以複式模擬法建構兩個製程能力指標CNpmk差異之信賴區間

Abstract

製程能力指標(Process Capability Indices, PCI)可以作為廠商間產品交易時的評估標準，以及工廠內部評估製程穩定度及產品良率之依據。至目前為止，學術界已發展了許多常態或非常態製程下之製程能力指標如：Cp、Cpk、Cpm、Cpmk、CNp、CNpk及CNpm等，其中Cp及Cpk為最早發展出來的製程能力指標，也是目前產業界最常使用的製程能力指標，但這兩個指標均未考慮到製程平均值偏移目標值的情形，而製程能力指標CNpmk不僅能同時反應製程良率及製程之期望損失，且當製程呈現非常態分配時，其偵測製程平均值偏移目標值的敏感度優於其他所有之製程能力指標，同時當製程分配為常態時，CNpmk指標之表現與常態製程下被譽為最有參考價值之製程能力指標Cpmk相同。但由於CNpmk指標之機率分配過於複雜，迄今尚未有學者能推導出其估計式之抽樣分配，因此其相關的假說檢定與信賴區間研究尚未被發展出來，導致CNpmk之應用價值受限。因此本研究之主要目的是針對兩個製程或兩供應商之CNpmk指標差異值，以一種藉由重複抽樣的複式模擬法（Bootstrap Simulation），來推導此差異值之信賴區間，並以此信賴區間來判斷哪一個製程或供應商擁有較佳的製程能力。本研究所推導之兩個CNpmk指標差異值之信賴區間在不同之非常態製程分配（均一、指數與珈瑪）及常態分配的模擬資料下，其有效性與敏感度分析均顯示估計績效良好且穩健。最後，本研究亦將建構此信賴區間的過程整理成一套簡易的操作程序，以供業界製程人員方便且快速的應用，並引用兩個業界實際製程資料來說明本研究方法之實務評估流程。

The process capability indices are utilized to evaluate a supplier’s general process capability. A larger process index value usually leads to a more capable production process, that is, more products will meet the specifications. However, conventional process capability indices can not accurately evaluate the performance of a non-normal distribution process. This inability would lead to an engineer making misleading when comparing processes or selecting an alternative material supplier. CNp,, CNpk,, CNpm and CNpmk which adopt Clements’ method are more efficient than conventional PCIs with non-normal distribution process, among the available process capability indices, CNpmk is the newest and most efficient index. Generally speaking, the probability distribution function of an estimated process capability index can develop the related hypotheses testing and confidence interval to accurately evaluate a certain process. However, the exact probability distribution of CNpmk is too complicated, only the approximate probability distribution of , which is the estimators of CNpmk, can be derived. Therefore, the main objective of this study is to utilize Bootstrap simulation method to construct confidence intervals for the difference between two CNpmk under a non-normal process distribution. The confidence interval of the difference between two CNpmk is utilized to compare two processes or select an alternative material supplier. A detailed procedure was written so that process engineers can construct the confidence interval of the difference between two CNpmk flexibly and efficiently. Finally, there were two real-world process data been employed to illustrate the effectiveness of the processed method.