製程能力指標Cpk估計方法之比較

Abstract

製程能力指標Cpk被視為高科技製造產業中用來衡量製程或產品品質最普遍的指標之一。主要解決多重工製造產業之製程能力量測與評估等問題並進行處理與分析，進而提昇產品品質以達超低不良率之品質要求。對於製程能力之量測與評估，指標Cpk提供了製程良率的信賴下界之重要訊息，因此被業界廣泛應用且被認為是一個可信度極高的尺度標準。為了正確地估計與準確地推論製程能力指標Cpk，許多文獻分別以傳統頻率學派與貝氏方法等觀點，進行製程能力之分析與推論。對業者而言，信賴下界可以提供最低之製程能力的重要資訊，對於品質工程師在監控製程與評估製程之績效，可提供製程或產品之品質保證，以提高顧客滿意度之服務水準。另外，樣本大小之決定對於能否掌握品質特性之關鍵亦是另一個需要探討的主題，相對來說，在在影響到資料收集過程中成本之提昇。本篇論文主要的目的是以傳統頻率學派與貝氏方法等觀點來比較Cpk之信賴下界，並且略述其優點與缺點，以及點出適用的情況與重要發現。並從實務的觀點出發，同時考慮信賴下界之績效，我們以各樣本下推薦適用的信賴下界得以準確地估計與推論製程能力指標Cpk。最後，我們以一個現實生活中晶圓電阻器製程的例子作結。

Process capability index Cpk has been the most popular one used in the manufacturing industry dealing with problems of measuring reproduction capability of processes to enhance product development with very low fraction of defectives (in Parts Per Million; PPM). The index Cpk provides a lower bound on the process yield, a widely recognized criterion for measuring process capability. To properly estimate and accurately infer of the capability index, numerous methods of the Frequentist and the Bayesian perspectives are proposed. In the manufacturing industry, lower confidence bound estimates the minimum process capability providing pivotal information to quality engineers on monitoring the process and assessing process performance for quality assurance. The sample size determination on key quality characteristics is also an important subject directly related to the cost of data gathered procedure. The main objective of this paper is to compare and contrast the lower confidence bounds on Cpk using two approaches, Frequentist and Bayesian approaches, and to outline correspondent advantages and disadvantages of the methods and the keynotes of the applicable discoveries. From practical point of view, we tabulate the accurate and proper lower bound for given n based on the consideration of the performance of lower confidence bounds as sample size n in the fulfillment of capability assessment. A real-world example taken from a MELF resistor manufacturing process is investigated to illustrate the applicability of the proposed approach.