"vii© 2024 SAE InternationalContentsPreface xvAcronyms xviNomenclature xxviiiIntroduction xxxiC H A P T E R 7Tolerancing for Assembly and Manufacturing 17.1. Tolerance Design 17.1.1. Analytic Methods 27.1.2.

Linear Dimensional Chain 47.1.3. Vector-Loop Model 57.1.4. Tolerance Analysis Example: One-Way Clutch Assembly 67.1.

5. Tolerance Allocation 77.1.6. Average, Variance, Skewness, and Kurtosis 87.2. Dimensional Management 87.2.

1. Cost Function for Part Fabrication 97.2.2. Fabrication Capability 117.2.3. Control Plan Methodology 127.

3. Deterministic Tolerance Design 137.3.1. Worst-Limit Method 137.3.2. One-Way Clutch Example by DOEs 147.

3.3. Deterministic Tolerance Synthesis 167.3.4. Loss Function by Deterministic Tolerance Design 167.4. Statistical Tolerance Design by RSS Method 207.

4.1. Tolerance Analysis Using RSS Formulae 207.4.2. Modified Root-Mean-Squared Method 237.4.3.

Tolerance Allocation by Machining Capability 267.4.4. Tolerance Allocation by Cost-Benefit Equation 287.4.5. Nonlinear Case: Capability Study on One-Way Clutch 31Contentsviii7.5.

Statistical Tolerance Design by Monte Carlo Simulations 347.5.1. Concerns of Dimensional Control over Normality Assumption 347.5.2. Monte Carlo Simulations 357.5.

3. Characterizing Dimensions Using Statistical Distributions 367.5.4. Example: Actuating Mechanism 397.5.5. Example: Electric Circuits 407.

5.6. Histogram 417.6. Mean Shift 427.6.1. Tolerance Due to Mean Shift 437.

6.2. Mean Shift Due to Tool Wear Using Monte Carlo Simulation 447.7. Hole and Shaft Effects 457.7.1. International Standards for Holes and Shafts 467.

7.2. Virtual Condition 477.7.3. Resultant Condition 487.7.4.

Equal Bilateral Tolerance of Pin and Hole 497.7.5. Tolerance Stack-Up with Material Conditions 507.8. Identification of Dimensions by Method of Moments Estimator (MME) 527.8.1.

Moment-Generating Functions 527.8.2. Blend of Method of Moments and Monte Carlo Simulation 537.9. Identification of Dimensions by MLE 537.9.1.

Log-Likelihood Function and Likelihood Equations for Normal Distribution 547.9.2. Log-Likelihood Function and Likelihood Equations for Weibull Distribution 557.9.3. Identification of Dimensions Using Minitab 567.10.

Finite Element Tolerance Analysis with Skin Model Shapes 567.11. Homogenous Transformations for Tolerance Analysis 587.11.1. Homogeneous Transformations in 3D Space 587.11.2.

Translational and Rotational Matrices for Both Kinematic and ToleranceVariations 607.11.3. Stochastic Contact Variations 657.12. Perturbation Analysis and Direct Linearization Method (DLM) 697.13. T-Map Algorithm 727.

14. Tolerance Design Procedure and Software 727.14.1. Variation Simulation Analysis (VSA) 737.14.2. CETOL 6σ 747.

14.3. 3DCS 757.14.4. ANATOLEFLEX 757.15. Overview of GD&T 757.

15.1. Datum 767.15.2. Dimensions 77Contents ix7.15.3.

Tolerancing 787.15.4. Material Conditions 797.15.5. Surface Textures 797.15.

6. Units 80References 81Problems 85C H A P T E R 8Lognormal Transformations in DOE 878.1. Reliability DOEs 878.1.1. Logarithmic Transformations 888.1.

2. Data Types 908.1.3. Data Censoring 908.1.4. Type I Censoring 918.

2. Lognormal Distribution 928.2.1. Lognormal PDF 928.2.2. Lognormal CDF 938.

2.3. Characteristics of Lognormal Distribution 948.2.4. Multiplicative Property of Two Lognormal Distributions 948.2.5.

Curve Fitting to the Lognormally Distributed Data 958.2.6. Standardized Residuals for Lognormal Distribution 958.3. DOE-LN by Means of DOE-t or DOE-F 958.3.1.

Logarithmic Transformation 968.3.2. Example: Tool Life Subjected to Turning Operations 968.4. Maximum-Likelihood Method for DOE-LN 988.4.1.

Coupling between Process Acceleration Model and Lognormal DistributionModel 998.4.2. MLE 998.4.3. Null Hypothesis for Maximum-Likelihood Method 1008.4.

4. Maximum-Likelihood Method with Test-to-Failure, Suspended, andInterval Data 1018.4.5. Maximum-Likelihood Regression with Test-to-Failure and Right-Suspended Data 1038.4.6. Standardized Residuals for Lognormal Distribution 1048.

5. Statistical Inference Using LR by χ2 Distribution 1048.5.1. Statistical Inference by χ2 Distribution 1058.5.2. Acceptance Sampling Plans by Chi-Squared Statistic 1078.

6. Reduction in Product Variability 1098.6.1. Robust Engineering Design 1108.6.2. Logarithmic Transformation of Sample Variances for Variability Study 1108.

6.3. Noises 112Contentsx8.7. MLE for DOE-LN Parameters 1128.7.1. Lognormal Distribution Solution by DOE-t 1138.

7.2. Lognormal Distribution Solution by MLE 1138.8. Example: Insulation Aging of Electric Motor Windings 1158.8.1. Insulation Aging of Electric Motor Windings via DOE-t 1168.

8.2. Insulation Aging of Electric Motor Windings via MLE 1188.9. MLE for DOE-LN Parameters with Incomplete Data 1208.10. Alternate Viable Transformations 1228.10.

1. Individual Distribution Identification 1228.10.2. Box-Cox Transformations 1268.10.3. Adjustment to ln or log Transformation 1278.

10.4. Y 1/2 Transformation 1278.10.5. Sin −1(Yδ) Transformation 1278.10.6.

Sinh Transformation 1298.10.7. Sinh-Arcsinh Transformation 1298.10.8. Signal-to-Noise Ratio 1298.11.

Finite Lognormal Mixture Distribution 1318.12. Statistical Inference from Fisher Information 1328.12.1. FIM for DOEs in Lognormal Distribution 1348.12.2.

Bounds on Estimated Lognormal Parameters by FIM 1368.12.3. Bounds on Estimated Lognormal Parameter σy by FIM 1378.12.4. Confidence Bounds on Function lnLln() 1388.12.

5. Bounds on Estimated Functional Coefficients and Parameters 1388.12.6. Bounds on Estimated Model Parameter σy for Ball Grid Array Packaging 140References 140Problems 142C H A P T E R 9Weibull Reliability and DOEs 1439.1. Product Reliability as Measured by Noncompliance 1439.1.

1. Hazard Rate 1449.1.2. Reliability and Unreliability 1449.2. Product Reliability Growth Based on the Weibull Distributions 1459.2.

1. Shape Factor β 1479.2.2. Scale Factor η 1499.2.3. Guaranteed Value t0 1499.

2.4. Mean and Standard Deviation 1549.2.5. Median and Mode 1549.2.6.

Two-Parameter Weibull Distribution 1559.2.7. Standard Weibull Distribution 155Contents xi9.2.8. SEV Distribution 1559.2.

9. Standard SEV Distribution 1579.2.10. Largest Extreme-Value Distribution 1589.3. Reliability Demonstration Testing (RDT) 1589.3.

1. Statistics of RDT 1589.3.2. Substantiation Test 1599.3.3. Cumulative Fault Frequency (CFF) 1609.

3.4. Weibull RDT 1609.3.5. Reliability, Confidence, and Sample Size Based on the Weibull Distribution 1639.3.6.

Decision-Making Rule with Statistical Thinking 1679.4. Calculating Weibull Parameters by the Maximum-Likelihood Method 1679.4.1. MLE of Weibull Parameters with Test-to-Failure Data 1679.4.2.

MLE of Weibull Parameters with Incomplete Data 1699.4.3. MLE of Weibull Parameters with Interval Data 1709.4.4. Unbiased Estimate of Shape Factor 1719.5.

Confidence Level for Product Life Prediction 1729.5.1. Tolerance Interval 1729.5.2. Lower and Upper Bounds of Lifetime by MLE 1739.5.

3. Lower Bound of Lifetime 1759.5.4. Upper Bound of Lifetime 1769.5.5. Upper and Lower Bounds of Estimated Parameters 1779.

5.6. CI for the Predicted Lifetime by the Bootstrap Method 1779.6. Estimating Weibull Parameters by Method of Moments 1789.7. Assessing Weibull Parameters by MRR 1809.7.

1. Estimating Weibull Parameters with MRR 1819.7.2. MRR (Confidence = 50%) 1829.7.3. Weibull Plot 1839.

7.4. Upper and Lower Limits of General Ranking 1859.7.5. Comparison of the Estimators 1929.8. Reliability DOE-W 1929.

8.1. Coupling between DOE Model and Weibull Distribution 1939.8.2. Finite Mixture Distribution in Two-Parameter Weibull Statistics 1939.8.3.

MLE for a Homogeneous Two-Parameter Weibull Distribution 1959.8.4. Hypotheses in DOEs 1979.8.5. LR Test 1989.8.

6. Standardized Residual for Weibull Distribution 1989.9. Product Life Prediction Examples Using DOE-W 1999.9.1. Product Life Prediction Using 2V5-1 Design with Right-Suspended Data 1999.9.

2. Product Life Prediction for Design with Right-Censored Data and Interval Data 203Contentsxii9.10. Multi-Objective Optimization with Pareto Optimality Based on DOE-W 2059.10.1. Central Composite Design for Evaluating Product Lifewith Right-Censored Data 2069.10.

2. ANOVA for Examining Flow Rate 2089.10.3. Pareto Frontier for Design Optimization 2089.11. Exponential Distribution 2099.12.

MLE of Hazard Rate of Exponential Distribution 2129.12.1. MLE of λ with No Censored Data 2129.12.2. MLE of Hazard Rate λ with Type I Right-Censored Data 2139.12.

3. Standardized Residual for Exponential Distribution 2149.12.4. CIs for the Exponential Hazard Rate 2159.12.5. Product Life Prediction Based on Exponential Distribution 215References 216Problems 218C H A P T E R 1 0Product Reliability Growth 22110.

1. DFR Tests 22110.1.1. Compliance Tests 22210.1.2. Production Tests 22410.

1.3. Acceptance Test Commissioning Measurements 22410.1.4. Service and Repair Tests 22410.1.5.

Regression Tests 22410.2. Kaplan-Meier Product Limit Estimator 22510.3. RG Analysis 22810.3.1. Product Failure Rate 22810.

3.2. RG: Homogeneous Poisson Process (HPP) 22910.3.3. RG: Non-HPP (NHPP) 23210.3.4.

RG-Weibull Density Function 23510.3.5. Effectiveness of a Corrective Action 23510.3.6. RG Management 23610.4.

Qualitative Accelerated Life Tests 23610.4.1. FMVT 23710.4.2. FSLT 23710.4.

3. ESS Test 23710.4.4. HALT 23810.4.5. HASS 23910.

4.6. SSALT 23910.4.7. Mechanical Components 24010.4.8.

Electronic Components 240Contents xiii10.5. Cumulative Exposure Model for Stepwise Accelerated Life Test (SALT) 24210.5.1. Material Transformations 24210.5.2.

SALTs 24410.5.3. Cumulative Exposure Model for SALTs with One Stress Factor 24610.6. SSALTs by Weibull Statistics 24810.6.1.

Stepwise Loading 24910.6.2. Weibull Statistics for Accelerated Life Tests 25010.6.3. Load-Life Relationship 25210.6.

4. MLE of Parameters 25210.6.5. Estimating Reliability and Associated Confidence Bounds: WeibullStatistics 25410.6.6. Conditional Reliability: Weibull Statistics 25410.

7. SALT in Lognormal Distribution 25410.7.1. MLE for Lognormal Distrib.