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Exploring Best Practises in Design of Experiments: A Data Driven Approach to DOE Increasing Robustness, Efficiency and Effectiveness

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Learn about best practises in the
design of experiments and a data-driven approach to DOE that increases robustness, efficiency and effectiveness. This was presented at a JMP seminar in the UK.

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Exploring Best Practises in Design of Experiments: A Data Driven Approach to DOE Increasing Robustness, Efficiency and Effectiveness

  1. 1. Copyright © 2014, SAS Institute Inc. All rights reserved. Exploring best practises in Design of Experiments A Data Driven Approach to DOE Increasing Robustness, Efficiency and Effectiveness
  2. 2. Copyright © 2014, SAS Institute Inc. All rights reserved.
  3. 3. Malcolm Phil Copyright © 2014, SAS Institute Inc. All rights reserved. Julie Who’s here from jmp Bernard Luke
  4. 4. jmp helps you make better decisions, faster Copyright © 2014, SAS Institute Inc. All rights reserved.
  5. 5. We will show you how you can § Simplify and make DoE work for more people in more situations § Make use of existing data to have better informed experiments § Make better decisions in less time Copyright © 2014, SAS Institute Inc. All rights reserved.
  6. 6. What we will cover today Time Topic Speaker 0940 Introduction to Design of Experiments (DoE) Malcolm Moore 1025 Identifying key factors and optimising Copyright © 2014, SAS Institute Inc. All rights reserved. processes using the key factors Phil Kay 1100 Break 1130 Example of DOE in Service Industries Malcolm Moore 1155 Effective experimentation when we have constraints on the factor combinations Phil Kay 1220 Data Driven DoE and Choice Experiments Malcolm Moore 1250 Summary and close Malcolm Moore 1300 Adjourn for lunch
  7. 7. Help us to help you . . . Copyright © 2014, SAS Institute Inc. All rights reserved.
  8. 8. Copyright © 2014, SAS Institute Inc. All rights reserved. How often is DoE used in your organisation? (Select one) 1. Never 2. Rarely 3. Often 4. The default approach for experimentation
  9. 9. Copyright © 2014, SAS Institute Inc. All rights reserved. What is you organisation’s general view of DoE (not your view which can be different)? (Select one) 1. Committed to it 2. Unsure what it is 3. Not really bothered 4. Tried it but it didn’t work 5. Against it
  10. 10. Copyright © 2014, SAS Institute Inc. All rights reserved. Are your experimental problems ever complex (factor constraints, disallowed combinations)? (Select one) 1. Never 2. Rarely 3. Often 4. Always 5. Don’t know
  11. 11. Do you have existing data that you would like to use to inform future experiments? (Select one) 1. Never 2. Rarely 3. Often 4. Always Copyright © 2014, SAS Institute Inc. All rights reserved.
  12. 12. Contents § Background to DOE § Why Use DOE? § Tips for Effective DOE with Classical Designs § Definitive Screening § Case Studies 1-3 § Role of Statistical Modelling and DOE in Learning § Data Driven DOE § Case Study 4 Copyright © 2014, SAS Institute Inc. All rights reserved.
  13. 13. BACKGROUND TO DESIGN OF EXPERIMENTS (DOE) Copyright © 2014, SAS Institute Inc. All rights reserved.
  14. 14. Copyright © 2014, SAS Institute Inc. All rights reserved. FATHER OF DOE RONALD A. FISHER Rothamstead Experimental Station, England – Early 1920’s
  15. 15. Copyright © 2014, SAS Institute Inc. All rights reserved. FISHER’S FOUR DESIGN PRINCIPLES 1. Factorial Concept - rather than one-factor-at-a-time 2. Randomization - to avoid bias from lurking variables 3. Blocking - to reduce noise from nuisance variables 4. Replication - to quantify noise within an experiment
  16. 16. Copyright © 2014, SAS Institute Inc. All rights reserved. AGRICULTURAL IMPACT US corn yields Cornell University, http://usda.mannlib.cornell.edu/MannUsda
  17. 17. WHY USE DOE? Copyright © 2014, SAS Institute Inc. All rights reserved.
  18. 18. Inputs Factors Machine Operator Temperature Pressure Humidity Copyright © 2014, SAS Institute Inc. All rights reserved. Typical Process The properties of products and processes are often affected by many factors: Typical Process Outputs Responses Yield Cost … In order to build new or improve products and processes, we must understand the relationship between the factors (inputs) and the responses (outputs).
  19. 19. Traditional One-Factor-at-a-Time § A common approach is one-factor-at-a-time experimentation. § Consider experimenting one-factor-at-a-time to determine the values of temperature and time that optimise yield. Copyright © 2014, SAS Institute Inc. All rights reserved.
  20. 20. Traditional One-Factor-at-a-Time Copyright © 2014, SAS Institute Inc. All rights reserved.
  21. 21. Traditional One-Factor-at-a-Time Copyright © 2014, SAS Institute Inc. All rights reserved.
  22. 22. Traditional One-Factor-at-a-Time Copyright © 2014, SAS Institute Inc. All rights reserved.
  23. 23. Traditional One-Factor-at-a-Time Copyright © 2014, SAS Institute Inc. All rights reserved.
  24. 24. Copyright © 2014, SAS Institute Inc. All rights reserved. Traditional One-Factor-at-a-Time § One-factor-at-a-time experimentation frequently leads to sub-optimal solutions. § Assumes the effect of one factor is the same at each level of the other factors, i.e. factors do not interact. § In practice, factors frequently interact.
  25. 25. Copyright © 2014, SAS Institute Inc. All rights reserved. Interaction between factors
  26. 26. Experimental Design § Most efficient way of investigating relationships. § Runs (factor combinations) chosen to maximize the information § Ideally balanced for ease of analysis and interpretation Copyright © 2014, SAS Institute Inc. All rights reserved.
  27. 27. Copyright © 2014, SAS Institute Inc. All rights reserved. ITERATIVE AND SEQUENTIAL NATURE OF CLASSICAL DOE
  28. 28. TIPS FOR EFFECTIVE DOE WITH CLASSICAL DESIGNS Copyright © 2014, SAS Institute Inc. All rights reserved.
  29. 29. Stages of Experimental Design § Designing an experiment involves much more than just selecting the sequence of experimental runs: Plan Design Conduct Analyse Confirm § Historically, improper planning is the most common cause of failed experiments. Copyright © 2014, SAS Institute Inc. All rights reserved.
  30. 30. Some Planning Steps § Review what we know • Have peer discussions § Determine new questions to answer § Identify factors and ranges to investigate § Define responses • Easy and precise to measure Copyright © 2014, SAS Institute Inc. All rights reserved.
  31. 31. Common Experimental Objectives Copyright © 2014, SAS Institute Inc. All rights reserved. Identify Important Factors Screening Design Classical Fractional Factorial Optimise Process RSM Design Classical Central Composite Optimise Ingredients Mixtures Classical Simplex & Extreme Vertices
  32. 32. Common Experimental Objectives Copyright © 2014, SAS Institute Inc. All rights reserved. Identify Important Factors Screening Design Classical Fractional Factorial Sequential Experimentation Reduces Total Cost Optimise Process RSM Design Classical Central Composite Optimise Ingredients Mixtures Classical Simplex & Extreme Vertices
  33. 33. Common Experimental Objectives Definitive Screening Design Simplifies Experimental Workflow Copyright © 2014, SAS Institute Inc. All rights reserved. Sequential Experimentation Identify Important Factors Screening Design Classical Fractional Factorial Optimise Process RSM Design Classical Central Composite Optimise Ingredients Mixtures Classical Simplex & Extreme Vertices
  34. 34. Common Experimental Objectives Copyright © 2014, SAS Institute Inc. All rights reserved. Sequential Experimentation Identify Important Factors Screening Design Classical Fractional Factorial Definitive Screening Design Optimise Process RSM Design Classical Central Composite Optimal Design Manages Experimental Constraints Optimise Ingredients Mixtures Classical Simplex & Extreme Vertices
  35. 35. Determining the Appropriate Factors § Determining the factors to be included in your experiment is a critical part of planning. • Exploring too many factors may be costly and time consuming. • Exploring too few may limit the success of your experiment. § Prior knowledge and analysis of existing data are useful aids to identifying and prioritising factors for study. Other methods may include: • Brainstorming • Ishikawa Copyright © 2014, SAS Institute Inc. All rights reserved.
  36. 36. Selection of Factor Range is Critical With Two Level Designs … Copyright © 2014, SAS Institute Inc. All rights reserved.
  37. 37. Selection of Factor Range is Critical With Two Level Designs … Copyright © 2014, SAS Institute Inc. All rights reserved. By experimenting at the two settings in yellow, X would be declared unimportant
  38. 38. Selection of Factor Range is Critical With Two Level Designs … By using half and often times much less than than half the factor range X is declared important Copyright © 2014, SAS Institute Inc. All rights reserved.
  39. 39. Selection of Factor Range is Critical With Two Level Designs … By using half and often times much less than than half the factor range X is declared important Copyright © 2014, SAS Institute Inc. All rights reserved. Often leads to narrow factor ranges to force linear relationships but consequence is high risk of determining sub-optimal solution
  40. 40. Determining the Appropriate Responses § Selection of your responses will also be critical to the success of your experiment. Whenever possible: • Choose variables that correlate to internal or external customer requirements • Find responses that are easy to measure • Make sure your measurement systems are precise, accurate, and stable § Analysis of current data, prior knowledge, measurement systems analysis are useful aids. Copyright © 2014, SAS Institute Inc. All rights reserved.
  41. 41. DEFINITIVE SCREENING Copyright © 2014, SAS Institute Inc. All rights reserved.
  42. 42. Copyright © 2014, SAS Institute Inc. All rights reserved. Fractional Factorials: Complex workflow from many factors to optimum settings Tempting to miss out middle step which can result in selection of wrong factors and decisions
  43. 43. Copyright © 2014, SAS Institute Inc. All rights reserved. Definitive Screening Design § Identifies active main effects, uncorrelated with other effects. § May identify significant quadratic effects, uncorrelated with main effects and at worst weakly correlated with other quadratic effects. § If few factors turn out to be important, can identify significant two-way interactions uncorrelated with main effects and weakly correlated with other higher order effects. § One stage experiment if three or fewer factors important: • progress straight to full quadratic model • optimise process with no further experimentation • otherwise augment DSD for optimization goals
  44. 44. Copyright © 2014, SAS Institute Inc. All rights reserved. New Class of Screening Design § Three-level screening design • 2m + 1 runs when m is even • 2m + 3 runs when m is odd • 1 additional run for categorical factors • based on m fold-over pairs and an overall center point, where m is number of factors • the values of the ±1 entries in the odd-numbered runs are determined using optimal design. the structure illustrated in Table 1. We use xi,j to denote the setting of the jth factor for the ith run. For m factors, there are 2m + 1 runs based on m fold-over pairs and an overall center point. Each run (excluding the centerpoint) has exactly one factor level at its center point and all others at the ex-tremes. As described in the next section, the val-ues of the ±1 entries in the odd-numbered runs of TABLE 1. General Design Structure for m Factors Factor levels Foldover Run pair (i) xi,1 xi,2 xi,3 · · · xi,m 1 1 0 ±1 ±1 · · · ±1 2 0 !1 !1 · · · !1 2 3 ±1 0 ±1 · · · ±1 4 !1 0 !1 · · · !1 3 5 ±1 ±1 0 · · · ±1 6 !1 !1 0 · · · !1 ... ... ... ... ... . . . ... m 2m − 1 ±1 ±1 ±1 · · · 0 2m !1 !1 !1 · · · 0 Centerpoint 2m + 1 0 0 0 · · · 0 of linear and quadratic main-effects terms. 5. Quadratic effects are orthogonal to main effects and not completely confounded (though corre-lated) with interaction effects. 6. With 6 through (at least) 12 factors, the de-signs are capable of estimating all possible full quadratic models involving three or fewer fac-tors with very high levels of statistical effi-ciency. We use the term “definitive screening” because of points one through five above. These are small de-signs that, unlike resolution III and IV factorial de-signs, permit the unambiguous identification of ac-tive main effects, active quadratic effects, and, in the presence of a moderate level of effect sparsity, active two-way interactions. In our view, another practical advantage of the designs we propose is the explicit use of three levels. It has been our experience that engineers and scien-tists often feel some discomfort using two-level de-signs for two reasons. First, statisticians advise them to experiment boldly by choosing a substantial inter-val between low and high values of each factor. But their scientific training inculcates the notion that the functional relationship between independent and de-pendent variables is usually nonlinear, particularly over a wide range. This leads to some cognitive dis-sonance in considering the use of two-level designs. Second, even in the early stages of a study, investiga-tors frequently have an opinion regarding the “best” Journal of Quality Technology Vol. 43, No. 1, January 2011
  45. 45. Copyright © 2014, SAS Institute Inc. All rights reserved. Use of Three Level Designs Advantageous § Scientists and engineers are uncomfortable using two-level designs • Restricting factor ranges may result in sub-optimal solutions • Scientific/engineering judgment suggests relationships nonlinear over wide ranges § Investigators frequently have an opinion regarding the “best” levels of each factor for optimizing a response • Experimental region centered at these levels. • Two-level design might screen out an important factor when experimental region centred at “best” • Adding centre points allows test for curvature • However ambiguity over factors causing curvature • DSD avoids ambiguity by making it possible to uniquely identify the source(s) of curvature.
  46. 46. CASE STUDIES Copyright © 2014, SAS Institute Inc. All rights reserved.
  47. 47. Case Study 1: Optimising a Chemical Process Why Consider Definitive Screening Designs? Copyright © 2014, SAS Institute Inc. All rights reserved.
  48. 48. Copyright © 2014, SAS Institute Inc. All rights reserved. Background § Five factors § One response yield § Goal optimise yield § Keep total cost of experimentation to minimum § Contrast traditional approach of main effect screening design plus augmentation to RSM with DSD
  49. 49. § Traditional screening approach correlates main effects with two factor interaction effects § Cost constraint and inexperience with such designs can lead to missed DOE steps § Investigator missed step of augmenting main effect design to separate correlated interaction effects from assumed important main effects § Resulted in wrong set of factors selected for RSM design which results in wrong solution Copyright © 2014, SAS Institute Inc. All rights reserved. Background
  50. 50. Copyright © 2014, SAS Institute Inc. All rights reserved. Traditional Approach with Missed Step
  51. 51. Resolution III Design Perfectly Correlates Main Effects With Interaction Effects Copyright © 2014, SAS Institute Inc. All rights reserved.
  52. 52. Model Interpretation § Fitted Model Y = b0 + b1*X1 + b2*X2 + b3*X3 + Error § Correct Interpretation of Fitted Model Y = b0 + b1*(X1+X2X3) + b2*(X2+X1X3) + b3*(X3+X1X2) + Error Copyright © 2014, SAS Institute Inc. All rights reserved.
  53. 53. Missed Step Augments Initial Design to Separate Main Effects From Interactions Copyright © 2014, SAS Institute Inc. All rights reserved.
  54. 54. Model Interpretation of Augmented Design § Correct Interpretation of Model Fitted to Augmented design Y = b0 + b1*X1 + b2*X2 + b3*X3 + b12*X1X2 + b13*X1X3 + b23*X2X3 + Error § Allows clear separation of main and interaction effects § This step was missed in case study prior to modelling curvature Copyright © 2014, SAS Institute Inc. All rights reserved.
  55. 55. § DSD results in correct identification of important factors due to non correlated main and two factor interaction effects § Because just three factors are important DSD results in one step design: • In addition to correctly identifying correct factors • DSD requires no augmentation to identify optimal settings of important factors Copyright © 2014, SAS Institute Inc. All rights reserved. Background
  56. 56. CASE STUDY 1 Copyright © 2014, SAS Institute Inc. All rights reserved.
  57. 57. Copyright © 2014, SAS Institute Inc. All rights reserved. Conclusions § Fractional factorial designs can lead to selection of wrong factor set § Complex workflow for avoiding this risk which may be misunderstood or not applied by users new to DOE § May lead to conclusion that DOE does not work for us! § DSD simplifies DOE process and removes risk of selecting wrong factor set § Provides one step DOE when three or fewer important factors • Sufficient to identify correct factor set and determine best settings of selected factors
  58. 58. Case Study 2: Optimising Marketing Response Rate and Profitability Definitive Screening Design for Efficiency Copyright © 2014, SAS Institute Inc. All rights reserved.
  59. 59. Copyright © 2014, SAS Institute Inc. All rights reserved. Background § Goal is to maximise return from credit card marketing campaigns. Two outputs: • Response rate - percentage mailed a credit card offer who accept the offer; • Indexed usage – average profit per individual over a twelve month period. § Factors are balance transfer period, interest free period for new purchases and %APR at end of any introductory offers. § Goal: determine characteristics of credit card offer that maximises response rate and profitability.
  60. 60. CASE STUDY 2 Copyright © 2014, SAS Institute Inc. All rights reserved.
  61. 61. Copyright © 2014, SAS Institute Inc. All rights reserved. Conclusions § DSD can be cost effective with few factors when cost of experimental run is high § Tradeoff is greater uncertainty (reduced power) in decisions
  62. 62. CASE STUDY 3 Copyright © 2014, SAS Institute Inc. All rights reserved.
  63. 63. Case Study 3: Optimising Yield What About Constrained Factor Spaces? Copyright © 2014, SAS Institute Inc. All rights reserved.
  64. 64. Copyright © 2014, SAS Institute Inc. All rights reserved. Background § From chapter 5 of Goos & Jones § Chemical reaction § Goal: maximise yield § 2 factors: Temperature and Time
  65. 65. Copyright © 2014, SAS Institute Inc. All rights reserved. Background § Expert knowledge tells us • Certain conditions will give poor results (hence, constraints) • Behaviour very non-linear § We will show • Design where prior knowledge is ignored. • Fitting the design to the problem
  66. 66. Copyright © 2014, SAS Institute Inc. All rights reserved. Example of Process Constraint
  67. 67. Copyright © 2014, SAS Institute Inc. All rights reserved. Shrink Experimental Range to Factorial
  68. 68. Copyright © 2014, SAS Institute Inc. All rights reserved. Shrink Experimental Range to Factorial
  69. 69. Copyright © 2014, SAS Institute Inc. All rights reserved. Shrink Experimental Range to Factorial
  70. 70. Optimal Design: Use Actual Factor Range Copyright © 2014, SAS Institute Inc. All rights reserved.
  71. 71. Optimal Design: Fit to Model The process is not seen as a black box anymore… … optimal designs allow investigation of complete factor space properly adjusted for constraints Copyright © 2014, SAS Institute Inc. All rights reserved. Typical Process Machine Operator Temperature Pressure Humidity Yield Cost … Inputs Factors Outputs Responses Model Y = f(X)
  72. 72. CASE STUDY 3 Copyright © 2014, SAS Institute Inc. All rights reserved.
  73. 73. Copyright © 2014, SAS Institute Inc. All rights reserved. Conclusions § Custom Design permits studying any: • combination of factors with or without constraints, • number of factor levels, • blocking structure. § Build your design to suit the problem instead of fitting the problem into a design
  74. 74. Case Study 4: Designing Products People Want to Buy Copyright © 2014, SAS Institute Inc. All rights reserved. Data Driven DOE
  75. 75. ROLE OF STATISTICAL MODELLING AND DOE IN LEARNING Copyright © 2014, SAS Institute Inc. All rights reserved.
  76. 76. LEARNING IN THE FACE OF UNCERTAINTY Data Driven DOE Integrates Incremental Learning Across DOE and Observational Sources of Data Able to Consistently Meet Customer Requirements What is really happening Y = F(X) + Error Measurement and Data Collection Situation Appraisal Situation Appraisal Adapted from Box, Hunter and Hunter Copyright © 2014, SAS Institute Inc. All rights reserved. 76 What we think is happening Measurement and Data Collection Analysis Situation Appraisal Measurement and Data Collection Design Real World Model Unable to Consistently Meet Customer Requirements
  77. 77. Copyright © 2014, SAS Institute Inc. All rights reserved. Simple Process of Statistical Learning DOE Data ….…. Observational Data
  78. 78. Copyright © 2014, SAS Institute Inc. All rights reserved. Data Sources § DOE and/or observational (historical) § Potential problems with observational data: • X’s are correlated – identification of “best” model difficult • Outliers (potential or real) - bias model estimation • Missing data cells – result in loss of whole data rows with traditional least squares based analysis • Range over which X’s varied may be limited – restricting model usefulness • May not have measured all relevant X’s § In some situations these can also be issues with DOE datasets
  79. 79. WHAT IS DATA DRIVEN DOE? Copyright © 2014, SAS Institute Inc. All rights reserved.
  80. 80. Copyright © 2014, SAS Institute Inc. All rights reserved. Data Driven DOE: Integrating Statistical Modelling and DOE § Learning is incremental and effective statistical modelling of observational data aids design of next experiment. § Analysis approach needs to manage real (messy) data simply • Correlated X’s, outliers, missing cells • Quickly deliver “best” current model to revise with new DOE data • Aid better analysis of new experimental data when unexpected occurs • Build models based on individual datasets and aggregated data § Good statistical modelling integrated with DOE helps reduce total learning time, effort and cost § It would be a shame to not use pre-existing data that comes for free
  81. 81. Copyright © 2014, SAS Institute Inc. All rights reserved. JMP Statistical Discovery: Integrating Statistical Modelling with DOE Effectiveness Of Learning Statistical Discovery Speed of Learning Traditional Approaches § Integrated methods § Ease of use § Manage messy data § Wide array of DOE approaches § Satisfy (customer) needs § Reduce learning time § Save effort and cost
  82. 82. DATA DRIVEN DOE EXAMPLE Copyright © 2014, SAS Institute Inc. All rights reserved.
  83. 83. Copyright © 2014, SAS Institute Inc. All rights reserved. Background § PC retailer is observing appreciable retail price variation in its laptop computer line. § Goals: • Investigate factors associated with retail price variation. • Perform further experimentation in key factors to optimise and standardise pricing across stores.
  84. 84. CASE STUDY 4 Copyright © 2014, SAS Institute Inc. All rights reserved.
  85. 85. Copyright © 2014, SAS Institute Inc. All rights reserved. Conclusions § Analysis of prior data helps identify factors and ranges to use in next DOE. § Analysis of prior data helps reduce risk and increase efficiency and effectiveness of future experiments. § Exploit prior data that comes for free to inform next experiment.
  86. 86. Copyright © 2014, SAS Institute Inc. All rights reserved. Data Driven DOE: Integrated Statistical Modelling and DOE § Supports wide range of user skills § Exploratory analysis and statistical modelling of historical messy data simplifies and shortens whole DOE process. § Next generation DOE enables more staff to apply DOE with reduced learning and implementation effort § Interact with model predictions to build consensus § Integrated simulation capabilities enables rapid progression from models to decisions § Manage risk better by correctly identifying signal from noise
  87. 87. QUESTIONS? Copyright © 2014, SAS Institute Inc. All rights reserved.
  88. 88. We have shown you how you can § Reduce the risk of wrong decisions • Make DoE work for more people in more situations § Fit the best design to your problem • Find the best solution while managing system constraints § Mine your “messy” data to inform future experiments • Make better decisions in less total time using Data Driven DOE Copyright © 2014, SAS Institute Inc. All rights reserved.
  89. 89. Copyright © 2014, SAS Institute Inc. All rights reserved. Make better decisions, faster with jmp
  90. 90. Supplier of Digital Printing Materials § Needed to double capacity of a product line to meet growing demand. § Poor understanding of key process step responsible for increasing capacity. § Large number of potentially important variables and limited budget for experimentation. § Definitive Screening Design enabled screening of all factors and process optimisation in a small number of runs to achieve doubling of production rate without additional capital investment. § Saved £100,000s off development budget and enhanced the credibility of the site as a location for cost-effective high-value manufacturing within a multi-national organisation. Copyright © 2014, SAS Institute Inc. All rights reserved.
  91. 91. Large Multi-National Chemical Company § Losing market share to start-ups who were faster at introducing new products and more agile at adapting to changing customer requirements. § Needed to get more products to market faster. § Instituted a culture of experimentation with JMP Pro for variable selection and DOE to accelerate cycles of learning, enabling more new products to be introduced faster. § Helped retain and grow market share, facilitating increased dividend growth to shareholders and increased staff retention and satisfaction. Copyright © 2014, SAS Institute Inc. All rights reserved.
  92. 92. What are you going to do next? Ask us to help you Download a trial of JMP § Visit our website: www.jmp.com Join our Design of Experiments Webcasts: § Exploring Best Practise in DoE: 14:00 on 20 November § Invite your colleagues § Mastering JMP on DoE: 1400 on 14:00 on 14 November Copyright © 2014, SAS Institute Inc. All rights reserved. Register on our website

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