On the Distribution of the Usual Estimator of C_pk and Some Applications in SPC

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.

KEYWORDS:

• average run length
• capability indices
• process capability
• statistical process control