以複式模擬法構建兩個製程能力指標Spmk差異值之信賴區間

Abstract

製程能力指標是指在排除所有造成製程不穩定的非機遇性因素後，製程處於統計管制狀態下之實際能力，可幫助廠商瞭解本身產品製程之穩定度及產品良率，亦可作為廠商之間產品交易或議價依據。至目前為止，學術界已發展出許多常態或非常態製程下的製程能力指標如：Cp、Cpk、Cpm、Cpmk、CNp、CNpk、CNpm、CNpmk及Spmk等，其中Cp和Cpk由於觀念簡單且易於計算，已成為目前業界最常使用的製程能力指標。而製程能力指標Spmk，不僅適用於任何製程母體，並且能同時反映製程變異、製程平均偏離目標值所造成的期望損失，且與製程良率呈現一對一的關係，比Cp、Cpk、Cpm和Cpmk更具實用價值。但在利用製程能力指標Spmk來評選兩個製程（或供應商）的製程能力時，由於指標之機率分配過於複雜，迄今未能推導出其相關的統計假說檢定或信賴區間，因此無法發展出檢定兩個製程能力指標Spmk是否有差異的統計檢定程序。本研究之主要目的即是以複式模擬法（Bootstrap Simulation）來建構兩個製程能力指標Spmk差異值之100（1-α）%信賴區間，然後以此信賴區間取代統計檢定程序來評估兩個製程（或供應商）製程能力之優劣。本研究亦將此信賴區間建構流程撰寫成簡單之應用流程，以供業界沒有太多統計背景之工程人員使用，藉以增加本研究方法之實用性。

The process capability indices（PCIs）are utilized to evaluate a manufacturer’s general process capability. A large process index value usually implies to a capable production process, that is, most products will meet the specifications. Among many developed process capability indices, Cp and Cpk are two most popular indices adopted by industry, but Cp and Cpk can only be utilized in a normal process. The process capability index Spmk can be applied to any process distributions since this index simultaneously takes into account the process variation and the effect of process mean deviating from its target value. Furthermore, the value of process capability index Spmk agrees with the process yield. Therefore, the index Spmk is more efficient than Cp and Cpk. However, the exact probability distribution of Spmk is too complicated to be derived, consequently, the related hypothesis testing and confidence interval cannot be developed. The main objective of this study is to utilize Bootstrap simulation method to construct confidence interval for the difference between two process capability indices, Spmk1 - Spmk2. The proposed Bootstrap interval for Spmk1 - Spmk can be effectively utilized to compare two processes. A detailed procedure of constructing the confidence interval for Spmk1 - Spmk2 is also provided by this study for engineers without much statistics background.