The concepts of statistical control theory as they are used in the design and operation of control charts will now be discussed. It is important to note that these basic principles of control apply to any control problem, e.g. stock control, accidents, overheads, etc., and examples of the use of the control theory to these wider management areas will be given later in the book.
This chapter contains a brief revision of the statistical theory used in process control. The techniques covered are the basic concepts of Poisson and normal distributions together with the use of the χ2 goodness-of-fit test.
The measurement of process capability is carried out by taking a number of relatively small samples from the process at regular intervals of time and analysing the data to ensure that no assignable factors are present. In practice a minimum of 25 samples are required and the sample size taken depends on many factors, including production rate of process, cost of measurement, etc.
The concept of a control chart was evolved by Dr. Shewhart in America in 1924 — the initial development in Britain being mainly by Dr. Dudding and W. Jennett. Dr. Shewhart suggested that the control chart should have three main objectives.
Conventional charting techniques, such as the Shewhart control charts, described in Chapter 5, have the feature that although points are plotted in time, any testing done on them does not take previous values into account. A technique developed in the late 1950s, however, attempts to include information contained in past data points in order to comment on current performance. This is done, not by looking at the individual data point, but by studying their cumulative sums or ‘cusum’.
In the previous chapter, the calculation of the CuSum was covered together with the use of the CuSum chart as a visual diagnostic tool. The sensitivity of the CuSum chart in detecting changes was also clearly shown, with a range of practical examples.
The British Standard (Shewhart) control system, described in Chapter 5 and the CuSum control system, described in Chapter 7 are compared in this chapter.
The quality control systems described in this book are usually linked in practice to sampling inspection schemes. These inspection schemes are required as an additional safety check on the control system since as was clearly illustrated no process control chart can ensure that it detects immediately when a process goes out of control, i.e. there is a finite run length before detection. Therefore, sampling inspection is carried out before finally accepting the product. Again there is a need for inspecting incoming products into the factory and sampling inspection schemes are used to ensure greater control over the quality levels accepted into the factory.
