标题: | Clements 方法于制程能力指标之效能分析 Performance Analysis of Clements' Estimators for Process Capability Indices |
作者: | 钟海婷 Chung, Hai Ting 洪志真 Jyh-Jen Horng Shian 统计学研究所 |
关键字: | 制程能力指标;皮尔森家族;Clements;Pearson family;Process Cabability indices |
公开日期: | 1997 |
摘要: | 对于制程能力指标在非常态的情况下, Clements (1989) 在皮尔森家族的 假设下提出以Up - Lp 取代 6倍标准差 和利用中位数取代平均数的方法, 并且应用在Cp, Cpk 这两个指标上. Pearn 和 kotz (1994) 把此方法应 用在Cpm, Cpmk. 在此篇论文中, 我们选了六个皮尔森家族的分配作为母 体假设. 另外为了观察非皮尔森家族分配下的Clements估计量的表现, 我 们选了五个非皮尔森家族分配作为母体假设. 观察发现Clements估计量的 偏误颇大而且会随着kurtosis增加而变大. 所以使用者需要谨慎. 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. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#NT860338011 http://hdl.handle.net/11536/62706 |
显示于类别: | Thesis |