Many of the techniques developed by mathematical statisticians for the analysis of data may be used in control of product quality. The expression “Statistical Process Control” may be used to cover all uses of statistical techniques for this purpose. Statistical Process Control is a method of monitoring a process during its operation in order to control the quality of product while they are being produced rather than relying on inspection to find problems after the fact. It involves gathering information about the product, or the process itself, on a near real-time basic so that the operator can take action on the process. This is done in order to identity special causes of variation and other non-normal processing conditions, thus bringing the process under statistical control and reducing variation.
Several statistical tools are available to analyse quality problems and improving the performance of production processes. A common one is the “Control Chart” tool. However, these tools often rely on four separate but related technique which constitute the basic statistical tools in quality control. These four techniques are:
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The Shewhart control charts for measurable quality characteristics. In the technical language of the subject, these are described as charts for variables, or as charts for
X and ‘R’ (average and range) and Chart for X and ‘s’ (average and standard deviation).
- The Shewhart control charts for fraction rejected, or ‘p’ chart.
- The Shewhart control charts for number of nomconformities, or ‘c’ chart.
- The portion of sampling theory that deals with the quality protection given by any specified sampling acceptance procedure.
They are used for cost reduction and quality improvement that are the most widely applied.
Two tools of the Shewhart controls charts are extremely useful in statistical quality control are the range ‘R’ and the standard deviation ‘s’. The range tool measure spread or dispersion, but it is almost never used for large subgroups, that is, for subgroups of more than 20 or 25 items.
Expressed algebraically
R= X max –X min
Where X max is largest number and X min is the smallest number in the set.
The standard deviation of the set of numbers from their arithmetic mean is designated by ‘s’.
Expressed algebraically
The standard deviation is often used in measuring the dispersion of a frequency distribution such as might be pictured in a histogram. This is true particularly when the data have not been recorded in subgroups in order of production. The mathematical formula for ‘s’ is applicable whether we are taking about a subgroup draws for control-chart purposes or any other group of data.
Still another measure of dispersion is the sample variance. This measure is the sum of the squares of the deviations from the arithmetic mean divides by “n-1”. In other words, the standard deviation is the square root of the sample variance. In many of the derivations in mathematical statistics that the deal with the relationship between samples and the universes from which samples are drawn, there are mathematical advantages in the use of variance a the measure of dispersion.
The calculation of Shewhart control-chart limits for variables data is the normal or gaussian distribution. The expressed algebraically for this distribution is :
The normal distribution is probably the most important distribution in both the theory and application of statistics. If ‘x’ is a normal random variable, then the probability distribution of ‘x’ is defined as follows. The normal distribution is used so much that frequently employ a special notation. ‘x’≅ N*( μ, σ2 ), to imply that ‘x’ is normally distributed with mean (μ) and variance (σ2). This visual appearance of the normal distribution is a symmetric, unimodal or bell-shaped curve, and is shown in this figure:
A plot of this function over its full range -∝ to +∝ produces the familiar symmetrical bell-shaped curve. It is a continuous curve over its fully range and has a mean value of zero and a standard deviation of one.
Although control charts and statistical types of acceptance sampling procedures were originally developed for use in mass production manufacturing, these techniques are applicable to most other types of activities in all sectors of the economy including service business, government, education, and health care.