兩個多品質特性製程能力指標Cpm* 差異的複式信賴區間之構建

Abstract

製程能力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。製程能力指標則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之依據。至目前為止，學術界已發展出許多常態或非常態製程及多品質特性製程下的製程能力指標。在眾多的指標當中，單變量製程能力指標的發展已趨成熟，而多品質特性的製程能力指標還在持續的發展中，其中多品質特性製程能力指標 是所有多品質製程能力指標中估計值最準確的指標，但在利用多品質製程能力指標Cpm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Cpm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）來建構兩個多變量製程能力指標Cpm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）能力之優劣。本研究亦將此信賴區間建構流程撰寫成應用流程，並以實例說明其使用方法，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 widely used to evaluate a manufacturer’s general process capability. PCIs are generally defined as the ratio of the allowable tolerance of a quality characteristic to the actual process performance. Furthermore, the quality of many products is usually determined by more than one characteristic. Univariate indices are not adequate for assessing the capability of processes with multiple characteristics. Among all developed multivariate process capabilities, index has the most accurate estimation of Cpm. takes into account both the ratio of the tolerance region to the process region and the probability of nonconforming product. However, the exact probability distribution of 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 of two process capability indices, Cpm1 - Cpm2. The proposed Bootstrap interval for Cpm1-Cpm2 can be effectively utilized to compare two multivariate processes. A simplified procedure of constructing the confidence interval for Cpm1 -Cpm2 is also provided by this study for engineers without much Statistics background.