The performance of the Cpk chart

Abstract

The Cpk is the distance between the process mean and the closest specification limit divided by three times the process standard deviation. The index Cpk was created to quantify the ability of the process to produce products within specified limits, but in recent studies the sample estimator $\stackrel{⌢}{C}pk$ of the index Cpk has also been used to control processes and to decide whether a lot should be accepted or not. As a monitoring statistic, the $\stackrel{⌢}{C}pk$ has the aim to signal changes in the mean and/or in the variance of the X distribution. It is worth to note that in this new use, the specification limits can no longer be seen as the limits beyond which a product is considered defective; they are now tunning parameters of the control chart, that is, the choice of the specification limits affects the speed with which the Cpk chart signals. In this article, we study the $\stackrel{⌢}{C}pk$ distribution.

Keywords:

• Cpk chart
• $\mathit{C}\mathit{p}\mathit{k}$ distribution
• Joint control the process mean and variance
• Process monitoring

Acknowledgments

The author is thankful to the reviewers and editor for the useful comments to improve the initial version of the article. This work was supported by CNP_q – National Council for Scientific and Technological Development (grant no. 305133/2020-9).