Probabilistic Design for Optimization and Robustness for Engineers

BRYAN DODSON, Executive Engineer, SKF, USA PATRICK C. HAMMETT, Lead Faculty Six Sigma Program, Integrative Systems & Design, College of Engineering, University of Michigan, Ann Arbor, USA RENÉ KLERX, Principal Statistician, SKF, The Netherlands

• Preface ixAcknowledgments xi1 New product development process 11.1 Introduction 11.2 Phases of new product development 21.2.1 Phase I—concept planning 31.2.2 Phase II—product planning 41.2.3 Phase III—product engineering design and verification 61.2.4 Phase IV—process engineering 91.2.5 Phase V—manufacturing validation and ramp-up 101.3 Patterns of new product development 111.4 New product development and Design for Six Sigma 131.4.1 DfSS core objectives 131.4.2 DfSS methodology 151.4.3 Embedded DfSS 161.5 Summary 17Exercises 172 Statistical background for engineering design 192.1 Expectation 192.2 Statistical distributions 242.2.1 Normal distribution 242.2.2 Lognormal distribution 272.2.3 Weibull distribution 302.2.4 Exponential distribution 322.3 Probability plotting 342.3.1 Probability plotting—lognormal distribution 352.3.2 Probability plotting—normal distribution 362.3.3 Probability plotting—Weibull distribution 372.3.4 Probability plotting—exponential distribution 392.3.5 Probability plotting with confidence limits 402.4 Summary 43Exercises 443 Introduction to variation in engineering design 463.1 Variation in engineering design 463.2 Propagation of error 473.3 Protecting designs against variation 483.4 Estimates of means and variances of functions of several variables 513.5 Statistical bias 593.6 Robustness 593.7 Summary 60Exercises 614 Monte Carlo simulation 634.1 Determining variation of the inputs 634.2 Random number generators 644.3 Validation 664.4 Stratified sampling 704.5 Summary 74Exercises 755 Modeling variation of complex systems 765.1 Approximating the mean, bias, and variance 775.2 Estimating the parameters of non-normal distributions 815.3 Limitations of first-order Taylor series approximation for variance 845.4 Effect of non-normal input distributions 915.5 Nonconstant input standard deviation 935.6 Summary 93Exercises 956 Desirability 986.1 Introduction 986.2 Requirements and scorecards 996.2.1 Types of requirements 1006.2.2 Design scorecard 1016.3 Desirability—single requirement 1036.3.1 Desirability—one-sided limit 1046.3.2 Desirability—two-sided limit 1066.3.3 Desirability—nonlinear function 1076.4 Desirability—multiple requirements 1096.4.1 Maxi-min total desirability index 1146.5 Desirability—accounting for variation 1156.5.1 Determining desirability—using expected yields 1156.5.2 Determining desirability—using non-mean responses 1166.6 Summary 118Exercises 1187 Optimization and sensitivity 1237.1 Optimization procedure 1237.2 Statistical outliers 1287.3 Process capability 1297.4 Sensitivity and cost reduction 1337.4.1 Reservoir flow example 1347.4.2 Reservoir flow initial solution 1357.4.3 Reservoir flow initial solution verification 1367.4.4 Reservoir flow optimized with normal horsepower distribution 1387.4.5 Reservoir flow optimized with normal horsepower distribution verification 1407.4.6 Reservoir flow horsepower variation sensitivity 1417.4.7 Reservoir flow horsepower lognormal probability plot 1437.4.8 Reservoir flow horsepower Cpk optimization using a lognormal distribution 1447.5 Summary 149Exercises 1508 Modeling system cost and multiple outputs 1538.1 Optimizing for total system cost 1538.2 Multiple outputs 1588.2.1 Optimization 1598.2.2 Computing nonconformance 1598.3 Large-scale systems 1648.4 Summary 166Exercises 1679 Tolerance analysis 1709.1 Introduction 1709.2 Tolerance analysis methods 1749.2.1 Historical tolerancing 1749.2.2 Worst-case tolerancing 1759.2.3 Statistical tolerancing 1759.3 Tolerance allocation 1789.4 Drift, shift, and sorting 1799.5 Non-normal inputs 1829.6 Summary 182Exercises 18210 Empirical model development 18510.1 Screening 18510.2 Response surface 19310.2.1 Central composite designs 19410.3 Taguchi 20010.4 Summary 200Exercises 20111 Binary logistic regression 20211.1 Introduction 20211.2 Binary logistic regression 20511.2.1 Types of logistic regression 20511.2.2 Binary versus ordinary least squares regression 20611.2.3 Binary logistic regression and the logit model 20811.2.4 Binary logistic regression with multiple predictors 21111.2.5 Binary logistic regression and sample size planning 21111.2.6 Binary logistic regression fuel door example 21211.2.7 Binary logistic regression—significant binary input 21311.2.8 Binary logistic regression—nonsignificant binary input 21411.2.9 Binary logistic regression—continuous input 21411.2.10 Binary logistic regression—multiple inputs 21511.3 Logistic regression and customer loss functions 21711.4 Loss function with maximum (or minimum) response 22011.5 Summary 223Exercises 22312 Verification and validation 22512.1 Introduction 22512.2 Engineering model V&V 22812.3 Design verification methods and tools 23012.3.1 Design verification reviews 23012.3.2 Virtual prototypes and simulation 23112.3.3 Physical prototypes and early production builds 23212.3.4 Confirmation testing comparing alternatives 23212.3.5 Confirmation tests comparing the design to acceptance criteria 23312.4 Process validation procedure 23312.5 Summary 238References 239Bibliography 242Answers to selected exercises 246Index 251