Clements 方法於製程能力指標之效能分析

Abstract

對於製程能力指標在非常態的情況下, Clements (1989) 在皮爾森家族的 假設下提出以Up - Lp 取代 6倍標準差 和利用中位數取代平均數的方法, 並且應用在Cp, Cpk 這兩個指標上. Pearn 和 kotz (1994) 把此方法應 用在Cpm, Cpmk. 在此篇論文中, 我們選了六個皮爾森家族的分配作為母 體假設. 另外為了觀察非皮爾森家族分配下的Clements估計量的表現, 我 們選了五個非皮爾森家族分配作為母體假設. 觀察發現Clements估計量的 偏誤頗大而且會隨著kurtosis增加而變大. 所以使用者需要謹慎. 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.