## About this lesson

Process Capability is often correlated with process Sigma. The calculation of process capability is quite different depending upon whether the data is variable or attribute data. This lesson will present the technique and practice using the variable data process capability ratios.

## Exercise files

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## Quick reference

### Process Capability with Variable Data

The calculation of process capability is quite different depending upon whether the data is variable or attribute data. This lesson will explain the formulas for calculating process capability with variable data.

### When to use

Process data is either variable data or attribute data. Variable data is measured on a scale and a value is determined. Attribute data consists of placing the data value in a category. If the process generates variable data, the variable data Process Capability ratios must be used.

### Instructions

Variable data process capability is established using ratios of the customer expected process performance divided by a value representing normal process spread. There are four different indices. They represent the difference between using near-term recent process data versus long-term historical data and the difference between considering the best-case process performance as compared to the current actual process performance. The differences will be in what process performance measures are used in the calculations.

Cp and Pp

The Cp and Pp indices provide a best-case view of the process capability. These indices are often used during the product and process design process to determine whether a particular type of process is capable of delivering satisfactory performance. These indices have the difference between the upper spec limit and the lower spec limit in the numerator. That means the numerator is the spread of allowable variation that will meet the customer requirements. The denominator in the ratio is the value from minus three standard deviations to plus three standard deviation. Which is a spread of six standard deviations. This is where the difference between Cp and Pp come in.

Cp uses recent, near-term data for calculating the standard deviation. Pp uses long-term historic data. The reason that a spread of minus three standard deviations to plus three standard deviations is used is because that is the way in which Walter Shewhart designed the ratios in the early 1900s. At that time, he felt that process that could deliver all the process output within the limits of minus three standard deviations to plus three standard deviations was a n excellent process With this philosophy, Shewhart set as a target for a process to be considered capable it must have a ration greater than or equal to one. Meaning the process normal spread or variation was less than the allowed variation in the customer specifications.

The Cpk and Ppk process capability indices are derived from the Cp and Pp indices. These indices modify the Cp and Pp indices by taking into consideration the current mean or average point of the process performance. The values for the numerator and denominator are both split into two parts. The numerator is split at the value of the mean. So one numerator will be the difference between the mean and the lower spec limit and the other numerator will be the difference between the upper spec limit and the mean. The denominator is split exactly in half. The value for three standard deviations is used in each ratio. This splitting creates two ratios for Cpk and Ppk instead of just one. The process capability function selects the smaller of the two to report as the process capability. When the process is exactly centered (the mean is half way between the upper and lower spec limits); the numerator for both ratios will be the same. However, if the mean is not centered, one ratio will be larger than the other. A process then can have a Cp or Pp value that is greater than one – showing that the basic design of the process is capable of delivering good results. But if the process management has not centered the process, the actual results can be much less than one, indicating that process has drifted outside the bounds of acceptable performance. And like with the other indices, Cpk uses short-term recent data to calculate the mean and standard deviation while the Ppk relies on long-term historic data.

### Hints & tips

- Cpk and Ppk can never be greater than the Cp or Pp value. Once the process is exactly in the center of the allowable limits, the two Cpk/Ppk ratios will be identical and they will also equal the corresponding Cp or Pp ratio.
- When looking at process results, you only need to calculate the Cpk/Ppk ratio for the condition where the mean is closest to the spec limit. That will always be the smallest value.’
- Cp and Pp normally do not change unless there is a major change to the process. But Cpk and Ppk can often change if machines wear out or different operators setup the process slightly differently.

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