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# The Capability Index

Quality Tools > Tools of the Trade > 28: The Capability Index

One of the major problems with many processes is that we demand more of them than they are capable of delivering. Exhorting or punishing the people in the process is particularly futile in such circumstances. Only through full understanding of the process capability in relation to the given specification limits can we determine the real potential of the process.

## How it works

Given a single specification, for example when manufacturing a steel rod, no two rods will be exactly the same length and there will be a measurable distribution of sizes of rod. If we look at the distribution of rod sizes relative to the lower  and upper specification limits, the diagram below show some possible results. We can see that all rods in case (a) will easily be within specification whilst a number of rods in (d) will be rejected.

Process output within specifcation limits

This fitting within given limits may be given a numerical value which is known as ‘Cp’. Cp compares the width of the distribution with the width between the specification limits and will thus highlight the problem case (d) in the above diagram. However, cases (b) and (c) are at risk because a slight shift in the average will result in the distribution sliding out of specification on one side or the other. Cp does not capture this, but a modified (and more commonly used) measurement, known as ‘Cpk’, is used to take into account off-centre distributions.

Calculation for Cp and Cpk

## How to do it

1. Identify the process to be measured and the upper and lower specification limits (USL and LSL).

2. Measure the performance of the process under standard working conditions (Note: do not take it off line or measure just after calibration as these optimal conditions will not highlight the true operating capability).

3. Verify that the process is in a state of statistical control with no special causes of variation. This can be done by plotting a Control Chart and looking for trends, shifts, cycles or outliers.

4. Calculate the mean and standard deviation of the distribution of measures.

5. Calculate Cp and/or Cpk as in the diagram below.

Calculation detail for Cp and Cpk

6. The table below may be used to help interpret the final measure and derive consequent improvement action.

 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.

Next time: Morphological Analysis

This article first appeared in Quality World, the journal of the Institute for Quality Assurance

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