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A Toolbook for Quality Improvement and Problem Solving (contents)

Process Capability: How to understand it

The Quality ToolbookProcess Capability > How to understand it

When to use it | How to understand it | Example | How to do it | Practical variations

 

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How to understand it

The outputs of any process will vary, as discussed in the chapter on Variation, and it is common for specification limits to be defined such that if the measured output of the process exceeds the specified limits, the process is deemed to have failed. The term 'specification limits' is most commonly used for the dimensions of a manufactured item, but can be used in any process. Thus, for example, the specification limits for the time a telesales operator may take to answer a customer call may be between zero and five seconds.

The results of most processes will vary around a central value, as described in Chapter 5, and the 'capability' of the process is defined as the spread of results around this value, with high capability occurring when process results group closely around it. Thus a process that can produce parts to within 0.001mm of a target value is more capable than one which can only produce them to within 0.015mm.

The most common measure of this spread is standard deviation, and 'Process Capability' may be defined as the range between three standard deviations either side of the average.

 

 

Fig. 1. Standard deviation

 

Specifications are often defined separately from the process that is being measured and without a great deal of consideration of how easily the process can meet them. This can result in either many failures and rejects or effectively redundant specifications, as the variation in the process fits badly or well within the specified limits.

Specification limits and process capability thus need to be considered together. The limits still cannot be too tight as if calibration is done under ideal conditions, process distribution may subsequently drift or spread, for example as a result of wear in a machine tool.

 

 

Fig. 2. Natural distribution fit within defined specification limits

 

A common Process Capability measure, Cp (often called a Process Capability Index), indicates how well the process distribution fits within its specification limits, and is simply the ratio of the specification width to the variation width. Thus, in the figure above , processes (a) and (b) have Cp greater than one, (c) is equal to one and (d) is less than one.

The problem with Cp is that it does not take account of how well the process distribution is centered within its limits, which can result in a process with both a low Cp and many rejects. The solution to this is a second measure, Cpk, which measures a similar ratio, but considers only the variation half that is closest to the specification limits, as in the figure below. Thus Cp and Cpk, taken together, give a measure of both the potential and centering of the process distribution within the specification limits.

Process Capability measures are only as good as the data used, and there is plenty of opportunity for misinterpretation. In particular, Process Capability measurement is based on three important assumptions which are thus preconditions for valid calculations:

  1. The process is in a state of statistical control, and there are no special causes of variation. The implication of this is that before Cp and Cpk can be measured, special causes must be found and eliminated. This may be done using the Control Chart over a period of time long enough to give confidence that this has been successfully completed.
  2. The process distribution is bell-shaped or 'Normal', which allows the width of the distribution to be calculated as six times the standard deviation. In practice, there are many situations where the distribution is not normal, and in Process Capability measurement the Central Limit Theorem does not act to normalize this, as it does when using a Control Chart.

 

 

Fig. 3. Capability measurement

  1. The measured data is representative of the process. This means that it should be a randomly selected and large sample, taken over a long period. Samples taken over a short period can suffer from a limited range of changes in either external seasonal effects or internal process variables, such as humidity or tool wear.

When interpreting values of Cpk, there are three significant regions which may be considered, and a general rule is given in the table below . The value of 3 as a 'total confidence' limit may be lowered if measurements are taken as the average of sample batches. This commonly happens when Cpk is measured using the same data that is used to plot the Control Chart (e.g. the confidence limit reduces to 2 for the common sample size of 4).

In the broader sense, studying Process Capability is more than just measuring Cp and Cpk; it involves understanding the statistical performance and operational working of the process. Most importantly, it means understanding what causes variation within the process, under what conditions, and how these variables interact. The purpose of doing this is to enable confident process improvement that steadily reduces variation.

 

Table 1. Cpk values and capability

 

Value of Cpk Capability Action
Less than 1 Incapable Improve by reducing common causes of variation in process variables. Use 100% inspection.
Between 1 and 3 Capable Do nothing or some process improvement. Dependent on sample size.
Greater than 3 Very capable Do nothing or reduce specification limits. No inspection necessary.

 

 

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