製程能力指標

Abstract

製程能力指標(Process capability indices (PCIs)研究的主要目是希望 能藉由一個指標的數值便能衡量出製程的能力與績效，並了解一個製程的 產品規格是否能滿足工程師所制定的界限規格。有許多製程能力指標的研 究出現在品管及統計的文獻裡，而大部份的研究均假設產品的品質特性服 從常態分配。在本文的第一章，我們回顧了對稱規格區間情況下的一些現 有指標。在本文的第二章，當規格區間為非對稱情況下，我們回顧了一些 現有指標，並提出了一個新類形的指標來處理非對稱規格區間。藉由製程 良率、製程集中目標值程度及一個製程特性來比較這個新類形指標與現有 指標，結果發現這個新類形指標優於這些現有指標。在本文的第三章，當 規格區間為對稱情況下，我們探討了一些現有指標估計式的統計性質。同 時相對於 Bissell 對製程平均數 m 的假設，我們提出了一個 Cpk 的新 估計式，只要在這個新估計式增加一個調整項 bf，便可得到 Cpk 的不偏 估計式，而且其變異數比 Bissell 的估計式及自然估計式的變異數小。 因此，這個新的不偏估計式使我們能更準確的用 Cpk 來評估製程能力。 在本文的第四章，我們探討了新類形指標估計式的統計性質。在本文的第 五章，對於非常態皮爾森母體，我們探討了 Clements 的對四個指標 Cp, Cpk, Cpm, 與 Cpmk 的估算方法，同時提出一個新的估算方法。我們 以對稱規格區間的例子做比較，發現新的估算方法能分辨製程是否偏離目 標值但 Clements 的 估算方法卻不能，所以說新的估算方法優於 Clements 的估算方法。 Process capability indices (PCIs), whose initial purpose is to provide a numerical measure on whether a production process is capable of producing items within the specification limits preset by the designer. In chapter 1, we review several existing process capability indices with symmetric tolerances. In chapter 2, we review several existing process capability indices and proposed a new class of capability indices to handle processes with asymmetric tolerances. The proposed new indices are compared with the existing PCIs in terms of process yield, process centering, and other process characteristics. The results indicated that the new indices are superior to the existing capability indices. In chapter 3, we investigate the statistical properties of the estimators of the several existing process capability indices with symmetric tolerances. In addition, we considered a new (Bayesian-like) estimator Cpk to relax Bissell's assumption on the process mean. It can be showed that by adding a well-known correction factor bf to the new estimator, we obtained an unbiased estimator of Cpk whose standard deviation is smaller than those given in Bissell (1990) and Kotz, Pearn and Johnson (1993). The variability reduction of the estimator provides a greater reliability in current practices of using Cpk to monitor process quality. In chapter 4, we investigate the statistical properties of the natural estimators of the new class of capability indices. In chapter 5, we first investigated Clements' method for calculating the estimators of the four capability indices, Cp, Cpk, Cpm, and Cpmk for non-normal Pearsonian populations. Then, we considered a new estimating method to calculate estimators of the four capability indices for non-normal Pearsonian populations. The analysis showed that the estimators calculated from the proposed new method can differentiate on-target processes from off-target processes better than those obtained by applying Clements'method.