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