ABSTRACT
This article presents a new and appealing derivation of the distribution of Ĉ
pk
when the quality characteristic is normally distributed. Our derivation is based on the folded normal distribution and the fact that sample mean and sample standard deviation are independent. The final result is a complete and self-contained formula that can be easily implemented in any modern math package. We illustrate the use of the pdf of Ĉ
pk
in joint hypothesis testing of process parameters and in process control and monitoring. The ARL performance of a proposed control chart based on Ĉ
pk
is compared against the performance of and R charts.