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研究生:鍾海婷
研究生(外文):Chung, Hai Ting
論文名稱:Clements方法於製程能力指標之效能分析
論文名稱(外文):Performance Analysis of Clements' Estimators for Process Capability Indices
指導教授:洪志真洪志真引用關係
指導教授(外文):Jyh-Jen Horng Shian
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計學類
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:45
中文關鍵詞:製程能力指標皮爾森家族
外文關鍵詞:ClementsPearson familyProcess Cabability indices
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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.

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