製程能力指標估計式的分配與統計推論

Abstract

製程能力指標被設計用來量測製程的績效。事先訂定的產品規格界限與目標值，能夠藉由製程能力指標的值反應出該製程的良率、損失以及中心化的程度。目前，製程能力指標的研究有三個方向。其一為指標特性的研究；其二為指標估計式的研究；其三為指標的應用。關於指標估計式的研究，一般有兩個假設前題。其一為製程特徵服從常態分配；其二為製程特徵的母體平均值是未知的常數。本文針對目前被廣泛使用的三個基礎指標Cp，Ca與Cpk，分別在不同的製程條件(製程特徵不一定服從常態分配，製程特徵的母體平均值為隨機變數)下，研究其估計式的統計性質。本文的具體貢獻在於，將目前文獻上對指標估計式的研究條件予與放寬。以更接近真實製程的條件，研究指標估計式的分配並進行統計推論。本文的研究成果，有助於品管工程師對製程的監控與績效評估。

Process capability indices were designed to measure the performance of a process. The preset specification limits and target values can be passed by the values of capability indices to reflect process yields, process loss, and process centering. There were three areas on the development of process capability indices presently. The first one focused on the characteristics of capability indices. The second one focused on the estimators of capability indices. The third one focused on the application for the capability indices. There were two common assumptions with regard to the investigation on the estimators of capability indices. The process characteristic followed the normality assumption and the process mean was an unknown constant. In this dissertation, we investigated the statistical properties of the three widely used basic indices Cp, Ca, and Cpk under different process conditions (process characteristic do not follow the normality assumption and the process mean was a random variable). The concrete contributions of this dissertation were to ease the assumptions made in the previous efforts on the literature presently. The dissertation provided a more practical conditions for manufacturing processes on the investigation of the distributional and inferential properties of the estimated capability indices. The results in this dissertation will facilitate quality engineers on process monitor and performance assessment.