In general, variations that occur in a production process fall into two broad categories: chance variations and variations with assignable causes. Chance variations may have a complex of minor actual causes, none of which can account for a significant part of the total variation. The result is that these variations occur in a random manner, and there is very little that we can do about them, given the process. On the other hand, variations with assignable causes are relatively large and can be traced. In general, assignable causes are the result of
1. Differences among workers
2. Differences among machines
3. Differences among materials
4. Differences due to the interaction between any two or among all three of the preceding causes.
A comparable set of assignable causes could be developed for any process. For example, assignable causes for variation in absenteeism might be disease epidemics, changes in interpersonal relations at home or in the employeeâ€™s work situation, and others.
When a process is in a state of statistical control, variations that occur in the number of defects, the size of a dimension, the chemical composition, the weight, and so on are due only to normal chance variation. With the control chart, we set up standards of expected normal variation due to chance causes. Thus, when variations due to one or more of the assignable causes are superimposed, they â€œstick out like a sore thumbâ€ and tell us that something basic has changed. Then it is possible to investigate to find the assignable cause and correct it. These statistical control mechanisms are called controls.
If we take a set of measurements in sequence, we can arrange the data into a distribution and compute the mean and standard deviation. If we can assume that the data come from a normal population distribution, we can make precise statements about the probability of occurrence associated with the measurements, given in standard deviation units as follows:
68.26 % of the values normally fall within Âµ Â± (Î± )
95.45% of the values normally fall within Âµ Â± 2 (Î±)
99.73% of the values normally fall within Âµ Â± 3 (Î±)
These percentage values represent the area under the normal curve between the given limits; therefore they state the probability of occurrence for the values that come from the normal distribution that generated the measurements. For example, the chances are 95.45 out of 100 that a measurement taken at random will fall within 2 (Î±) limits and only 4.55 out of 100 that it will fall outside these limits. These values, as well as decimal values for (Î±), come from the table for the normal probability distribution available. The natural tolerance of a process, that is, the expected process variation, is commonly taken to be Âµ Â± 3 (Î±) Estimates of the natural tolerance would be based on sample information. We will use the following notation:
Âµ = The population mean (parameter)
x = The mean of a sample drawn from the population (statistics)
(Î±) = The population standard deviation (parameter)
s = The standard deviation of a sample drawn from the population (statistic)
Since we must use sample information to estimate population means and standard deviations, we estimate the natural tolerance of a process by substituting in the sample statistics x Â± 3s
Kinds of Control Charts
Two basic types of control charts, with variations are commonly used:
1. Control charts for variables
2. Control charts for attributes
Control charts for variables are used when the parameter under control is some measurement of a variable, such as the dimension of a part, the time for work performance, and so forth. Variables charts can be based on individual measurements, mean values of small samples, and mean values of measures of variability
Control charts for attributes are used when the parameters under control is the proportion or fraction of defectives. There are several variations for attributes control charts. Control charts for the number of defects per unit are used when single defect may not be of great significance but a large number of defects could add up to a defective products, such as the number of blemishes on the surface of a painted surface.