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

Cho Joong-Jae (충북대학교 자연과학대학 정보통계학과)
Park Byoung-Sun (한국표준과학연구원 측정품질그룹)
Park Hyo-il (청주대학교 이공대학 통계학과)
Publication Information
Journal of Korean Society for Quality Management / v.32, no.4, 2004 , pp. 229-241 More about this Journal
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.
Keywords
Process capability index; Asymptotic distribution; Bootstrap consistency; Monte-carlo simulation; Statistical inference; Bootstrap confidence limits;
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