Statistics for Technology

A Course in Applied Statistics, Third Edition

Chris Chatfield

• Publisher: Chapman and Hall/CRC
• Year: 2018
• ISBN:
  9781351414074
• Edition: 3
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

One of the most popular introductory texts in its field, Statistics for Technology: A Course in Applied Studies presents the range of statistical methods commonly used in science, social science, and engineering.The mathematics are simple and straightforward; statistical concepts are explained carefully; and real-life (rather than contrived) examples are used throughout the chapters.Divided into three parts, the Introduction describes some simple methods of summarizing data. Theory examines the basic concepts and theory of statistics. Applications covers the planning and procedures of experiments, quality control, and life testing.Revised throughout, this Third Edition places a higher priority on the role of computers in analysis, and many new references have been incorporated. A new appendix describes general methods of tackling statistical problems, including guidance on literature searching and report writing.

Part one

Introduction

‘Surely,’ said the governor, ‘Her Radiancy would admit that ten is nearer to ten than nine is – and also nearer than eleven is.’

Chapter 1

Outline of statistics

Statistical methods are useful in many types of scientific investigation. They constitute the science of collecting, analysing and interpreting data in the best possible way. Statistics is particularly useful in situations where there is experimental uncertainty and may be defined as ‘the science of making decisions in the face of uncertainty’. We begin with some scientific examples in which experimental uncertainty is present.

Example 1

The thrust of a rocket engine was measured at ten-minute intervals while being run at the same operating conditions. The following thirty observations were recorded (in newtons × 10⁵):

The observations vary between 989·4 and 1014·5 with an average value of about 1000. There is no apparent reason for this variation which is of course small compared with the absolute magnitude of each observation; nor do the variations appear to be systematic in any way. Any variation in which there is no pattern or regularity is called random variation. In this case if the running conditions are kept uniform we can predict that the next observation will also be about a thousand together with a small random quantity which may be positive or negative.

Example 2

The numbers of cosmic particles striking an apparatus in forty consecutive periods of one minute were recorded as follows.

The observations vary between zero and four, with zero and one observed more frequently than two, three and four. Again there is experimental uncertainty since we cannot exactly predict what the next observation would be. However, we expect that it will also be between zero and four and that it is more likely to be a zero or a one than anything else. In Chapter 4 we will see that there is indeed a pattern in this data even though individual observations cannot be predicted.

Example 3

Twenty refrigerator motors were run to destruction under advanced stress conditions and the times to failure (in hours) were recorded as follows.

104·3	158·7	193·7	201·3	206·2
227·8	249·1	307·8	311·5	329·6
358·5	364·3	370·4	380·5	394·6
426·2	434·1	552·6	594·0	691·5

We cannot predict exactly how long an individual motor will last, but, if possible, we would like to predict the pattern of behaviour of a batch of motors. For example we might want to know the over-all proportion of motors which last longer than one week (168 hours). This problem will be discussed in Chapter 13.

When the scientist or engineer finishes his education and enters industry for the first time, he must be prepared to be faced frequently with situations which involve experimental uncertainty. The purpose of this book is to provide the scientist with methods for treating these uncertainties. These methods have proved to be very useful in both industry and research.

A scientific experiment has some or all of the following characteristics.

(1) The physical laws governing the experiment are not entirely understood.

(2) The experiment may not have been done before, at least successfully, in which case the instrumentation and technique are not fully ...