Statistics in Research and Development

483 Pages·1991·8.391 MB·English

by  Roland Caulcutt (auth.)

Statistics in Research
and Development
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Further information of the complete range of Chapman & Hall statistics books is
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Statistics in Research
and Development
Second edition
Roland Caulcutt
BP Chemicals Lecturer
University of Bradford
IU!ll
Springer-Science+Business Media, B.Y.
First edition 1983
Second edition 1991
© 1983, 1991 Roland CauIcutt
Originally published by Chapman and Hall in 1991.
Softcover reprint ofthe hardcover 2nd edition 1991
Typeset in 10/12 Times by Excel Typesetters Co. Hong Kong.
ISBN 978-0-412-35890-6 ISBN 978-1-4899-2943-3 (eBook)
DOI 10.1007/978-1-4899-2943-3
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British Library Cataloguing in Publication Data
Cauicutt, Roland
Statistics in research and development. - 2nd ed.
1. Industrial research. Applications of statistical
methods
I. Title
607.2
Library of Congress Cataloging-in-Publication Data
Available
Contents
Preface x
1 What is statistics? 1
2 Describing the sampie 5
2.1 Introduction 5
2.2 Variability in plant performance 5
2.3 Frequency distributions 7
2.4 Measures of location and spread 13
2.5 Cumulative frequency distributions 19
2.6 The seven basic tools 20
2.7 Summary 22
Problems 24
3 Describing the population 27
3.1 Introduction 27
3.2 Probability distributions 28
3.3 The Poisson distribution 29
3.4 The normal distribution 32
3.5 Normal proba bility graph paper 40
3.6 Process capability 43
3.7 Summary 47
Problems 48
4 Testing and estimation: one sampie 51
4.1 Introduction 51
4.2 Has the yield increased? 51
4.3 The significance testing procedure 56
4.4 What is the new mean yield? 58
4.5 Is such a large sampie really necessary? 61
4.6 Statistical significance and practical importance 63
4.7 Summary 64
Problems 64
Contents
VI
5 Testing and estimation: two sampies 66
5.1 Introduction 66
5.2 Comparing the precision of two test methods 66
5.3 Comparing the bias of two test methods 70
5.4 Does the product deteriorate in storage? 72
5.5 A much better experiment 76
5.6 Summary 79
Problems 79
6 Testing and estimation: qualitative data 81
6.1 Introduction 81
6.2 Does the additive affect the taste? 81
6.3 Where do statistical tables come from? 84
6.4 Estimating percentage rejects 87
6.5 Has the additive been effective? 89
6.6 Significance tests with percentages 91
6.7 The binomial distribution 95
6.8 Summary 97
Problems 97
7 Testing and estimation: assumptions 100
7.1 Introduction 100
7.2 Estimating variability 100
7.3 Estimating variability for at-test 102
7.4 Assumptions underlying significance tests - randomness 106
7.5 Assumptions underlying significance tests - the normal
distribution 108
7.6 Assumptions underlying significance tests - sampie size 109
7.7 Outliers 110
7.8 Summary 114
Problems 114
8 Statistical process control 117
8.1 Introduction 117
8.2 A control chart for the me an yield 117
8.3 How quickly will change be detected? 121
8.4 Increasing the sensitivity of the control chart 122
8.5 Improving the control chart by averaging 128
8.6 Moving me an charts 132
8.7 Assumptions underlying control charts 138
8.8 Summary 144
Problems 144
Contents
Vll
9 Detecting process changes 146
9.1 Introduction 146
9.2 Examining the previous 50 batches 146
9.3 Significance testing 151
9.4 Interpretation 156
9.5 Has the process variability increased? 159
9.6 The use of cusums in statistical process control 163
9.7 Scientific method 165
9.8 Some definitions 168
9.9 Summary 170
Problem 170
10 Investigating the process - an experiment 172
10.1 Introduction 172
10.2 The plant manager's experiment 172
10.3 Selecting the first independent variable 174
10.4 Is the correlation due to chance? 179
10.5 Fitting the best straight line 180
10.6 Goodness of fit 182
10.7 The 'tme' regression equation 185
10.8 Accuracy of prediction 186
10.9 An alternative equation 189
10.10 Summary 190
Problems 190
11 Why was the experiment not successful? 196
11.1 Introduction 196
11.2 An equation with two independent variables 196
11.3 Multiple regression analysis on a computer 199
11.4 An alternative multiple regression equation 205
11.5 Graphical representation of a multiple regression equation 207
11.6 Non-linear relationships 208
11.7 Interactions between independent variables 210
11.8 Summary 211
Problems 212
12 Some simple but etTective experiments 218
12.1 Introduction 218
12.2 The classical experiment (one variable at a time) 218
12.3 Factorial experiments 221
12.4 Estimation of main effects and interaction from the results
of a 22 experiment 223
12.5 Distinguishing between real and chance effects 225
12.6 The use of multiple regression with a 22 experiment 231
viii Contents
12.7 A 23 factorial experiment 237
12.8 The use of multiple regression with a 23 experiment 240
12.9 Two replicates of a 23 factorial experiment 243
12.10 More regression analysis 247
12.11 Factorial experiments made simple 250
12.12 Summary 254
Problems 254
13 Adapting the simple experiments 258
13.1 Introduction 258
13.2 The design matrix 258
13.3 Half replicates of a 2n factorial design 260
13.4 Quarter replicates of a 2n factorial design 266
13.5 A useful method for selecting a fraction of a 2n
factorial experiment 267
13.6 Finding optimum conditions 269
13.7 Central composite designs 273
13.8 Screening experiments 276
13.9 B10cking and confounding 278
13.10 Summary 282
Problems 283
14 Improving a bad experiment 287
14.1 Introduction 287
14.2 An alternative first experiment 287
14.3 How good is the alternative experiment? 292
14.4 Extending the original experiment 293
14.5 Final analysis 297
14.6 Inspection of residuals 303
14.7 Summary 306
Problems 306
15 Analysis of variance 310
15.1 Introduction 310
15.2 Testing error and sampling variation 310
15.3 Testing error and process capability 320
15.4 Analysis of variance and simple regression 324
15.5 Analysis of variance with multiple regression 328
15.6 Analysis of variance and factorial experiments 331
15;7 Summary 335
Problems 336
16 An introduction to Taguchi techniq~es 338
16.1 Introduction 338
Contents IX
16.2 Orthogonal arrays 338
16.3 Linear graphs 344
16.4 Design, quality and noise 347
16.5 Experiments for robust design 352
16.6 Quality, variability and cost 361
16.7 Summary 363
Problems 364
Appendix A The sigma (l:) notation 368
Appendix B Notation and formulae 369
Appendix C Sampling distributions 373
Appendix D Copy of computer print-out from a multiple
regression program 378
Appendix E Partial correlation 381
Appendix F Significance tests on effect estimates from a
pr factorial experiment 385
Solutions to problems 389
References and further reading 450
Statistical tables 452
Index 466