Table Of Content

Statistics in Engineering CHAPMAN & HALL STATISTICS TEXTBOOK SERIES Editors: Dr Chris Chatfield Professor Jim V. Zidek Reader in Statistics Department of Statistics School of Mathematical Sciences University of British Columbia, Canada University of Bath, UK OTHER TITLES IN THE SERIES INCLUDE Practical Statistics for Medical Research An Introduction to Generalized Linear D. G. Altman Models Interpreting Data A.J. Dobson A. J. B. Anderson Multivariate Analysis of Variance and Repeated Measures Statistical Methods for SPC and TQM D. J. Hand and C. C. Taylor D. Bissell The Theory of Linear Models Statistics in Research and Development Second edition B. Jorgensen R. Caulcutt Statistical Theory Fourth edition The Analysis of Time Series Fourth edition B. Lindgren C. Chatfield Essential Statistics Second edition Problem Solving - A Statistician's Guide D. G. Rees C. Chatfield Decision Analysis: A Bayesian Approach Statistics for Technology J. Q. Smith Third edition C. Chatfield Applied Nonparametric Statistical Methods Introduction to Multivariate Analysis Second edition C. Chatfield and A. J. Collins P. Sprent Modelling Binary Data Elementary Applications of Probability D. Collett Theory Modelling Survival Data in Medical Research H. C. Tuckwell D. Collett Statistical Process Control: Theory and Applied Statistics practice D. R. Cox and E. 1. Snell Third edition Statistical Analysis of Reliability Data G. B. Wetherill and D. W. Brown M. J. Crowder, A. C. Kimber, T. J. Sweeting and R. L. Smith Full itiformation on the complete range of Chapman & Hall statistics books is available from the publishers. Statistics in Engineering .A practical approach Andrew V. Metcalfe Department of Engineering Mathematics, University of Newcastle, Newcastle upon Tyne, UK Springer-Science+Business Media, B.Y. First edition 1994 © 1994 Andrew V. Metcalfe Originally published by Chapman & Hall in 1994. Typeset in 10/12 Times by Thomson Press (India) Ltd, New Delhi ISBN 978-0-412-49220-4 ISBN 978-1-4899-6623-0 (eBook) DOI 10.1007/978-1-4899-6623-0 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A catalogue record for this book is available from the British Library Library of Congress Catalog Card Number: 94-70979 @ Printed on permanent acid-free text paper, manufactured in accordance with ANSIjNISO Z39 .48-1992 and ANSIjNISO Z39.48-1984 (Permanence of Paper). Contents Preface ix 1 Why understand 'statistics'? 1 2 Probability in engineering decisions 4 2.1 Introduction 4 2.2 Defining probability 7 2.3 The addition rule of probability 13 2.4 Conditional probability 15 2.5 Arrangements and choices 21 2.6 Decision trees 23 2.7 Summary 25 Exercises 26 3 Justifying engineering decisions 32 3.1 Presenting data 32 3.2 Summarizing data 43 3.3 Fatigue damage 54 3.4 Shape of distributions 54 3.5 Summary 57 Exercises 59 4 Modelling variability 63 4.1 Discrete probability distributions 63 4.2 Continuous probability distributions 75 4.3 Modelling rainfall 106 4.4 Summary 109 Exercises 113 5 Combining variables 121 5.1 Introduction 121 5.2 Sample covariance and correlation 125 5.3 Joint probability distributions 128 5.4 Population covariance and correlation 135 vi Contents 5.5 Linear combinations of random variables 136 5.6 Distribution of the sample mean 141 5.7 Statistical process control charts 146 5.8 Nonlinear functions of random variables 153 5.9 Summary 155 Exercises 156 6 Precision of estimates 161 6.1 Precision of means 161 6.2 Precision of standard deviations 165 6.3 Comparing standard deviations 166 6.4 Comparing means 167 6.5 Sample size 174 6.6 Proportions 177 6.7 Random breath tests? 183 6.8 Summary 185 Exercises 187 7 Asset management plan 193 7.1 Background 193 7.2 Statistical issues 194 7.3 Sampling scheme 196 7.4 Unit cost formulae 198 7.5 Zone costs 200 7.6 The stratum cost 201 7.7 Total cost of local distribution network 203 7.8 Discussion 205 7.9 Summary 206 8 Making predictions from one variable 208 8.1 Linear regression 208 8.2 Intrinsically linear models 224 8.3 Conditional distributions 226 8.4 Relationship between correlation and regression 234 8.5 Fitting straight lines when both variables are subject to error 236 8.6 Calibration lines 239 8.7 Summary 241 Exercises 243 9 Making predictions from several explanatory variables 248 9.1 Regression on two explanatory variables 248 9.2 Multiple regression model 254 9.3 Categorical variables 263 9.4 Chrome plating of rods for hydraulic machinery 267 Contents vii 9.5 Summary 273 Exercises 276 10 Design of experiments 279 10.1 Evolutionary operation 280 10.2 More than two factors 287 10.3 Comparing several means 300 10.4 Experimental design for welded joints 310 10.5 Summary 316 Exercises 317 11 Modelling variability in time and space 323 11.1 Evaluation of mini-roundabouts as a road safety measure 323 11.2 Predicting short-term flood risk 341 11.3 Spectral analysis for design of offshore structures 351 11.4 Endnote 358 Appendix A: Mathematical explanations of key results 359 Al Derivation of Poisson distribution 359 A2 Central limit theorem 360 A3 Derivation of EVGI distribution 366 A4 Estimated variance of ratio estimator 367 AS Multiple regression model 368 A6 DuMouchel's algorithm 379 Appendix B: Reference guide 381 Bl Notation 381 B2 Glossary 383 B3 Problem-solving guide 393 B4 Suggested short course 397 Appendix C: Summary of MINITA B commands used in text 399 Appendix D: Data sets 409 Appendix E: Statistical tables 422 Appendix F: Answers to selected exercises 429 References 433 Software references 438 Index 439 Preface Two common features of many modern engineering projects are a need for realistic modelling of random phenomena and a requirement that this be achieved within tight budgets and deadlines. This book is written for engineering students and professional engineers, and also for students of mathematics, statistics, and operations research who may be members of teams working on such projects. It has been my intention to motivate readers to use the methods I describe by demonstrating they are an essential part of practical problem-solving and decision-making. Examples range from oil rigs to designs of prosthetic heart valves. There is an emphasis on the valuable technique of multiple regression, which involves describing the variation of one 'dependent' variable in terms of several 'explanatory' variables. I have used this instead of algebraically equi valent but more formal models whenever possible. The advantages are simplicity and the availability of multiple regression routines in popular spreadsheet soft ware. The more formal models have advantages for complex experimental designs but these are well covered in more advanced texts. Many industrial experiments are based on relatively simple 'factorial designs' augmented with some extra runs when necessary. These are naturally described in terms of multiple regression, and the experimental design package DEX, written for the statistical novice, adopts this approach. I am grateful for permission to reference DEX and quote examples from the users' guide. There are many rather more specialist statistical packages, and I have chosen to refer to MINITA B at various points in the text (MINITAB is a registered trademark of Minitab Inc.). It is particularly easy to use, widely available, and I find its multiple regression routine one of the best I have used for standard applications. I am grateful to Minitab Inc. for permission to reference MINITA B throughout the book, and for the assistance provided under Minitab's Author Assistance Program. I have assumed that the reader is familiar with elementary algebra, and has had some acquaintance with simple calculus. Some of the appendices and exercises are slightly more mathematical than the main text, but these can be passed over by those without the time or inclination to follow them through. A list of notation is given in Appendix Bl. A suggested short course, for a reader in a hurry, is given at the end of the problem-solving guide in Appendix B4. I am grateful to many people for their contributions, especially my industrial contacts and the Master of Science graduates from our Department who have x Preface so clearly shown the value of statistical methods during their placements with companies. I have tried to acknowledge their work explicitly, but requests for commercial confidentiality have sometimes prevented this. I wish to thank Alan Jeffrey for encouraging me to submit the proposal for this book; Nicki Dennis of Chapman & Hall for her enthusiasm about it; and Tony Greenfield for many helpful comments during the first draft, several practical industrial examples, a case study, and his overall support for the project. Richard Leigh made further useful suggestions during his thorough final editing. I have greatly appreciated the editorial and production services provided by Lynne Maddock and other staff at Chapman & Hall. However, I am responsible for any errors and obscurities. It is also a pleasure to thank Mandy Knox for cheerfully typing the manuscript with great efficiency. Andrew Metcalfe Department of Engineering Mathematics University of Newcastle upon Tyne