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## Quick reference

### Process Capability Principles

Process capability is the statistical analysis conducted to determine if a process that is performing with only the normal process variation can be expected to meet the customer expectations at all time.

### When to use

Process Capability is normally used during the Analyze phase to determine whether an existing process can meet the customer expectations even under the best of conditions. It is also used during the Control phase to assist the team in determining whether the process operators and managers are maintain adequate process control.

### Instructions

Process capability is an assessment of whether a process is able to consistently deliver results that meet customer expectations. It is a ratio of what the customer expects, as expressed in the specification limits for a process parameter, and what the process is able to consistently deliver based upon actual process performance.

When determining process capability for attribute data, the process yield is first determined, typically using DPU, DPMO, or PPM. The yield value is then used with a lookup table to determine the process capability indices.

When determining process capability for variable data, direct calculations are performed. These calculations use the upper and lower specification limits for the parameter - which are normally found by adding and subtracting the tolerance limits from the performance target. The calculations also use the descriptive statistics of mean and standard deviation from the data set for the parameter.

There are four process capability indices that are a combination of the attributes of short term versus long term process performance, and the ideal or best case performance versus the current state performance. These are Cp, Cpk, Pp, And Ppk.

The Cp and Pp calculations are considered best case because they use the full width of the allowable specification limits. The width of the process performance for these indices is represented by the span from minus standard deviations to plus three standard deviations for a total of six standard deviations.

The Cpk and Ppk modify the formula so that only a portion of the specification width is used in the numerator and a portion of the process performance is used in the denominator. The portion used in the numerator is the width from the mean (average) of the process performance data to the closest specification limit. The portion used in the denominator is the one half of the amount used in the Cp calculation, that is three standard deviations.

### Hints & tips

- The Cp index is set at the time of the process design. The specification limits are known and the process standard deviation can be determined.
- The Cpk index often changes regularly as the center of the process performance drifts high or low.
- The Cpk can never be better than the Cp. When a process is exactly centered, the Cpk will equal the Cp, but as soon as it moves away from the center, the distance to one of the specification limits will shrink and that index will shrink (this is because we are using the “minimum” function which means that we take the smaller of the two ratios)
- It is impossible to have a negative Cp, however it is possible to have a negative Cpk if the process performance drifts to the point where the mean value is outside of the specification limits.

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