Confidence Intervals for Process Capability Ratios

Is it possible to calculate confidence intervals for Cp, Cpk, Pp, Ppk, and other process performance indices? The answer is "yes".

The value of a PCR (Process Capability Ratio) is calculated from data that represents a sample taken from a production process (the population). An inference is to be made about the population based on the results calculated from the sample data. As such, the PCR is a test statistic that has both a point estimate (which is what is commonly reported) and an interval estimate based on the sampling uncertainty. The interval estimate and the associated standard error of the estimate (of the PCR) reflects the uncertainty in the characterization of the population due to the limited information contained in the sample.

Many statistical software packages are capable of reporting both the point and interval estimate of process performance (or capability) ratios.

Formulas for calculating confidence intervals for Cpk, Ppk, etc. may be found in Statistical Quality Control (Montgomery).

Confidence intervals around a point estimate may also be calculated using Resampling and Bootstrap methods.

The following formulas have the common assumption that the characteristic being measured is normally distributed.

Confidence Interval on Cpk

Confidence Interval on Cp