Statistics in Engineering: A Practical approach

455 Pages·1994·8.833 MB·English

by  Andrew V. Metcalfe (auth.)

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
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Library of Congress Catalog Card Number: 94-70979
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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