 5),however,we also need to detect possible nonlinear relationships between the factors and the response(s).Therefore,it is useful to complement the design with center points to enable det

193、ection of the possible occurrence of a curvature effect(a nonlinear relationship).The center point experiments are also replicated for estimation of the experimental variation.In the example above,the center point will be at a flow rate of 3 mL/min.If a significant curvature is found,so called,star

194、points can be added to quantitate the nonlinear effects of individual factors.This type of design is described in more detail under Step 3 in this chapter and in Chapter 6.It is advisable and more economical to include more factors in the initial screening study than to add factors at a later stage.

195、In some cases,this means that the screening study includes a very large number of experiments.With a large number of factors,the most common way to reduce the number of experiments is to use a reduced design(as described in Step 3).Alternatively,one can reduce the number of factors and runs by intro

196、ducing dimensionless factors.A dimensionless factor consists of the ratio between two parameters that each was initially considered to be factors of their own.For example,if both the concentration of NaCl and the concentration of the additive urea were considered as factors in a DoE study,the ratio

197、between the molar concentrations of NaCl and urea could be used as a single factor to reduce the number of experiments.If we have three variables with the same unit in our study,the three variables x1,x2,and x3 can sometimes be combined in the ratios x1/x2 and x3/x2 to give the same information as f

198、or two variables.The introduction of dimensionless factors adds a new level of complexity to the interpretation of the results,but is sometimes highly relevant,as interactions between dimensionless factors or between a dimensionless factor and a physical parameter can increase our understanding of t

199、he process.31Yield,HCP,purity,etc.Column packingSampleWashStripMeasurement systemsLoadElutionCIPHETPAssymetry factorMedium volumeFlow distributionLeakageBed stabilityMedium identityConcentration of target molecule ConductivitypHTemperatureSample variabilityViscosityHold timespHTemperatureActive moni

200、toring of pH,conductivity,UV ConductivityWash volume(CV)Flow rateIntermediate washAdditivespHTemperatureMedium stabilityConductivityWash volume(CV)Flow rateBuffer and salt typesTemperatureConductivityWash volume(CV)Flow rateBuffer and salt typesAdditivesAdditivesTemperatureConcentration/stabililtypH

201、 and conductivityVolumeFlow rateBuffer and salt typeMedium stabililtyViscosity/pressureGradient profilesAdditivesTemperatureConductivitypHVolumeFlow rateBuffer and salt typeMedium stabililtyTemperatureSample flowEquilibration pre load pH,cond,vol.Sample pressureSample amountBuffer and salt typePassi

202、ve monitoring of flow,pressure,amount,pH,conductivity Quantitative and qualitative factorsQuantitative factors are characterized by being on a continuous scale,for example,pH,flow rate,and conductivity.Qualitative factors are discrete(discontinuous),for example,column type,type of chromatography med

203、ium,and buffer substance.Controllable and uncontrollable factorsControllable factors can be managed in experiments.Uncontrollable factors might affect the response but are difficult to manage,for example,ambient temperature or target protein amount in the cell culture.Monitor uncontrollable factors

204、when possible.When entered into the DoE software,the effects of the uncontrollable factors can be evaluated.Structured approach to selecting factorsA fishbone diagram(also known as cause-and-effect or Ishikawa diagram)is a useful tool for documenting factors believed to have the greatest impact on t

205、he process,for example,in an initial cause-and-effect analysis.Fishbone diagrams also provide an easy reference for a preliminary risk assessment.The diagram is useful in process development,providing a structured way to list all possible causes of a problem or a desired process outcome before start

206、ing to think about a solution.An example of a fishbone diagram is given in Figure 3.3.The way this diagram is constructed includes the following steps:Identifying the process goal(s)(e.g.,yield,purity,etc.),represented by the middle horizontal arrow Identifying the major process steps(e.g.,sample lo

207、ad,wash,elution,etc.),represented by the tilted lines Identifying possible factors affecting the goal(s),represented by the numerous horizontal lines going from the tilted lines Analyzing the diagramA fishbone diagram enables detection of the root causes(factors)to discover bottlenecks,or to identif

208、y where and why a process is not working.Fig 3.3.Example of a fishbone diagram showing possible contributors leading to a desired process output.The example shows the majority of process parameters in an ion exchange step.Only a fraction of these are relevant for a specific application.HETP=height e

209、quivalent to theoretical plate,CV=column volume,CIP=cleaning in place.32Independent measurements of factor effectsOrthogonality in an experimental design means that each factor can be evaluated independently of all other factors.For example,in a two-factor,two-level factorial design,this is achieved

210、 by arranging experiments so that each level of one factor is paired with each of an equal number of levels of the other factor.By setting the factor levels at the combined low and high values,we outline the factorial part of the experimental plan.For each factor to have an equal opportunity to inde

211、pendently affect the outcome,the factor levels are transformed.The coding is a linear transformation of the original measurement scale,so that if the high value is XH and the low value is XL,the factor level is converted to(X-a)/b,where a=(XH+XL)/2 and b=(XH-XL)/2,that is,the high value becomes+1 an

212、d the low value becomes-1.If k is the number of variables included in our DoE,we have 2k experimental runs(in a full factorial design),of which each corresponds to a unique combination of factor settings.An example of a coded design matrix,where+1 and-1 are used for the high and low settings,respect

213、ively,is shown in Figure 3.4.Exp.no.617181911-111-1-1-1-11-11-11111-1-11211-111-1-1-1-11-11-11111-1-13-111-111-1-1-1-11-11-11111-14-1-111-111-1-1-1-11-11-1111151-1-111-111-1-1-1-11-11-1111611-1-111-111-1-1-1-11-11-1117111-1-111-111-1-1-1-11-11-1181111-1-111-111-1-1-1-11-11-19-1

214、1111-1-111-111-1-1-1-11-11101-11111-1-111-111-1-1-1-11-111-11-11111-1-111-111-1-1-1-11121-11-11111-1-111-111-1-1-1-113-11-11-11111-1-111-111-1-1-114-1-11-11-11111-1-111-111-1-115-1-1-11-11-11111-1-111-111-116-1-1-1-11-11-11111-1--1-1-1-11-11-11111-1--1-1-1-11-11-11111-1-111-119-1

215、11-1-1-1-11-11-11111-1-11120-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-00000000000220000000000000000000230000000000000000000Fig 3.4.A coded data matrix with high(+1)and low(-1)settings for each factor.In this case,based on a Plackett-Burman screening design,19 factors were investigated in only

216、23 runs.This corresponds to 23 219(524 288)runs(the number of runs in a full factorial design).33Step 2.Define responses and measurement systemsStep 2 contains the following elements:Define what to measure as an output from the process,and set the specification limits(i.e.,our criteria for acceptabl

217、e results)for these responses(critical-to-quality CTQ attributes)Define a reliable measurement methodology,and perform a measurement system analysisResponses are the output parameter(s)of a process.In protein purification,responses can,for example,be binding capacity of the chromatography medium or

218、purity and yield of the target protein(Fig 3.5).The strategy for defining a response is to find a response that maps the properties of a product,the performance characteristics of a process,or more specifically,the study objective.If several responses are required for describing the outcome,we need

219、to analyze the advantages and disadvantages of having multiple responses in the evaluation.Having multiple responses often leads to compromises.A response should be appropriate(address the desired process characteristics effectively and coherently in a manner suited to the context)and feasible(we sh

220、ould be able to measure the response efficiently with available resources in a timeframe suitable to describe the system or process).Quantitative and qualitative responsesQuantitative responses(e.g.,protein purity and yield)are characterized by being on a continuous scale.These responses enable easy

221、 model interpretation.When response metrics are not possible to obtain,response judgments can instead be used.Such judgments,or qualitative responses(e.g.,product quality),are discrete and result in outcomes such as yes/no,or low/medium/high.When possible,qualitative responses should be made semiqua

222、ntitative by transforming the judgments to discrete values such as 1=very low,2=low,3=medium,4=high,and 5=very high.Exp No Exp Name Run Order Incl/Excl Load pH Load Conductivity Dynamic Binding Capacity 1 N1 5 Incl 4,5 5 96 2 N2 6 Incl 5,5 5 137 3 N3 9 Incl 4,5 15 102 4 N4 7 Incl 5,5 15 4 5 N5 8 Inc

223、l 4,5 10 119 6 N6 3 Incl 5,5 10 84 7 N7 2 Incl 5 5 139 8 N8 4 Incl 5 15 54 9 N9 10 Incl 5 10 121 10 N10 1 Incl 5 10 137 11 N11 11 Incl 5 10 127 Fig 3.5.Responses and their values are entered in the UNICORN software for evaluation.34Measurement system requirementsOne major step,sometimes overlooked i

224、n scientific work,is to make sure that the measurements error is smaller than the variation in the process outputs.As managing a defined process requires knowledge of the progress and its end product or response,we need to define what to measure and the measurement system requirements.The selected o

225、utput parameter should be valid for the process,that is,valid to detect the input-output relationship.A continuous variable is preferred and the response should be relatively easy to measure.When we have defined what to measure,we can determine the quality of our measurement system,including measure

226、ment accuracy,acceptable measurement errors,stability,capability,and acceptable level of variation in the method.A measurement system needs to have good accuracy and precision,with minimal variability(noise),to enable reaching the correct optimal conditions for the process.A poor measurement system

227、might overestimate or underestimate the process outcome and prevent detection of improvements made during screening and optimization.Measurement system analysis(MSA)refers to a method for determining accuracy and precision of a measurement system.The overall goal of MSA is to determine how much the

228、variation of the measurement system contributes to the overall process variability(Fig 3.6).Automatic peak integration and densitometry is supported by modern software.Manual operations,being more subjective,might sometimes introduce an abnormally large variation in the measurement system,such as a

229、lack of accuracy and precision.Acceptable:Unacceptable:Measured=20ObservedProcess2Process2MeasuredMeasured=2ObservedProcess2Process2MeasuredFig 3.6.Analyzing measurement system capability,that is,measurement error(gage R&R)in relation to process output variation.The triangles show the relationship b

230、etween the actual process variance(Process),gage(measurement system)variance(Measured),and the observed process variance(Observed).A variance ratio of less than 2 is unacceptable,whereas a ratio greater than 20 is acceptable.Values between 2 and 20 indicate situations that should be handled cautious

231、ly.35Step 3.Create the designStep 3 contains the following elements:Use the information from Step 1 and 2 to create an experimental design,by hand or in a DoE software program (for easy setup)The experimental design should include all factors believed to be relevant and to affect the CTQ responses T

232、he design setup can include all or a fraction of all high and low value combinations of all factors Decide the extent of the study.Are we interested in the main effects only or do we wish to include interactions and/or curvature;do we suspect a nonlinear relationship between the factors and the resp

233、onses?Setup of the experimental plan and review accuracy in the selection of design type,for example,by reviewing the correlation matrix and design power List constraints/assumptions/limitations The defined experiments should represent a relevant sample size and an independent,unbiased,and randomize

234、d selection Review the plan to make sure that every experiment is reasonable and feasible,and describe how the experiments are to be executed The corner points high and low value combinations of a design will provide information on how the factors,one by one or together,create a certain effect on th

235、e measured responses.Creating an experimental design is a straightforward process performed by defining factors,factor ranges,and the objective.The experimental design is also related to the modeling.A specific design allows addition of specific mathematical terms to the model(mathematical descripti

236、on of the process),which depends on the complexity of the selected design(Fig 3.7).Terms used in modeling,and defined in the context of this handbook,are the main(linear),interaction(two-factor),and quadratic terms.Screening designs are useful when we wish to measure the main effects or when we wish

237、 to disregard parameter interactions or nonlinear relationships.Screening designs are also useful for robustness testing when we wish to reduce the number of runs.In optimization designs,more experiments are added.These additional experiments,as defined by the factor settings,are used for quantitati

238、on of nonlinear cause-and-effect relationships and allow us to increase the complexity of the mathematical modeling by adding square terms,and hence,to spot a minimum or maximum for our process.x1x3x2x1x3x2Screening/robustness testingScreeningOptimizationx1x3x2(A)Fractional factorial design(B)Full f

239、actorial design(C)RSM designFig 3.7.An overview of the key design types used in DoE:(A)fractional factorial design,with a fraction of corner point experiments excluded(white circles).Fractional designs are suggested for screenings,as the information provided using this design is often sufficient to

240、find the factors(main effects)affecting the process;and for robustness testing,as the optimal factor settings have already been found and only minor changes in the factor settings are used to test the robustness of the process.(B)The full factorial design uses all corner point experiments.This desig

241、n is often suggested for screening.Information about which factors that are important(main effects)and about factor interaction effects is obtained.(C)For optimization studies,especially if curvatures are detected,the basic full factorial design is extended with additional experiments outside the bo

242、x,called star-point experiments,in the response surface modeling design(RSM).Star points enhance the detection capability for curvatures and give information about main factor effects,factor interaction,and curvature.Replicated center-point experiments(yellow)are always included in the designs.The u

243、se of DoE does not eliminate the need for or purpose of single experiments.Careful selection and execution of single experiments based on a hypothetical experimental design can address initial questions.Single experiments can be used to test initial predictions and hypotheses on a subject.As an exam

244、ple,single experiments can be used to investigate the effect of two parameters at two levels by using the corner points of a design instead of the traditional one-factor-at-a-time approach.36Figure 3.8 displays an example of a DoE setup where the dynamic binding conditions for a chromatographic puri

245、fication method is to be investigated.The low and high levels of each factor(in this case two)are entered into the DoE software and a worksheet is generated based on the selected design(Fig 3.9).Star-point values for quantitating curvature effects and a randomized run order(to ensure a nonbiased stu

246、dy)are generated.After the experimental series has been finished,the results(responses)for each experimental point are entered for evaluation of the DoE setup.The evaluation involves statistical analysis of the data generated.Exp.no.Exp.nameRun orderFactorial partStar pointsReplicated center pointsL

247、oad pHLoad conductivityDynamic binding capacity4.55964.5151025.551375.5544.5101195.5load conductivitypHFig 3.8.An example worksheet for the optimization of dynamic binding conditions for a chromatographic purification method.The upper part of the table shows the fact

248、orial part of the design(corner points)for estimating main effects,the middle part shows the star points for assessing curvature effects,and the bottom part shows that three replicated center points are used for determination of the true experimental error(noise).Exp.no.Exp.nameRun orderIncl./excl.L

249、oad pHIncl4.5Incl5.5Incl4.5Incl5.5Incl4.5Incl5.5Incl5Incl5Incl5Incl5Incl5Load conductivity55475863728491010111N15N2N3N4N5N6N7N8N9N10N111Fig 3.9.Design selection in the UNICORN software.The low and high levels of each factor are entered whereupon a worksheet is generated for the

250、 design,suggested based on the user-selected objective.The design can also be selected from an extended design list.37Design resolutionThe term resolution in DoE tells us the type of effects that can be revealed(and the mathematical terms that can be added to the modeling)with the design in question

251、.Resolution depends on the number of factors and the number of runs and the given resolution value refers to the confounding pattern(Fig 3.10).For example,Resolution III designs offer some support for linear main effects,but no support for two-factor interactions or nonlinear quadratic effects(more

252、on these model terms in Step 5 of this chapter).With Resolution III designs,linear effects are pairwise uncorrelated(there is no correlation between them),but each linear effect is confounded(mixed-up)with a two-factor interaction effect and we cannot tell which one is affecting our response.With Re

253、solution IV or higher,we can distinguish between linear and two-factor interaction effects.With Resolution V or higher we can quantitate two-factor interactions.As an example,the frequently used full factorial design offers good support for linear effects and all interaction effects,but no support f

254、or explaining nonlinear cause-and-effect relationships.The reason for failing to detect the effects often relates back to a large variation in data.To find significant effects,the results should point out the direction and magnitude in relation to measurement errors and process variation.Number of e

255、xperiments neededAs shown in Table 3.1,the number of experiments required depends on the number of factors to be included and the level of detail needed.Table 3.1.Number of runs required for some common experimental designsDesignObjectivesNumber of runsEffects explained by modelNumber of factorsLine

256、arTwo-factor interactionCurvature234567Fractional factorial(Res III)*S,R7111111Fractional factorial(Res IV)S(R)111919Fractional factorial(Res V)S(O,R)193565Rechtschaffner(Res V)S(O,R)1014192532Full factorialS(O,R)7Central composite RSMO1Rechtschaffner RSMO1318243139Box-Behnken

257、RSMO1527435159Factors2345678954FullIII8FullIVIIIIIIIII16FullVIVIVIVIIIIIIIIIIIIIIIIIIIII32FullVIIVIVIVIVIVIVIVIVIV64FullVIIVIVIVIVIVIVIVIV128FullVIIIVIVVIVIVIVIVRunsFig 3.10.Resolution depends on the number of factors and runs.Three resolution levels are usually referred to Resolution III

258、,IV,and V.Resolution III gives some support for linear effects,without support for two-factor interactions or nonlinear relationships.Resolution IV,on the other hand,gives good support for linear effects,limited support for two-factor interactions,but no support for nonlinear relationships.Resolutio

259、n V,or higher,generally supports both linear and two-factor interaction effects,but does not give support for nonlinear relationships.S=screening,O=optimization,R=robustness test,Res=resolution.*For example,Plackett-Burman design.Note!The level of support in a model depends on the design.38Systemati

260、c biasExperimental investigations might be systematically biased,causing misinterpretation of the results.Bias is due to uncontrolled changes in known or unknown factors,also called“lurking variables”(Fig 3.11).As a practical example,sample material might degrade over time,causing uncontrolled chang

261、es in the series of experiments.For example,if the high level setting of a factor is performed early in the series,using fresh samples,and the low setting is performed later in the series,using aged samples,the difference in response for low and high level of the factor might be caused by a factor e

262、ffect on the response or by the aging of the samples used.Hence,the effects of the factor and the age of the samples are confounded.To avoid such bias,materials and methods should be homogenous,data should be collected over a short period of time,and experiments performed in a random order.Lurking v

263、ariables are factors that we intentionally or unintentionally select not to be included in a study because we cannot control them(i.e.,we have no data to enter into the experimental plan).We should,however,not exclude these factors from being confounded with the factors we are investigating.Lurking

264、variables could in fact be confounded with our factor main effects due to the lurking variable variation ending up in the residuals.Avoid uncontrolled changes in the experiments by using homogenous materials and methods and by performing the experiments in a random order during a short period of tim

265、e.Order of experimentsWe use our knowledge,experience,and judgment to decide what parameters to include in a study.However,it is difficult to remain unbiased when deciding in which order the experiments are performed.Randomization is the most reliable method of creating homogeneous treatment groups

266、without involving potential biases or judgments;the effect of lurking variables can also be effectively avoided through randomization.Groups can be harmonized through randomizing the order in which the experiments are performed,so that the differences we see in the response variable can be attribute

267、d to the factors.A completely randomized experimental design is achieved when all parameter settings are randomly allocated among the experiments and is readily achieved by using any DoE software where this functionality is included.Randomization should always be used to prevent systematic biases.Fi

268、rst,the design is set up with systematic variation of the factor settings.The experiments and measurements are thereafter performed in a randomized order.Randomization thus reduces uncontrollable variability.Variability is very unlikely to vary with the same pattern as any of the factors.Randomizati

269、on should always be used,even if all significant sources of errors have been eliminated,to ensure that no new uncontrollable factor turns up in the experiment.FactorsUncontrolled factorsResponsesMethod/processFig 3.11.Uncontrollable factors can give systematic bias.A fully randomized study should al

270、ways be the goal,although it is not always achievable because of the nature of the controlled parameters.It is important to consider the use of appropriate conditions in steps adjacent to the ones that are subject for optimization of a chromatographic process(e.g.,sometimes it is necessary to manual

271、ly ensure that the right conditions are used in an equilibration step prior to a wash or elution step).39Replication of experimentsThe tool for increasing the signal-to-noise ratio,for example,in order to quantitate the variability of the responses in a study,is replication.Replication,the repetitio

272、n of experiments,helps to improve the significance of an experimental result and the quality of a model by increasing the reliability of the data for each point.If a performed experiment shows conditions necessary for affecting the response,replication will increase the credibility of the study.Thus

273、,replication reduces the variability in the experimental results,thereby increasing their significance and the confidence level by which a researcher can draw conclusions about the study.It is important that new data is obtained by rerunning the entire experiment(experimental errors),not only the an

274、alyses(measurement errors).Replicating a series of experiments,or even the entire design,is often less expensive than to make a design with double the number of design points,and it can give a strong improvement of the quality of the investigation.Replication of an entire study gives us confidence i

275、n our results and helps us validate the process and is sometimes essential in order achieve statistical relevance in the data.Replication allows us to generalize to the larger population with more confidence.Arranging experiments into blocksTo minimize the effect of lurking variables,we randomize de

276、signs when we can and block the designs when direct randomization is not feasible.In a block design,the experimental subjects are divided into homogeneous blocks (i.e.,groups similar to each other)before randomly assigned a run number.Blocking reduces known,but assumed irrelevant,sources of variatio

277、n between units and thereby enables greater control of the sources of variation.Blocking also allows us to map if any external source of variability related to the groups will influence the effects of the factors.An alternative to blocking is to keep the blocking factor constant during a study.In bl

278、ocking,we divide the runs into several sets performed group by group.As an example,consider a full factorial design,with five factors that equals 32 experiments,for investigation of the batch size of raw material or the conductivity range of the buffer used.If there are constraints that only allow y

279、ou to perform eight runs per batch,we might wish to run the experiments in four blocks,each composed of eight runs using a homogeneous raw material or a single buffer system.The method of dividing,for example,32 runs into four blocks of eight runs is called orthogonal blocking.In orthogonal blocking

280、,each run is performed in a way that the difference between the blocks(the raw material or buffer salt)does not affect the responses.Blocking designs can readily be generated using DoE software.40When systematic bias cannot be avoided,blocking can be used to include the uncontrolled term into the mo

281、del.Thus,blocking introduces an extra factor in the design and model,and the blocking variables result in reduction of the degree of freedom(see Appendix 2)and also affect the resolution of the design.The block size and the number of blocks of the two-level factorial designs are always a power of tw

282、o;there is one blocking factor for two blocks,two for four blocks,and three for eight blocks,and so forth.The pseudo-resolution of the block design is the resolution of the design when all the block effects(blocking factors and all their interactions)are treated as main effects with the assumption t

283、hat there are no interactions between blocks and main effects.A blocking factor can be treated as a fixed or random effect.When the external variability can be set intentionally and the primary objective for blocking is to eliminate that source of variability,the blocking factor is considered a fixe

284、d effect.When the external variability cannot be controlled and set purposely and the primary blocking objective is to make a prediction without specifying the block level taking into account the external variability,the blocking factor is seen as a random effect.Blocking in the UNICORN software is

285、done manually by addition of a block factor to the design and dividing the experimental plan into the consequent blocks.When blocking a design,additional center points divided between each block should be run.Experimental design center pointsCenter points are added to a design for two reasons:to pro

286、vide a measure of process stability and inherent process variability and to check for curvature.To allow estimation of the experimental error,it is common to add center points performed at least in triplicate.Center points can be excluded in resolution III designs as these designs are selected for k

287、eeping the number of experiments to a minimum.In the worksheet outlined in Figure 3.6,we have added three center point runs to the otherwise randomized design matrix,giving a total of eleven runs.True replicates,and not only repeated measurements,measures the process variation.The repetition of meas

288、urements on the same center point could result in essentially the same value for our response,thus inducing a significant lack of fit.In an experimental design,any replicated design point could be used for estimation of the process variation,not only the selected center point(if we wish to select an

289、other).41Evaluation of design quality(condition number)The condition number,generally a software generated number based on the selected design,can be conceptually regarded as the sphericity of the design or as the ratio of the longest and the shortest diagonals of the design(Fig 3.12).Table 3.2 list

290、s general guidelines for using condition number as a tool for evaluation of the quality of a design.The more symmetrical the design,the greater the quality and the lower the condition number.Two-level factorial designs without center points are completely symmetrical as all of the design points are

291、situated on the surface of a circle or a sphere and have condition number 1.Asymmetrical designs,such as designs with qualitative factors(or mixture factors),have condition numbers greater than 1.Whenever a design is optimized or changed,the condition number obtained from the modeling should be chec

292、ked and a value deviating from acceptable values(Table 3.2)should initiate re-evaluation of the entire experimental setup.The correlation matrix is another tool for estimating design quality.In the matrix in Figure 3.13,the linear correlation coefficients R between all the terms in the model and all

293、 the responses are displayed.The R value represents the extent of the linear association between two terms and ranges from-1 to 1.When R is near zero there is no linear relationship between the terms.Table 3.2.Guidelines for use of condition number in evaluation of design quality(data from Eriksson

294、et al.Design of Experiments.Principles and Applications.Umetrics Academy ISBN-10:91-973730-4-4,ISBN-13:978-91-973730-4-3 2008)Design qualityCondition numberScreening and robustness testingOptimizationGood 3 6 12(A)(B)Fig 3.12.Conceptual schematic of condition numbers.(A)A completely symmetrical desi

295、gn has condition number 1.(B)A skewed design has a condition number greater than 1.LopHLoCoLopH*LopHLoCo*LoCoLopH*LoCoDBCLopH10000-0.285047LoCo01000-0.656848LopH*LopH0010.2666670-0.316677LoCo*LoCo000.26666710-0.362633LopH*LoCo00001-0.52746DBC-0.285047-0.656848-0.316677-0.362633-0.527461Fig 3.13.The

296、correlation matrix displays the correlation pattern in the data.In this case,the effect of load pH and conductivity on dynamic binding capacity(DBC)was examined.Each individual factor is correlated with itself,but we also see a slight correlation between the quadratic pH and conductivity terms(0.27)

297、,and a negative correlation between the factors and the response(i.e.,the DBC),which decreases with increasing factor levels.42Step 4.Perform experimentsStep 4 contains the following elements:Perform the experiments and analyses Review the measurement system analysis and expected measurement variati

298、on as compared to the variation in the experiments Check the data quality Make sure that all the experiments are well-defined,controlled,and validatedIn protein purification,the process studied can be one or several steps in the protocol,for example,for a chromatographic separation.Proceeding with t

299、his process in an efficient way requires automation.DoE with UNICORN software and KTA systemsThe use of UNICORN software together with an KTA system enables automatic execution of a sequence of runs following the setup of the DoE study(Fig 3.14).Based on the user-defined objective and number of fact

300、ors and settings,DoE in the UNICORN software creates a designed set of experiments.The presented experimental plan contains the experiments to be performed.For minimal manual handling,the automated method events and sequential runs can be controlled automatically.Automatic control is achieved throug

301、h the different modules (i.e.,valves,pumps,etc.)and method events of the KTA systems.KTA systems offer high flexibility in configuration to meet the needs in factor and condition screening and optimization designs.Data from finalized runs are integrated in the UNICORN DoE software and can be complem

302、ented with results from external analyses for subsequent statistical evaluation.Statistical analyses include creating a model,refining the model,and displaying a number of plots to aid evaluation of the results.The model and visualized information is used to draw conclusions from the results,assist

303、in decision making,predict responses for new parameter settings,and to optimize parameter settings for a desired combination of responses.UNICORN methodDesign inputDesign and scoutingRun Definition of factors,factor types,and settings Definition of objective for creating the designModel evaluationUs

304、e of model for prediction and decisionsMethod SettingsEquilibrationEquilibrationElutionColumn WashSample ApplicationFig 3.14.Using the UNICORN software to create a DoE workflow of which the main steps are creating a chromatography method for the process;setting up an experimental design,that is,defi

305、ning the study objective(screening,optimization,or robustness testing),factors,and factor ranges;and performing the runs generated by the experimental design and entering the response values for subsequent statistical evaluation.43Configuration of KTA systemsThe wide variety of applications requires

306、 configurability of the chromatography system.When we wish to study different process conditions,flexibility in system configuration is important.KTA systems can be equipped with valves for additional inlets and different flow directions,and with a range of columns and external equipment such as an

307、autosampler via the I/O box.For determination of factor settings,such as buffer pH or conductivity,in a DoE study using KTA avant,for example,is greatly facilitated by the possibility of using the quaternary valve for buffer mixing according to predefined or customized recipes or by using the user-d

308、efined quaternary gradient mixing ratio.If several buffer concentrations or additional buffer components are required when using KTA systems,it is possible to add an extra inlet prior to the quaternary valve.Step 5.Create modelStep 5 contains the following elements:Enter the response data and use th

309、e DoE software to create a model Use multiple linear regression for the mathematical modelingExperiments generate data that can later be transformed in to pictures for easy interpretation.In modeling,we move data to formulas that are mathematical descriptions of the relationships we are studying(Fig

310、 3.15).DoE software is used for calculation of a mathematical model for the behavior of the process and helps reduce the effort required from the user.The model is used to investigate which factors have significant effects on the selected response.The level of the random variation(noise),a key attri

311、bute in modeling,is estimated and included in the model.To refine the model,factors that do not have significant effects on the response are deleted.A refined model can thereafter be used in predictions of responses to other factor levels and combinations not tested,allowing optimization of the proc

312、ess.Studies of more than one response could result in the introduction of more advanced graphs such as sweet-spot plots and a more advanced analysis(i.e.,process simulations).FactorsMethod/process description(i.e.,transfer function=mathematical model)Yk=f(Xl)+eResponsesMethod/processFig 3.15.The DoE

313、 model concept.Different factors(inputs)may affect the response(output).Multiple factors and responses can be involved.The transfer function or model is the mathematical description of the cause-and-effect relationship.44To explain modeling,we use some basic calculus notations,in which f(x)represent

314、s the formula that describes the relationship between the factors and responses.This way of describing a model or transfer function is commonly used and helps us understand what we can obtain from different designs and models:y=f(x)+eOr exemplified in a linear,one-factor,cause-and-effect relationshi

315、p:y=b0+b1x1+ewherey=measured response f(x)=function(i.e.,the model)describing the relationship between factors and the response e=residual(error)term x1=factor(value)b0=constant obtained at the y-axis intercept when x is zero b1=the(correlation)coefficient,in this case for a linear term(main effect)

316、The residual term is also called error term or noise and is the random variation that cannot be explained by the model.A simple set of data from a single response and a single factor can serve as an example of this regression analysis.In Figure 3.16,a model of the linear relationship between y and x

317、 is plotted.The difference between the observed value(data point)and predicted value on the line is termed(raw)residual.The residuals are minimized by using the least squares regression calculation.Factor xnResponse ynResidual Fig 3.16.Linear regression analysis,where the red line corresponds to the

318、 model function y=f(x)+e.The residuals(e)(i.e.,the minimized errors between the measured data)and the theoretical data,calculated according to the model,are indicated by the arrow between the line and the blue dots.45Signal and noiseThe variation in response observed in an experimental series can be

319、 divided into systematic variability(signal)and random variability(noise)(Fig 3.17).The signal is the part of the response value that depends on the factor effect.That is,when the factor levels are changed,there will be a change in the response.The noise is additional variations in the response.The

320、causes of the noise can be divided into model prediction error and replicate error.The replicate error in turn can be divided into errors related to the execution of the experiments(experimental error)and errors related to the execution of the response measurements(measurement error).If the noise is

321、 found to be large compared with the signals,it can be necessary to reduce the errors to obtain useful data.Experimental error can be reduced by improving the precision of the execution of the experiments,for example,by a more careful manual handling or by using adjusted equipment.While certain vari

322、ables are either too difficult or too expensive to control in the actual process,it might still be possible to test or measure them using other resources and controls.Environmental conditions,for example,can be controlled to set levels for temperature and humidity during lab testing.The noise strate

323、gy involved in DoE planning includes selection of design type,factor selection and level control accuracy,type of response data,measurement of uncontrolled factors(if possible),and randomization of the experiments.We also need to take into account that there might be factors that have large effects

324、on the response but that have been overlooked.Evaluation of the relevance of different signals compared with the residuals in the investigated process is the core of the statistical methods used in DoE.The purpose of the evaluation is to determine if the observed effect of a factor is relevant.The u

325、se of DoE software greatly simplifies this evaluation.As noise is defined as the variation derived from conducting the experiments or process runs and the variation in the analyses of the samples,this is what we are trying to differentiate from our signals.Hence,a critical step in conducting well-de

326、signed experiments is to first quantitate the total experimental error.The precision of the analysis method can be determined in a separate series of experiments(e.g.,in a gage R&R study)by making repeated analyses of a single data point from the investigation.It is recommended to determine the meas

327、urement error before conducting the experiments.Make sure that the analysis method is sufficiently accurate for the investigation to be conducted.The replicates(often performed in the center point)are used for estimation of the experimental error.DoE resolves systematic variability(signal)from unsys

328、tematic variability(noise).x1x2x3x4x5x6NoiseSignalResponse valueLack-of-fit varianceReplicate varianceFig.3.17.The signal(systematic variability,i.e.,the variance accounted for by each factor)and the noise(random variability)are both part of the measured response.Noise can be further divided into mo

329、del prediction error(lack of fit)and replicate error.The replicate error in turn can be divided in to errors related to the execution of the experiments(experimental error)and execution of the response measurements(measurement error).The figure shows a hypothetical experiment with six factors x1 to

330、x6.46Model detailsThe relationship between input factors and the measured response needs to be described and displayed.These quantitative values may be arranged to display the correlation in the data,that is,the comparison of two paired sets of values to determine if an increase in one parameter cor

331、responds to an increase or decrease in the other parameter.As illustrated in Figure 3.16,scatter plots are commonly used to compare paired sets of values.In the simplest case with linear correlations in the data,we express the relationship in a single value describing the correlation,the strength in

332、 the relationship(strong or weak)and the direction(positive or negative).The calculated value(the correlation coefficient)is a value between +1 and-1 where 0 indicates no correlation,+1 a complete positive correlation,and-1 a complete negative correlation.The greater the positive or negative value,t

333、he stronger the correlation.Regression is the process of drawing a trend line representing the optimal fit through the data.A strong correlation has data points that all fall on the regression line.The trend could be either positive or negative.The trend line can be either linear or nonlinear.Nonlinearity could be due to a found maximum or minimum in the cause-and-effect relationship.Multiple line