On the Distribution of the Usual Estimator of C_(pk) and Some Applications in SPC

摘要

This article presents a new and appealing derivation of the distribution of C_(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 C_(pk) in joint hypothesis testing of process parameters and in process control and monitoring. The ARL performance of a proposed control chart based on C_(pk) is compared against the performance of X and R charts.