of Engineering Statistics

Springerof Engineering Statistics

Hoang Pham (Ed.)

With CD-ROM, 377 Figures and 20 1+ Tables

Springer

Contents

List of Tables XXXIList of Abbreviations XLI

Part A Fundamental Statistics and Its Applications

1 Basic Statistical ConceptsHoang Pham 31.1 Basic Probability Measures 31.2 Common Probability Distribution Functions 71.3 Statistical Inference and Estimation 171.4 Stochastic Processes 321.5 Further Reading 42References 421.A Appendix: Distribution Tables 431.B Appendix: Laplace Transform 47

2 Statistical Reliability with ApplicationsPaul Kvam, lye-Chyi Lu 492.1 Introduction and Literature Review 492.2 Lifetime Distributions in Reliability 502.3 Analysis of Reliability Data 542.4 System Reliability 56References 60

3 Weibull Distributions and Their ApplicationsChin-Diew Lai, D.N. Pra Murthy, Min Xie 633.1 Three-Parameter Weibull Distribution 643.2 Properties 643.3 Modeling Failure Data 673.4 Weibull-Derived Models 703.5 Empirical Modeling of Data 733.6 Applications 74References 76

4 Characterizations of Probability DistributionsH.N. Nagaraja 794.1 Characterizing Functions 804.2 Data Types and Characterizing Conditions 814.3 A Classification of Characterizations 834.4 Exponential Distribution 844.5 Normal Distribution 854.6 Other Continuous Distributions 87

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XVIII Contents

4.7 Poisson Distribution and Process 884.8 Other Discrete Distributions 904.9 Multivariate Distributions and Conditional Specification 904.10 Stability of Characterizations 924.11 Applications 924.12 General Resources 93References 94

5 Two-Dimensional Failure ModelingD.N. Pra Murthy, Jaiwook Baik, Richard J. Wilson, Michael Bulmer 975.1 Modeling Failures 985.2 Black-Box Modeling Process 985.3 One-Dimensional Black-Box Failure Modeling 995.4 Two-Dimensional Black-Box Failure Modeling 1035.5 A New Approach to Two-Dimensional Modeling 1075.6 Conclusions 110References 110

6 Prediction Intervals for Reliability Growth Modelswith Small Sample SizesJohn Quigley, Lesley Walls 1136.1 Modified IBM Model - A Brief History 1146.2 Derivation of Prediction Intervals for the Time to Detection

of Next Fault 1156.3 Evaluation of Prediction Intervals for the Time to Detect Next Fault 1176.4 Illustrative Example 1196.5 Conclusions and Reflections 122References 122

7 Promotional Warranty Policies: Analysis and PerspectivesJun Bai, Hoang Pham 1257.1 Classification of Warranty Policies 1267.2 Evaluation of Warranty Policies 1297.3 Concluding Remarks 134References 134

8 Stationary Marked Point ProcessesKarl Sigman 1378.1 Basic Notation and Terminology 1388.2 Inversion Formulas 1448.3 Campbell's Theorem for Stationary MPPs 1458.4 The Palm Distribution: Conditioning in a Point at the Origin 1468.5 The Theorems of Khintchine, Korolyuk, and Dobrushin 1468.6 An MPP Jointly with a Stochastic Process 1478.7 The Conditional Intensity Approach 1488.8 The Non-Ergodic Case 1508.9 MPPs in Rd 150References 152

Contents XIX

9 Modeling and Analyzing Yield, Burn-In and Reliabilityfor Semiconductor Manufacturing: OverviewWay Kuo, Kyungmee 0. Kim, Taeho Kim 1539.1 Semiconductor Yield 1549.2 Semiconductor Reliability 1599.3 Bum-1n 1609.4 Relationships Between Yield, Bum-1n and Reliability 1639.5 Conclusions and Future Research 166References 166

Part B Process Monitoring and Improvement

10 Statistical Methods for Quality and Productivity ImprovementWeiJiang, Terrence E. Murphy, Kwok-Leung Tsui 17310.1 Statistical Process Control for Single Characteristics 17410.2 Robust Design for Single Responses 18110.3 Robust Design for Multiple Responses 18510.4 Dynamic Robust Design 18610.5 Applications of Robust Design 187References 188

11 Statistical Methods for Product and Process ImprovementKailash C. Kapur, Qianmei Feng 19311.1 Six Sigma Methodology and the (D)MAIC(T) Process 19511.2 Product Specification Optimization 19611.3 Process Optimization 20411.4 Summary 211References 212

12 Robust Optimization in Quality EngineeringSusan L. Albin, Di Xu 21312.1 An Introduction to Response Surface Methodology 21612.2 Minimax Deviation Method to Derive Robust Optimal Solution 21812.3 Weighted Robust Optimization 22212.4 The Application of Robust Optimization in Parameter Design 224References 227

13 Uniform Design and Its Industrial ApplicationsKai-Tai Fang, Ling-Yau Chan 22913.1 Performing Industrial Experiments with a UD 23113.2 Application of UD in Accelerated Stress Testing 23313.3 Application of UDs in Computer Experiments 23413.4 Uniform Designs and Discrepancies 23613.5 Construction of Uniform Designs in the Cube 23713.6 Construction of UDs for Experiments with Mixtures 240

XX Contents

13.7 Relationships Between Uniform Design and Other Designs 24313.8 Conclusion 245References 245

14 Cuscore Statistics: Directed Process Monitoringfor Early Problem DetectionHarriet B. Nembhard 24914.1 Background and Evolution of the Cuscore in Control Chart

Monitoring 25014.2 Theoretical Development of the Cuscore Chart 25114.3 Cuscores to Monitor for Signals in White Noise 25214.4 Cuscores to Monitor for Signals in Autocorrelated Data 25414.5 Cuscores to Monitor for Signals in a Seasonal Process 25514.6 Cuscores in Process Monitoring and Control 25614.7 Discussion and Future Work 258References 260

15 Chain SamplingRaj K. Govindaraju 26315.1 ChSP-1Chain Sampling Plan 26415.2 Extended Chain Sampling Plans 26515.3 Two-Stage Chain Sampling 26615.4 Modified ChSP-1 Plan 26815.5 Chain Sampling and Deferred Sentencing 26915.6 Comparison of Chain Sampling with Switching Sampling Systems 27215.7 Chain Sampling for Variables lnspection 27315.8 Chain Sampling and CUSUM 27415.9 Other Interesting Extensions 27615.10 Concluding Remarks 276References 276

16 Some Statistical Models for the Monitoringof High-Quality ProcessesMin Xie, Thong N. Goh 281.16.1 Use of Exact Probability Limits 28216.2 Control Charts Based an Cumulative Count of Conforming Items 28316.3 Generalization of the c-Chart 28416.4 Control Charts for the Monitoring of Time-Between-Events 28616.5 Discussion 288References 289

17 Monitoring Process Variability Using EWMAPhilippe Castagliola, Giovanni Celano, Sergio Fichera 29117.1 Definition and Properties of EWMA Sequences 29217.2 EWMA Control Charts for Process Position 29517.3 EWMA Control Charts for Process Dispersion 298

Contents XXI

17.4 Variable Sampling Interval EWMA Control Charts for ProcessDispersion 310

17.5 Conclusions 323References 324

18 Multivariate Statistical Process Control Schemesfor Controlling a MeanRichard A. Johnson, Ruojia Li 32718.1 Univariate Quality Monitoring Schemes 32818.2 Multivariate Quality Monitoring Schemes 33118.3 An Application of the Multivariate Procedures 33618.4 Comparison of Multivariate Quality Monitoring Methods 33718.5 Control Charts Based an Principal Components 33818.6 Difficulties of Time Dependence in the Sequence

of Observations 341References 344

Part C Reliability Models and Survival Analysis

19 Statistical Survival Analysis with ApplicationsChengjie Xiong, Kejun Zhu, Kai Yu 34719.1 Sample Size Determination to Compare Mean or Percentile

of hm Lifetime Distributions 34919.2 Analysis of Survival Data from Special Cases

of Step-Stress Life Tests 355References 365

20 Failure Rates in Heterogeneous PopulationsMaxim Finkelstein, Veronica Esaulova 36920.1 Mixture Failure Rates and Mixing Distributions 37120.2 Modeling the Impact of the Environment 37720.3 Asymptotic Behaviors of Mixture Failure Rates 380References 385

21 Proportional Hazards Regression ModelsWei Wang, Chengcheng Hu 38721.1 Estimating the Regression Coefficients ß 38821.2 Estimating the Hazard and Survival Functions 38921.3 Hypothesis Testing 39021.4 Stratified Cox Model 39021.5 Time-Dependent Covariates 39021.6 Goodness-of-Fit and Model Checking 39121.7 Extension of the Cox Model 39321.8 Example 394References 395

XXII Contents

22 Accelerated Life Test Models and Data AnalysisFrancis Pascual, William Q. Meeker, Jr., Luis A. Escobar 39722.1 Accelerated Tests 39822.2 Life Distributions 40022.3 Acceleration Models 40022.4 Analysis of Accelerated Life Test Data 40722.5 Further Examples 41222.6 Practical Considerations for lnterpreting the Analysis of ALT Data 42122.7 Other Kinds of ATs 42122.8 Some Pitfalls of Accelerated Testing 42322.9 Computer Software for Analyzing ALT Data 424References 425

23 Statistical Approaches to Planning of Accelerated ReliabilityTestingLoon C. Tang 42723.1 Planning Constant-Stress Accelerated Life Tests 42823.2 Planning Step-Stress ALT (SSALT) 43223.3 Planning Accelerated Degradation Tests (ADT) 43623.4 Conclusions 439References 440

24 End-to-End (E2E) Testing and Evaluation of High-AssuranceSystemsRaymond A. Paul, Wei-Tek Tsai, Yinong Chen, Chun Fan, Zhibin Cao,Hai Huang 44324.1 History and Evolution of E2E Testing and Evaluation 44424.2 Overview of the Third and Fourth Generations of the E2E T&E 44924.3 Static Analyses 45124.4 E2E Distributed Simulation Framework 45324.5 Policy-Based System Development 45924.6 Dynamic Reliability Evaluation 46524.7 The Fourth Generation of E2E T&E an Service-Oriented

Architecture 47024.8 Conclusion and Summary 473References 474

25 Statistical Models in Software Reliabilityand Operations ResearchP.K. Kapur, Amit K. Bardhan 47725.1 Interdisciplinary Software Reliability Modeling 47925.2 Release Time of Software 48625.3 Control Problem 48925.4 Allocation of Resources in Modular Software 491References 495

Contents XXIII

26 An Experimental Study of Human Factors in Software ReliabilityBased an a Quality Engineering ApproachShigeru Yamada 49726.1 Design Review and Human Factors 49826.2 Design-Review Experiment 49926.3 Analysis of Experimental Results 50026.4 Investigation of the Analysis Results 50126.5 Confirmation of Experimental Results 50226.6 Data Analysis with Classification of Detected Faults 504References 506

27 Statistical Models for Predicting Reliability of Software Systemsin Random EnvironmentsHoang Pham, Xiaolin Teng 50727.1 A Generalized NHPP Software Reliability Model 50927.2 Generalized Random Field Environment (RFE) Model 51027.3 RFE Software Reliability Models 51127.4 Parameter Estimation 513References 519

Part D Regression Methods and Data Mining

28 Measures of lnfluence and Sensitivity in Linear RegressionDaniel Pena 52328.1 The Leverage and Residuals in the Regression Model 52428.2 Diagnosis for a Single Outlier 52528.3 Diagnosis for Groups of Outliers 52828.4 A Statistic for Sensitivity for Large Data Sets 53228.5 An Example: The Boston Housing Data 53328.6 Final Remarks 535References 535

29 Logistic Regression Tree AnalysisWei-Yin Loh 53729.1 Approaches to Model Fitting 53829.2 Logistic Regression Trees 54029.3 LOTUS Algorithm 54229.4 Example with Missing Values 54329.5 Conclusion 549References 549

30 Tree-Based Methods and Their ApplicationsNan Lin, Douglas Noe, Xuming He 55130.1 Overview 55230.2 Classification and Regression Tree (CART) 55530.3 Other Single-Tree-Based Methods 561

XXIV Co nte nts

30.4 Ensemble Trees 56530.5 Conclusion 568References 569

31 Image Registration and Unknown Coordinate SystemsTed Chang 57131.1 Unknown Coordinate Systems and Their Estimation 57231.2 Least Squares Estimation 57531.3 Geometry of (9(p) and 40(p) 57831.4 Statistical Properties of M-Estimates 58031.5 Diagnostics 587References 590

32 Statistical Genetics for Genomic Data AnalysisJae K. Lee 59132.1 False Discovery Rate 59232.2 Statistical Tests for Genomic Data 59332.3 Statistical Modeling for Genomic Data 59632.4 Unsupervised Learning: Clustering 59832.5 Supervised Learning: Classification 599References 603

33 Statistical Methodologies for Analyzing Genomic DataFenghai Duan, Heping Zhang 60733.1 Second-Level Analysis of Microarray Data 60933.2 Third-Level Analysis of Microarray Data 61133.3 Fourth-Level Analysis of Microarray Data 61833.4 Final Remarks 618References 619

34 Statistical Methods in ProteomicsWeichuan Yu, Baolin Wu, Tao Huang, Xiaoye Li, Kenneth Williams,Hongyu Zhao 62334.1 Overview 62334.2 MS Data Preprocessing 62534.3 Feature Selection 62834.4 Sample Classification 63034.5 Random Forest: Joint Modelling of Feature Selection

arid Classification 63034.6 Protein/Peptide Identification 63334.7 Conclusion and Perspective 635References 636

35 Radial Basis Functions for Data Miningleyoung Shin, Amrit L. Goel 63935.1 Problem Statement 64035.2 RBF Model and Parameters 641

Co nte nts XXV

35.3 Design Algorithms 64235.4 Illustrative Example 64335.5 Diabetes Disease Classification 64535.6 Analysis of Gene Expression Data 64735.7 Concluding Remarks 648References 648

36 Data Mining Methods and ApplicationsKwok-Leung Tsui, Victoria Chen, Wei Y. Alp Aslandogan 65136.1 The KDD Process 65336.2 Handling Data 65436.3 Data Mining (DM) Models and Algorithms 65536.4 DM Research and Applications 66436.5 Concluding Remarks 667References 667

Part E Modeling and Simulation Methods

37 Bootstrap, Markov Chain and Estimating FunctionFeifang Hu 67337.1 Overview 67337.2 Classical Bootstrap 67537.3 Bootstrap Based an Estimating Equations 67837.4 Markov Chain Marginal Bootstrap 68137.5 Applications 68237.6 Discussion 684References 684

38 Random EffectsYi Li 68738.1 Overview 68738.2 Linear Mixed Models 68838.3 Generalized Linear Mixed Models 69038.4 Computing MLEs for GLMMs 69238.5 Special Topics: Testing Random Effects for Clustered Categorical

Data 69738.6 Discussion 701References 701

39 Cluster Randomized Trials: Design and AnalysisMirjam Moerbeek 70539.1 Cluster Randomized Trials 70639.2 Multilevel Regression Model and Mixed Effects ANOVA Model 70739.3 Optimal Allocation of Units 70939.4 The Effect of Adding Covariates 71239.5 Robustness Issues 713

XXVI Contents

39.6 Optimal Designs for the Intra-Class Correlation Coefficient 71539.7 Conclusions and Discussion 717References 717

40 A Two-Way Semilinear Model for Normalization and Analysisof Microarray DataPan Huang, Cun-Hui Zhang 71940.1 The Two-Way Semilinear Model 72040.2 Semiparametric M-Estimation in TW-SLM 72140.3 Extensions of the TW-SLM 72440.4 Variance Estimation and Inference for ß 72540.5 An Example and Simulation Studies 72740.6 Theoretical Results 73240.7 Concluding Remarks 734References 734

41 Latent Variable Models for Longitudinal Data with FlexibleMeasurement ScheduleHaiqun Lin 73741.1 Hierarchical Latent Variable Models for Longitudinal Data 73841.2 Latent Variable Models for Multidimensional Longitudinal Data 74141.3 Latent Class Mixed Model for Longitudinal Data 74341.4 Structural Equation Model with Latent Variables

for Longitudinal Data 74441.5 Concluding Remark: A Unified Multilevel Latent Variable Model 746References 747

42 Genetic Algorithms and Their ApplicationsMitsuo Gen 74942.1 Foundations of Genetic Algorithms 75042.2 Combinatorial Optimization Problems 75342.3 Network Design Problems 75742.4 Scheduling Problems 76142.5 Reliability Design Problem 76342.6 Logistic Network Problems 76642.7 Location and Allocation Problems 769References 772

43 Scan StatisticsJoseph Naus 77543.1 Overview 77543.2 Temporal Scenarios 77643.3 Higher Dimensional Scans 78443.4 Other Scan Statistics 786References 788

Co nte nts XXVI I

44 Condition-Based Failure PredictionShang-Kuo Yang 79144.1 Overview 79244.2 Kaiman Filtering 79444.3 Armature-Controlled DC Motor 79644.4 Simulation System 79744.5 Armature-Controlled DC Motor Experiment 80144.6 Conclusions 804References 804

45 Statistical Maintenance Modeling for Complex SystemsWenjian Li, Hoang Pham 80745.1 General Probabilistic Processes Description 80945.2 Nonrepairable Degraded Systems Reliability Modeling 81045.3 Repairable Degraded Systems Modeling 81945.4 Conclusions and Perspectives 83145.5 Appendix A 83145.6 Appendix B 832References 833

46 Statistical Models an MaintenanceToshio Nakagawa 83546.1 Time-Dependent Maintenance 83646.2 Number-Dependent Maintenance 83846.3 Amount-Dependent Maintenance 84246.4 Other Maintenance Models 843References 847

Part F Applications in Engineering Statistics

47 Risks and Assets PricingCharles S. Tapiero 85147.1 Risk and Asset Pricing 85347.2 Rational Expectations, Risk-Neutral Pricing and Asset Pricing 85747.3 Consumption Capital Asset Price Model and Stochastic Discount

Factor 86247.4 Bonds and Fixed-lncome Pricing 86547.5 Options 87247.6 Incomplete Markets and Implied Risk-Neutral Distributions 880References 898

48 Statistical Management and Modeling for Demand of Spare PartsEmilio Ferrari, Arrigo Pareschi, Alberto Regattieri, Alessandro Persona 90548.1 The Forecast Problem for Spare Parts 90548.2 Forecasting Methods 90948.3 The Applicability of Forecasting Methods to Spare-Parts Demands 911

XXVIII Contents

48.4 Prediction of Aircraft Spare Parts: A Case Study 91248.5 Poisson Models 91548.6 Models Based on the Binomial Distribution 91748.7 Extension of the Binomial Model Based on the Total Cost Function 92048.8 Weibull Extension 923References 928

49 Arithmetic and Geometric ProcessesKit-Nam F. Leung 93149.1 Two Special Monotone Processes 93449.2 Testing for Trends 93649.3 Estimating the Parameters 93849.4 Distinguishing a Renewal Process from an AP (or a GP) 93949.5 Estimating the Means and Variances 93949.6 Comparison of Estimators Using Simulation 94549.7 Real Data Analysis 94649.8 Optimal Replacement Policies Determined Using

Arithmetico-Geometric Processes 94749.9 Some Conclusions on the Applicability of an AP andlor a GP 95049.10 Concluding Remarks 95149.A Appendix 953References 954

50 Six SigmaFugee Tsung 95750.1 The DMAIC Methodology 96050.2 Design for Six Sigma 96550.3 Six Sigma Case Study 97050.4 Conclusion 971References 971

51 Multivariate Modeling with Copulas and Engineering ApplicationsJun Yan 97351.1 Copulas and Multivariate Distributions 97451.2 Some Commonly Used Copulas 97751.3 Statistical Inference 98151.4 Engineering Applications 98251.5 Conclusion 98751.A Appendix 987References 989

52 Queuing Theory Applications to Communication Systems:Control of Traffic Flows and Load BalancingPanlop Zeephongsekul, Anthony Bedford, James Broberg,Peter Dimopoulos, Zahir Tari 99152.1 Brief Review of Queueing Theory 99452.2 Multiple-Priority Dual Queue (MPDQ) 1000

Contents XXIX

52.3 Distributed Systems and Load Balancing 100552.4 Active Queue Management for TCP Traffic 101252.5 Conclusion 1020References 1020

53 Support Vector Machines for Data Modeling with SoftwareEngineering ApplicationsHojung Lim, Amrit L. Goel 102353.1 Overview 102353.2 Classification and Prediction in Software Engineering 102453.3 Support Vector Machines 102553.4 Linearly Separable Patterns 102653.5 Linear Classifier for Nonseparable Classes 102953.6 Nonlinear Classifiers 102953.7 SVM Nonlinear Regression 103253.8 SVM Hyperparameters 103353.9 SVM Flow Chart 103353.10 Module Classification 103453.11 Effort Prediction 103553.12 Concluding Remarks 1036References 1036

54 Optimal System DesignSuprasad V. Amari 103954.1 Optimal System Design 103954.2 Cost-Effective Designs 104754.3 Optimal Design Algorithms 105154.4 Hybrid Optimization Algorithms 1055References 1063

Acknowledgements 1065About the Authors 1067Detailed Contents 1085Subject Index 1113