Better Confidence Limits for Process Capability Index $C_{pmk}$ under the assumption of Normal Process

Cho Joong-Jae,; Park Byoung-Sun,; Park Hyo-il,

Journal of Korean Society for Quality Management > Volume 32(4); 2004 > Article

Journal of Korean Society for Quality Management 2004;32(4): 229-.

정규분포 공정 가정하에서의 공정능력지수 $C_{pmk}$ 에 관한 효율적인 신뢰한계

조중재¹, 박병선², 박효일³

¹충북대학교 자연과학대학 정보통계학과
²한국표준과학연구원 측정품질그룹
³청주대학교 이공대학 통계학과

Better Confidence Limits for Process Capability Index $C_{pmk}$ under the assumption of Normal Process

ABSTRACT

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

Key Words: Process capability index;Asymptotic distribution;Bootstrap consistency;Monte-carlo simulation;Statistical inference;Bootstrap confidence limits;