,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,New Results about Randomization and Split-Plotting,by,James M.Lucas,2003 Quality&Productivity Research Conference,Yorktown Heights,New York,May 21-23,2003,1,Contact Information,James M.Lucas,J.M.Lucas and Associates,5120 New Kent Road,Wilmington,DE 19808,(302)368-1214,JamesM.L,2,Research Team,Huey Ju,Jeetu Ganju,Frank Anbari,Peter Goos,Malcolm Hazel,Derek Webb,John Borkowski,3,PRELIMINARIES,How do you run Experiments?,4,QUESTIONS,How many of you are involved with running experiments?,How many of you“randomize to guard against trends or other unexpected events?,If the same level of a factor such as temperature is required on successive runs,how many of you set that factor to a neutral level and reset it?,5,ADDITIONAL QUESTIONS,How many of you have conducted experiments on the same process on which you have implemented a Quality Control Procedure?,What did you find?,6,COMPARING RESIDUAL STANDARD DEVIATION FROM AN EXPERIMENT WITHRESIDUAL STANDARD DEVIATION FROM AN IN-CONTROL PROCES,MY OBSERVATIONS,EXPERIMENTAL STANDARD DEVIATION,IS LARGER.,1.5X TO 3X IS COMMON.,7,HOW SHOULD EXPERIMENTS BE CONDUCTED?,“COMPLETE RANDOMIZATION,(and the completely randomized design),RANDOMIZED NOT RESET,(Also Called Random Run Order(RRO)Experiments),(Often Achieved When Complete Randomization is Assumed),SPLIT PLOT BLOCKING,(Especially When There are Hard-to-Change Factors),8,Randomized Not Reset(RNR)Experiments,A large fraction(perhaps a large majority)of industrial experiments are Randomized not Reset(RNR)experiments,Properties of RNR experiments and a discussion of how experiments should be conducted:,“Lk Factorial Experiments with Hard-to-Change and Easy-to-Change Factors Ju and Lucas,2002,JQT 34,411-421studies one H-T-C factor and uses Random Run Order(RRO)rather than RNR,“Factorial Experiments when Factor Levels Are Not Necessarily Reset Webb,Lucas and Borkowski,2003,JQT,to appear studies 1 HTC Factor,9,RNR EXPERIMENTS,(,Random Run Order Without Resetting Factors,),OFTEN USED BY EXPERIMENTERS,NEVER EXPLICITLY RECOMMENDED,ADVANTAGES,Often achieves successful results,Can be cost-effective,DISADVANTAGES,Often can not be detected after experiment,is conducted(Ganju and Lucas 99),Biased tests of hypothesis(Ganju and Lucas 97,02),Can often be improved upon,Can miss significant control factors,10,Results for Experiments with Hard-to-Change and Easy-to-Change Factors,One H-T-C or E-T-C Factor:use split-plot blocking,Two H-T-C Factors:may split-plot,Three or more H-T-C Factors:consider RNR or Low Cost Options,Consider“Diccons Rule:Design for the H-T-C Factor,11,New Results,Joint work with Peter Goos,Builds on the Kiefer-Wolfowitz Equivalence Theorem,Implications about Computer generated designs(especially when there are Hard-to-Change Factors),12,Kiefer-Wolfowitz Equivalence Theorem,is the design probability measure,M()=XX/n(kxk matrix for a n point design),d(x,)=x(M(),-1,x(normalized variance),So called Approximate Theory,The following are equivalent:,maximizes det M(),minimizes d(x,),Max(d(x,)=k,13,Very Important Theorem,Helps find Optimum Designs,Basis for much computer aided design work,Justifies using|XX|Criterion,Shows“Classical Designs are great,“Which Response Surface Design is Best Technometrics(1976)16,411-417,Computer generated designs not needed for“standard situations,14,Optimality Criteria,Determinant(D-optimality),Maximize,|XX|,D-efficiency=|XX/n|/|X*X*/n*|,1/k,where X*is an optimum n*point design,Global(G-optimality),Minimize the maximum variance,G-efficiency=k/Max,d(x,),G-efficiency 1.0,Drop,2,2,terms for one h-t-c factor results,21,Observations,Does not use Maximum Resolution or Minimum Abberation,Similar results for most 2,k,factorials,22,Super Efficient Experiments are not always Optimal,2,6-1,Main effects plus 2FI model,G-optimum design has 12 blocks when d gets large,23,Conclusions,Showed K-W Equivalence theorem does not hold for Split-Plot Experiments,Discussed Implications,Exciting research area,Much more to do,24,