Performance Analysis of Clements' Estimators for Process Capability Indices

• Main Authors: Chung, Hai Ting, 鍾海婷
• Other Authors: Jyh-Jen Horng Shian
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/50791188311818328830

碩士 === 國立交通大學 === 統計學類 === 86 === Process capability indices (PCIs) provide numerical measures for process performance. Most research and resulting statistical properties of PCIs are usually obtained under the normal distribution assumption. Clements (1989)proposed a method based on the assumption that the process distribution canbe characterized by a Pearsonian distribution. The main idea of Clements'method is to replace 6 sigma by Up - Lp and mu by M, where mu and sigma are the mean and standsrd deviation, while Up and Lp are the 0.99865 and 0.00135percentile of the process. Clements (1989) applied this method to Cp and Cpk indices. Pearn and Kotz (1994) extended the method to Cpk and Cpmk indices. In this paper, we conduct a simulation to generate a very large sample forClements' estimators to calculate the relative bias of these estimatorsto investigate the performance. We choose six Pearsonian distributions as our population distributions. In addition, we choose five non - Pearsonian distributions as our population distributions to see how the method performswhen the distribution is non - Pearsonian. We find that the relative bias increaseas kurtosis of the process distribution increases. The simulation results show that the relative bias of the Clements' estimators are fairly large. Therefore practitioner should be very careful when using Clements' estimators. Tables of the relative biasof Clements' estimators for the above mentioned distributions are reported for practitioner reference.