多製程特性的Cpmk之探討

A Study of Process Capability Index Cpmk with Multiple Characteristic

林炳勳(Bing-shiun Lin)

指導教授 ： 陳雲岫

元智大學/工程學院/工業工程與管理學系/碩士(2013年)

https://doi.org/10.6838/YZU.2013.00331

摘要

多製程特性能力指標是同時考量多個單一製程能力指標的衡量方式，且均考量製程資料服從常態分配。本文則是當製程資料不服從常態分配時，討論多製程特性的製程能力指標CT的表現。本論文中分別提出三種方式:1.中央極限定理之特性以樣本平均值具常態分配；2.以Box-Cox數據轉換方式將原始資料轉成常態分配；3.直接以非常態資料誤判成常態資料處理。數據分析採用模擬資料，且假設製程資料具伽瑪分配。本研究中，我們假設三項不同的製程量測值且分別具伽瑪分配。首先評估出資料對應之母體多製程特性能力指標值CT;其後分別使用三種方式計算出估計之CT值，CT。同時建立個別的信賴區間，並進行覆蓋率比較。分析結果顯示利用中央極限定理來轉換所得到的CT值表現最好，且和CT標準差最小，覆蓋率也是三個方法中最高的。樣本數越多則製程能力指標 之覆蓋率越高，而 的平均數也會越大與標準差越小。另當伽瑪分配之尺度參數β增加時，估計得之CT達到原始製程能力指標CT之樣本數遞降。

關鍵字

製程能力指標 ； Gamma分配 ； 多製程特性

並列摘要

Process capability index with multiple characteristics is to consider several capability indexes with single characteristic simultaneously and assume that data follow normal distributions. In this research, we studied the performance of process capability with multiple characteristics under non-normal distributions. We considered three different ways for the evaluation. 1. Sampling distribution of sample mean is close to normal based on the central limit theorem. 2. Transform non-normal data to normal by the method of Box-Cox transformation. 3. Treat data normally distributed falsely. In the simulation study, we assumed three different processes each following a Gamma distribution. First, we computed the true multiple process capability index,CT , then estimate CT by three methods accordingly. Secondly, built up the confidence intervals for each method. Finally, compared coverage rates among all three methods. The simulation result shows that method 1 has the highest estimate CT and the smallest standard deviation among three ways. We also observed that the average value of estimated CT increases and estimated standard deviation decreases as sample size increases. From sensitivity analysis, we observed that increasing shape parameter of gamma distribution then the estimate of CT closes to true value CT with smaller sample size.

並列關鍵字

Process capability index ； Gamma distribution ； multiple characteristics

參考文獻

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