P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics THOMAS P. RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION iii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 xx P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics i P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 ii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics THOMAS P. RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION iii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Copyright C 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com Wiley Bicentennial Logo: Richard J. Pacifico Library of Congress Cataloging-in-Publication Data: Ryan, Thomas P., 1945– Modern engineering statistics / Thomas P. Ryan. p. cm. Includes bibliographical references and index. ISBN 978-0-470-08187-7 1. Engineering–Statistical methods. I. Title. TA340.R93 2007 620.0072–dc22 20060521558 Printed in the United States of America 10987654321 iv P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 Contents Preface xvii 1. Methods of Collecting and Presenting Data 1 1.1 Observational Data and Data from Designed Experiments, 3 1.2 Populations and Samples, 5 1.3 Variables, 6 1.4 Methods of Displaying Small Data Sets, 7 1.4.1 Stem-and-Leaf Display, 8 1.4.2 Time Sequence Plot and Control Chart, 9 1.4.3 Lag Plot, 11 1.4.4 Scatter Plot, 12 1.4.5 Digidot Plot, 14 1.4.6 Dotplot, 14 1.5 Methods of Displaying Large Data Sets, 16 1.5.1 Histogram, 16 1.5.2 Boxplot, 20 1.6 Outliers, 22 1.7 Other Methods, 22 1.8 Extremely Large Data Sets: Data Mining, 23 1.9 Graphical Methods: Recommendations, 23 1.10 Summary, 24 References, 24 Exercises, 25 2. Measures of Location and Dispersion 45 2.1 Estimating Location Parameters, 46 2.2 Estimating Dispersion Parameters, 50 2.3 Estimating Parameters from Grouped Data, 55 v P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 vi contents 2.4 Estimates from a Boxplot, 57 2.5 Computing Sample Statistics with MINITAB, 58 2.6 Summary, 58 Reference, 58 Exercises, 58 3. Probability and Common Probability Distributions 68 3.1 Probability: From the Ethereal to the Concrete, 68 3.1.1 Manufacturing Applications, 70 3.2 Probability Concepts and Rules, 70 3.2.1 Extension to Multiple Events, 73 3.2.1.1 Law of Total Probability and Bayes’ Theorem, 74 3.3 Common Discrete Distributions, 76 3.3.1 Expected Value and Variance, 78 3.3.2 Binomial Distribution, 80 3.3.2.1 Testing for the Appropriateness of the Binomial Model, 86 3.3.3 Hypergeometric Distribution, 87 3.3.4 Poisson Distribution, 88 3.3.4.1 Testing for the Appropriateness of the Poisson Model, 90 3.3.5 Geometric Distribution, 91 3.4 Common Continuous Distributions, 92 3.4.1 Expected Value and Variance, 92 3.4.2 Determining Probabilities for Continuous Random Variables, 92 3.4.3 Normal Distribution, 93 3.4.3.1 Software-Aided Normal Probability Computations, 97 3.4.3.2 Testing the Normality Assumption, 97 3.4.4 t-Distribution, 97 3.4.5 Gamma Distribution, 100 3.4.5.1 Chi-Square Distribution, 100 3.4.5.2 Exponential Distribution, 101 3.4.6 Weibull Distribution, 102 3.4.7 Smallest Extreme Value Distribution, 103 3.4.8 Lognormal Distribution, 104 3.4.9 F Distribution, 104 3.5 General Distribution Fitting, 106 3.6 How to Select a Distribution, 107 3.7 Summary, 108 References, 109 Exercises, 109 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 contents vii 4. Point Estimation 121 4.1 Point Estimators and Point Estimates, 121 4.2 Desirable Properties of Point Estimators, 121 4.2.1 Unbiasedness and Consistency, 121 4.2.2 Minimum Variance, 122 4.2.3 Estimators Whose Properties Depend on the Assumed Distribution, 124 4.2.4 Comparing Biased and Unbiased Estimators, 124 4.3 Distributions of Sampling Statistics, 125 4.3.1 Central Limit Theorem, 126 4.3.1.1 Illustration of Central Limit Theorem, 126 4.3.2 Statistics with Nonnormal Sampling Distributions, 128 4.4 Methods of Obtaining Estimators, 128 4.4.1 Method of Maximum Likelihood, 128 4.4.2 Method of Moments, 130 4.4.3 Method of Least Squares, 131 4.5 Estimating σθˆ, 132 4.6 Estimating Parameters Without Data, 133 4.7 Summary, 133 References, 134 Exercises, 134 5. Confidence Intervals and Hypothesis Tests—One Sample 140 5.1 Confidence Interval for µ: Normal Distribution, σ Not Estimated from Sample Data, 140 5.1.1 Sample Size Determination, 142 5.1.2 Interpretation and Use, 143 5.1.3 General Form of Confidence Intervals, 145 5.2 Confidence Interval for µ: Normal Distribution, σ Estimated from Sample Data, 146 5.2.1 Sample Size Determination, 146 5.3 Hypothesis Tests for µ: Using Z and t, 147 5.3.1 Null Hypotheses Always False?, 147 5.3.2 Basic Hypothesis Testing Concepts, 148 5.3.3 Two-Sided Hypothesis Tests Vis-`a-Vis Confidence Intervals, 152 5.3.4 One-Sided Hypothesis Tests Vis-`a-Vis One-Sided Confidence Intervals, 153 5.3.5 Relationships When the t-Distribution is Used, 155 5.3.6 When to Use t or Z (or Neither)?, 155 5.3.7 Additional Example, 156 5.4 Confidence Intervals and Hypothesis Tests for a Proportion, 157 5.4.1 Approximate Versus Exact Confidence Interval for a Proportion, 158 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 viii contents 5.5 Confidence Intervals and Hypothesis Tests for σ 2 and σ , 161 5.5.1 Hypothesis Tests for σ 2 and σ , 163 5.6 Confidence Intervals and Hypothesis Tests for the Poisson Mean, 164 5.7 Confidence Intervals and Hypothesis Tests When Standard Error Expressions are Not Available, 166 5.8 Type I and Type II Errors, 168 5.8.1 p-Values, 170 5.8.2 Trade-off Between Error Risks, 172 5.9 Practical Significance and Narrow Intervals: The Role of n, 172 5.10 Other Types of Confidence Intervals, 173 5.11 Abstract of Main Procedures, 174 5.12 Summary, 175 Appendix: Derivation, 176 References, 176 Exercises, 177 6. Confidence Intervals and Hypothesis Tests—Two Samples 189 6.1 Confidence Intervals and Hypothesis Tests for Means: Independent Samples, 189 6.1.1 Using Z, 190 6.1.2 Using t, 192 6.1.3 Using Neither t nor Z, 197 6.2 Confidence Intervals and Hypothesis Tests for Means: Dependent Samples, 197 6.3 Confidence Intervals and Hypothesis Tests for Two Proportions, 200 6.3.1 Confidence Interval, 202 6.4 Confidence Intervals and Hypothesis Tests for Two Variances, 202 6.5 Abstract of Procedures, 204 6.6 Summary, 205 References, 205 Exercises, 205 7. Tolerance Intervals and Prediction Intervals 214 7.1 Tolerance Intervals: Normality Assumed, 215 7.1.1 Two-Sided Interval, 216 7.1.1.1 Approximations, 217 7.1.2 Two-Sided Interval, Possibly Unequal Tails, 218 7.1.3 One-Sided Bound, 218 7.2 Tolerance Intervals and Six Sigma, 219 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 contents ix 7.3 Distribution-Free Tolerance Intervals, 219 7.3.1 Determining Sample Size, 221 7.4 Prediction Intervals, 221 7.4.1 Known Parameters, 222 7.4.2 Unknown Parameters with Normality Assumed (Single Observation), 223 7.4.2.1 Sensitivity to Nonnormality, 223 7.4.2.2 Width of the Interval, 224 7.4.3 Nonnormal Distributions: Single Observation, 224 7.4.4 Nonnormal Distributions: Number of Failures, 225 7.4.5 Prediction Intervals for Multiple Future Observations, 225 7.4.6 One-Sided Prediction Bounds, 225 7.4.6.1 One-Sided Prediction Bounds for Certain Discrete Distributions, 226 7.4.7 Distribution-Free Prediction Intervals, 226 7.5 Choice Between Intervals, 227 7.6 Summary, 227 References, 228 Exercises, 229 8.