Statistical Quality Control Methods

Irving W. Burr

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351414197
• Edition: 1
• Topic: Business
• Subtopic: Operations
• Index: Business

This book focuses on statistical methods useful in quality control, emphasizing on data-analysis and decision-making. These techniques are also of great use in areas such as laboratory analyses and research. The problems and examples presented are from actual cases encountered in the industry.

CHAPTER 1

INTRODUCTION

1.1. What is Statistics? Statistics is the science concerned with the drawing of inferences and making decisions from data which are subject to variation. Wherever results vary from trial to trial, time to time or person to person, you have a statistical problem, whether you like it or not, whether you know it or not. Since random variation is so universally present in industry, engineering and science in general, the question becomes not whether you are going to perform the functions of a statistician; you are, each time you make a decision or draw an inference! The only question is as to how well you are going to perform that function.

Sometimes, of course, especially where the random variation is relatively minor, the decision is perfectly “obvious,” In such cases no statistical methods are needed. But often enough what appears obvious, proves to be unjustifiable or false. Moreover there are many cases where the decision is not at all clear, and statistical methods are invaluable in estimating the risks and providing objective decisions. Statistical methodology is also concerned with the setting up of experiments, the drawing of samples and the proper analysis of results, for maximum efficiency and objectivity.

1.2. Why Statistical Quality Control? Quality control in various forms has been practiced for thousands of years, certainly dating back to the building of the pyramids in Egypt. But the use of statistical quality control, that is, the use of statistical methods in the control and improvement of quality in industrial production, is a quite recent development. The real beginnings were made in the 1920’s by men in the Bell Telephone Laboratories, among whom we may mention Walter A. Shewhart, Harold F. Dodge, Harry G. Romig, George D. Edwards, Thornton C. Fry and E. C. Molina.

A basic reason for the need for statistical quality control is that industry is continually trying to work to ever closer tolerances. It is not difficult to make parts all “exactly” alike to some fairly gross degree of precision. But when we are asked to have a certain dimension of a part to always lie within an extremely narrow tolerance range (two limits), we may be forced to the utmost with our production and measurement capabilities, and statistical control becomes basic. For example, years ago, a diesel engine plant had to make plunger rods for forcing fuel through small holes. The diameter of the rods was to meet a total tolerance range of only .00004″. Even with guages they had constructed, measuring to the nearest .00001″, the problem was very difficult. They could of course produce rods all exactly alike to the nearest .001″ or even .0001″ perhaps. But to the nearest .00001″ there were varying diameters.

Another form of variation to be controlled is the incidence of non-conforming parts in industrial production. These may have one or another dimension out of tolerance, or have some defect of slight or substantial importance. Production completely free of all such non-conforming parts is the ideal of course. But it may be unnecessary, or uneconomic, or even impossible. In the latter case is the production of millions of parts each of which can have any one or more of 20 different defects of varying importance. Another common example in which we cannot have absolute assurance of all parts meeting standards, is that in which the test destroys the part. Some examples of such tests are tensile strengths of rivets, life tests of electronic parts, and muzzle velocity of ammunition. If we test every part and perhaps find that all met the standard in such a test, we have none left to use!

In all these cases statistical quality control methods are of basic importance.

1.3. Aim of Book. In the last, say, twenty years, there has been a great proliferation of methods of statistical quality control. In this book we cannot begin to cover this broad a field. What we can do is (a) to cover a basic set of methods of statistical quality control of wide usage and flexibility, (b) to emphasize general principles and philosophy, and (c) to provide the reader with background upon which to grow in his use and application of statistical quality control. To make full use in a company of just the techniques herein presented could take fifty years.

Furthermore the aim is not to present statistical methods in general, however interesting this would be, but instead to concentrate on those of particular use in statistical quality control.

1.4. Prerequisites. It will be assumed that the student is somewhat familiar with basic statistical methods, as covered in a beginning course. For those without such background, however, as well as a refresher for those with this background we present a review in Chapter 2. Also some knowledge of elementary calculus is assumed. However, in order to make the book readable to those who are weak in these two assumed prerequisites we shall try to make the early parts of sections and chapters as readable as possible and take up more technical aspects further along. The answers to problems can also be a considerable aid to those having difficulties.

1.5. Suggestions to the Student. In statistics it seems to be impossible to avoid some difficulties with notations. This is perhaps especially true in statistical quality control. Hence the student is urged to make full use of the glossary.

A great many of the problems in the book use data, in most cases, actually obtained in industry. Care in calculation is important as always. A slide rule is usually sufficient. (But please, not like some people’s idea of “slide-rule accuracy” permitting about a 3% error!) Of course a desk calculator, logarithms and tables of square roots are also useful. In substantial calculations, retaining more places than fully justified, and then rounding off at the end, is good practice.

In this book many different industrial parts and products occur in examples and problems. If you are not fully (or at all) acquainted with one, do not let this bother you, the author may not be either. The important thing is that the part or product has one or more measurable characteristics whose distribution we may study. Or there may be some properly defined “defects” we wish to study the incidence of. In both cases we can use statistical distributions without intimate knowledge of the product in question.

The student is urged to try to think of examples and illustrations in areas where he does have some background. This can considerably strengthen his grasp of the methods and make them more interesting.

A healthy skepticism of the obvious conclusion and an active seeking for all possible errors of tabulation, calculation, logic, nonapplicability of a technique or interpretation should be practiced and developed. Until one has made several serious blunders, it is difficult to realize the diabolical variety of traps which lie in wait for the unwary statistical worker. Only by eternal vigilance can they be avoided.

CHAPTER 2

BRIEF REVIEW OF STATISTICAL BACKGROUND

2.1. Population and Sample. In statistical work we are concerned with populations of objects, parts, people, trials or measurements. Such a population may be finite as in the first three cases or conceptually infinite as in the last two. Each individual in the population can be characterized by (a) a number such as length, weight or strength, or (b) can possess one or more attributes, such as, being defect-free or having one or more defects. These two ways of characterizing the individuals of a population gives rise to numerical or measurement data, and to attribute data respectively. Rather different statistical population models are used for the two different cases. The student should often be asking: Is this collection measurement or attribute data?

Probably the most basic question in all of statistics is the relation between a sample and the population from which it comes. How does the population determine what to expect of samples from it, and what does the sample tell about the population? Of course neither question has any answer unless the samples are drawn in an approved, unbiased manner, usually and hopefully at random, such as, by using a table of random numbers. (See Table IV in the back of the book.)

In general, no matter what the population is like, it will determine, in some manner, the behavior of the samples, whether or not we can fully characterize this relation.

2.2. Parameter ...