CONTENTS 1. Statistical Inference ... 1 1.1 Introduction ... 1 1.2 Populations and Samples ... 2 1.3 Measurement Scales in Engineering ... 6 1.4 Frequency Distributions ... 7 1.5 Population Parameters, Sample Statistics, and Sampling Distributions ... 14 2. Probability Models ... 23 2.1 Introduction ... 23 2.2 Probability Models ... 24 2.3 Discrete Variables ... 26 2.4 Continuous Variables ... 35 2.5 Joint Distribution Functions ... 41 2.6 Some Useful Probability Theorems ... 46 3. Descriptive Statistics ... 47 3.1 Introduction ... 47 3.2 The Sample Mean and Standard Deviation ... 47 3.3 The Median and Quartiles : A Second Summarization of the Sample ... 54 3.4 Graphical Presentations of the Data ... 57 3.5 Informal Detection of Outliers ... 60 3.6 Alternative Measures of Location and Dispersion ... 61 3.7 Transformations to Normality, Variance Stabilizers ... 63 3.8 Computer Example ... 68 4. Inferential Statistics : Mean Values ... 69 4.1 Introduction ... 69 4.2 Sampling Distributions and Point Estimation of the Mean ... 69 4.3 Confidence Interval Estimates of the Population Mean ... 73 4.4 Sample Size Required to Estimate Mean to a Specified Precision ... 79 4.5 Hypothesis Testing for the Population Mean ... 82 4.6 Tolerance Limits ... 91 4.7 Comparing the Means of Two Populations ... 92 4.8 Computer Example ... 103 5. Analysis of Proportions and Categorical Data ... 105 5.1 Introduction ... 105 5.2 Point Estimation of a Proportion ... 106 5.3 Confidence Intervals for a Proportion ... 107 5.4 Determination of Sample Size to Attain a Specified Precision ... 109 5.5 Hypothesis Testing for a Single Proportion ... 111 5.6 Comparing the Proportions of Two Populations ... 118 5.7 Categorical Data ... 128 5.8 Computer Examples ... 133 6. Variability ... 135 6.1 Introduction ... 135 6.2 Sampling Distributions and Point Estimation of the Variance ... 135 6.3 Confidence Interval Estimates of σ ... 136 6.4 Sample Size Required to Estimate σ² to a Specified Precision ... 137 6.5 Comparing Standard Deviations, σ₁ and σ₂, of Two Populations ... 138 6.6 Comparing the New Variance, \σ 1 2 , with the Standard Variance, \σ 0 2 ... 139 7 Analysis of Variance and Experimental Design Ⅰ ... 144 7.1 Introduction ... 144 7.2 OneFactor Experiments and ANOVA ... 144 7.3 Multiple Comparisons ... 148 7.4 Partitioning of Variability / ANOVA Table ... 153 7.5 Computational Formulas for the OneFactor ANOVA ... 154 7.6 Mathematical Model for the OneFactor ANOVA ... 155 7.7 TwoFactor Experiments and ANOVA, One Observation per Cell ... 156 7.8 TwoFactor Experiment and ANOVA, n Observatins per Cell ... 161 7.9 Computer Examples ... 166 8. Outliers ... 171 8.1 Introduction ... 171 8.2 Single outlier, Univariate Sample ... 172 8.3 Multiple Outliers, Univariate Sample ... 174 9. Extreme Value Analysis ... 180 9.1 Introduction ... 180 9.2 Exceedances ... 181 9.3 Return Periods ... 182 9.4 Characteristic Values ... 184 9.5 Record Values ... 186 9.6 Distribution of Maxima ... 186 9.7 Distribution of Minima ... 188 9.8 Joint Distribution of Two Order Statistics ... 190 10. Sensitivity Testing ... 192 10.1 Introduction ... 192 10.2 Karber Method of Analysis ... 193 10.3 Graphical (Probit) Method of Analysis ... 196 10.4 UpandDown Method of Analysis ... 200 11. Regression and Correlation ... 205 11.1 Introduction ... 205 11.2 Simple Linear Regression ... 205 11.3 Partitioning of Variability / ANOVA Table ... 218 11.4 Polynomial Regression ... 222 11.5 Multiple Regression ... 229 11.6 Stepwise Regression ... 234 11.7 Detection of Outliers and Influential Observations ... 243 12. Experimental Design Ⅱ ... 249 12.1 Introduction ... 249 12.2 Three Factors and Latin Square Designs ... 250 12.3 \ 2 P 2 P Factorial Experiments ... 255 13. Control Charts ... 259 13.1 Introduction ... 259 13.2 Control Charts for the Mean μ Based on X ‾ ... 260 13.3 Control Charts for the Variability σ Based on S and R ... 264 13.4 Sample Size Considerations ... 265 13.5 Control Chart for Fraction Defective ... 268 13.6 Control Chart for Number of Defects ... 270 13.7 CUSUM Charts ... 271 13.8 Acceptance Sampling ... 273 14. Reliability and Lifetime ... 276 14.1 Simple Systems ... 276 14.2 Complex Systems ... 277 14.3 System Lifetime ... 284 Appendix ... 289 Bibliography ... 305 Index ... 307