Effective Experimentation E-Book

Richard Boddy

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 285

Veröffentlichungsjahr: 2011

Beschreibung

Effective Experimentation is a practical book on how to design and analyse experiments. Each of the methods are introduced and illustrated through real world scenario drawn from industry or research. Formulae are kept to a minimum to enable the reader to concentrate on how to apply and understand the different methods presented. The book has been developed from courses run by Statistics for Industry Limited during which time more than 10,000 scientists and technologists have gained the knowledge and confidence to plan experiments successfully and to analyse their data. Each chapter starts with an example of a design obtained from the authors' experience. Statistical methods for analysing data are introduced, followed, where appropriate, by a discussion of the assumptions of the method and effectiveness and limitations of the design. The examples have been chosen from many industries including chemicals, oils, building materials, textiles, food, drink, lighting, water, pharmaceuticals, electronics, paint, toiletries and petfoods. This book is a valuable resource for researchers and industrial statisticians involved in designing experiments. Postgraduates studying statistics, engineering and mathematics will also find this book of interest.

Leseprobe

Contents

Preface

1 Why bother to design an experiment?

1.1 Introduction

1.2 Examples and benefits

1.3 Good design and good analysis

2 A change for the better – significance testing

2.1 Introduction

2.2 Towards a darker stout

2.3 Summary statistics

2.4 The normal distribution

2.5 How Accurate is My Mean?

2.6 Is the new additive an improvement?

2.7 How many trials are needed for an experiment?

2.8 Were the aims of the investigation achieved?

2.9 Problems

3 Improving effectiveness using a paired design

3.1 Introduction

3.2 An example: who wears the trousers?

3.3 How do we rate the wear?

3.4 How often do you carry out an assessment?

3.5 Choosing the participants

3.6 Controlling the participants

3.7 The paired design

3.8 Was the experiment successful?

3.9 Problems

4 A simple but effective design for two variables

4.1 Introduction

4.2 An investigation

4.3 Limitations of a one-variable-at-a-time experiment

4.4 A factorial experiment

4.5 Confidence intervals for effect estimates

4.6 What conditions should be recommended?

4.7 Were the aims of the investigation achieved?

4.8 Problems

5 Investigating 3 and 4 variables in an experiment

5.1 Introduction

5.2 An experiment with three variables

5.3 The design matrix method

5.4 Computation of predicted values

5.5 Computation of confidence interval

5.6 95% Confidence interval for an effect

5.7 95% Confidence interval for a predicted value

5.8 Sequencing of the trials

5.9 Were the aims of the experiment achieved?

5.10 A four-variable experiment

5.11 Half-normal plots

5.12 Were the aims of the experiment achieved?

5.13 Problems

6 More for even less: using a fraction of a full design

6.1 Introduction

6.2 Obtaining half-fractional designs

6.3 Design of 1/2(24) experiment

6.4 Analysing a fractional experiment

6.5 Summary

6.6 Did Wheelwright achieve the aims of his experiment?

6.7 When and where to choose a fractional design

6.8 Problems

7 Saturated designs

7.1 Introduction

7.2 Towards a better oil?

7.3 The experiment

7.4 An alternative procedure for estimating the residual SD

7.5 Did Doug achieve the aims of his experiment?

7.6 How rugged is my method?

7.7 Analysis of the design

7.8 Conclusions from the experiment

7.9 Did Serena achieve her aims?

7.10 Which Order Should I Use for the Trials?

7.11 How to obtain the designs

7.12 Other uses of saturated designs

7.13 Problems

8 Regression analysis

8.1 Introduction

8.2 Example: Keeping Quality of Sprouts

8.3 How good a fit has the line to the data?

8.4 Residuals

8.5 Percentage fit

8.6 Correlation coefficient

8.7 Percentage fit – an easier method

8.8 Is there a significant relationship between the variables?

8.9 Confidence intervals for the regression statistics

8.10 Assumptions

8.11 Problem

9 Multiple regression: the first essentials

9.1 Introduction

9.2 An experiment to improve the yield

9.3 Building a regression model

9.4 Selecting the first independent variable

9.5 Relationship between yield and weight

9.6 Model building

9.8 An alternative model

9.9 Limitations to the analysis

9.10 Was the experiment successful?

9.11 Problems

10 Designs to generate response surfaces

10.1 Introduction

10.2 An example: easing the digestion

10.3 Analysis of crushing strength

10.4 Analysis of dissolution time

10.5 How many levels of a variable should we use in a design?

10.6 Was the experiment successful?

10.7 Problem

11 Outliers and influential observations

11.1 Introduction

11.2 An outlier in one variable

11.3 Other outlier tests

11.4 Outliers in regression

11.5 Influential observations

11.6 Outliers and influence in multiple regression

11.7 What to do after detection?

12 Central composite designs

12.1 Introduction

12.2 An example: design the crunchiness

12.3 Estimating the variability

12.4 Estimating the effects

12.5 Using multiple regression

12.6 Second stage of the design

12.7 Has the experiment been successful?

12.8 Choosing a central composite design

12.9 Critique of central composite designs

13 Designs for mixtures

13.1 Introduction

13.2 Mixtures of two components

13.3 A concrete case study

13.4 Design and analysis for a 3-component mixture

13.5 Designs with mixture variables and process variables

13.6 Fractional experiments

13.7 Was the experiment successful?

14 Computer-aided experimental design (CAED)

14.1 Introduction

14.2 How it works

14.3 An example

14.4 Selecting the repertoire

14.5 Selecting the model and number of trials

14.6 How the program chooses the design set

14.7 Summary

14.8 Problems

15 Optimization designs

15.1 Introduction

15.2 The principles behind EVOP

15.3 EVOP: The experimental design

15.4 Running EVOP programmes

15.5 The principles of simplex optimization

15.6 Simplex optimization: an experiment

15.7 Comparison of EVOP, simplex and response surface methods

16 Improving a bad experiment

16.1 Introduction

16.2 Was the experiment successful?

17 How to compare several treatments

17.1 Introduction

17.2 An example: which is the best treatment?

17.3 Analysis of variance

17.4 Multiple comparison test

17.5 Are the standard deviations significantly different?

17.6 Cochran’s test for standard deviations

17.7 When should the above method not be used?

17.8 Was Golightly’s experiment successful?

17.9 Problems

18 Experiments in blocks

18.1 Introduction

18.2 An example: kill the sweat

18.3 Analysis of the data

18.4 Benefits of a randomized block experiment

18.5 Was the experiment successful?

18.6 Double and treble blocking

18.7 Example: a dog’s life

18.8 The Latin square design

18.9 Latin square analysis of variance

18.10 Properties and assumptions of the Latin square design

18.11 Examples of Latin squares

18.12 Was the experiment successful?

18.13 An extra blocking factor -– Graeco-Latin square

18.14 Problem

19 Two-way designs

19.1 Introduction

19.2 An example: improving the taste of coffee

19.3 Two-way analysis of variance

19.4 Multiple comparison test

19.5 Was the experiment successful?

19.6 Problem

20 Too much at once: incomplete block experiments

20.1 Introduction

20.2 Example: an incomplete block experiment

20.3 Adjusted means

20.4 Analysis of variance for balanced incomplete block design

20.5 Alternative designs

20.6 A design with a control

20.7 Was Jeremy's experiment successful?

20.8 Problem

21 23 Ways of messing up an experiment

21.1 Introduction

21.2 23 ways of messing up an experiment

21.3 Initial thoughts when planning an experiment

21.4 Developing the ideas

21.5 Designing the experiment

21.6 Conducting the experiment

21.7 Analysing the data

21.8 Summary

Solutions to problems

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 14

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Statistical tables

Index

This edition first published 2010

© 2010, John Wiley & Sons, Ltd

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Library of Congress Cataloguing-in-Publication Data

Boddy, Richard, 1939-

Effective experimentation : for scientists and technologists / Richard Boddy, Gordon Laird Smith.

p. cm.

Includes index.

ISBN 978-0-470-68460-3 (hardback)

1. Science—Experiments—Statistical methods. 2. Technology—Experiments—Statistical methods.

I. Smith, Gordon (Gordon Laird) II. Title. Q182.3.B635 2010

507.2’7—dc22

2010010298

A catalogue record for this book is available from the British Library.

ISBN: 978-0-470-68460-3

Preface

This is a practical book for those engaged in research within industry. It is concerned with the design and analysis of experiments and covers a large repertoire of designs. But in the authors’ experience this is not enough – the experiment must be effective. For this the researcher must bring his knowledge to the situations to which he needs to apply experimentation. For example, how can the design be formulated so that the conclusions are unbiased and the experimental results are as precise as needed?

Each chapter starts with a situation obtained from our experience or from that of our fellow lecturers. A design is then introduced and data analysed using an appropriate method. The chapter then finishes with a critique of the experiment – the good points and the limitations.

The book has been developed from the courses run by Statistics for Industry Limited for over 30 years, during which time more than 10,000 scientists and technologists have gained the knowledge and confidence to apply statistics to their own data. We hope that you will benefit similarly from our book. Every design in the book has been applied successfully.

The examples have been chosen from many industries – chemicals, plastics, oils, nuclear, food, drink, lighting, water and pharmaceuticals. We hope this indicates to you how widely statistics can be applied. It would be surprising if statistics could not be applied successfully by you to your work.

The book is supported by a number of specially designed computer programs and Excel Macros. These can be downloaded from Wiley’s website. Although the reader can gain much by just reading the text, he/she will benefit even more by downloading the software and using it to carry out the problems given at the end of each chapter.

The book gives a brief overview of introductory statistics. For those who feel they need a more comprehensive view before tackling this book can refer to Statistical Methods inPractice (2009) by the same authors.

Statistics for Industry Limited was founded by Richard Boddy in 1977. He was joined by Gordon Smith as a Director in 1989. They have run a wide variety of courses worldwide, including Statistical Methods in Practice, Statistics for Analytical Chemists, Statistics for Microbiologists, Design of Experiments, Statistical Process Control, Statistics in Sensory Evaluation and Multivariate Analysis. This book is based on material from their Design of Experiments course.

Our courses and our course material have greatly benefited from the knowledge and experience of our lecturers: Derrick Chamberlain (ex ICI), Frits Quadt (ex Unilever), Martin Minett (MJM Consultants), Alan Moxon (ex Cadbury), Ian Peacock (ex ICI), Malcolm Tillotson (ex Huddersfield Polytechnic), Stan Townson (ex ICI), Sam Turner (ex Pedigree Petfoods) and Bob Woodward (ex ICI). In particular we would like to acknowledge Dave Hudson (ex Tioxide) who wrote the Visual-Basic-based software, John Henderson (exChemdal) whowrote the Excel-based software and Michelle Hughes who so painstakingly turned our notes into practical pages.

Supporting software is available on the book companion website www.wiley.com/go_effective.

Richard Boddy

Gordon Smith

Email: [email protected]

April 2010

1

Why bother to design an experiment?

1.1 Introduction

There are many aspects involved in successful experimentation. This book concentrates mainly on designing and analysing experiments but there is much more required from you, the experimenter. You must research the subject well and include prior knowledge available from previous experiments within your organization. You should also consider a strategy for the investigation such as considering a series of small investigations. You must plan the experiment operationally so it can be successfully undertaken and, lastly, having analysed the experiment you must be able to interpret the analysis and draw valid conclusions.