臺灣博碩士論文加值系統

摘要
統計方法的運用在工業製程管制上扮演著重要的角色，這或許和戴明的倡導有關。而其中一種頗常用的統計方法是製程能力指標分析。在很多工業製程中，製程特性的集中趨勢和變異之量化是了解產品品質的主要依據。通常製程特性的平均數和標準差是衡量製程品質的兩個主要參數。若平均數和標準差未知則以樣本平均數和樣本標準差分別估計之，從實際的觀點來看，若在一個工廠中有數以百計的品質特性要管制，而樣本平均數和樣本標準差卻都帶者單位，這意味者樣本平均數和樣本標準差並不是便利的統計量。然而在製程能力指標的計算公式中，將平均數、標準差和工程規格都一起考慮，使得製程能力指標為無單位，因此製程能力指標為量化製程狀況之簡便易懂的溝通語言。

各種製程能力指標的運用普遍存在於日本、美國和其他國家的工業界。使用製程能力指標時，一般均假設樣本裡的量測值為互相獨立，然而這個假設未必為真，或許若把樣本裡的量測值假設為多變量隨機常態向量，可能來得更接近實際狀況。本論文運用文獻中的統計模式，對下列主題進行研究:

(1) 樣本的量測值存在著相關性對製程能力指標的影響;
(2) 當樣本的量測值存在著相關性時，製程能力指標的估計程序與其抽樣特性。

ABSTRACT
Statistical techniques applied to industrial process control have been revitalized due in part to effort by Deming. One of these techniques is the analysis of process capability indices. In many industrial processes, the quantification of process location and variation is central to under standing the quality of units produced form a manufacturing process. Usually the process mean and standard deviation are two important parameters to measure the process quality. From a practical view point sample mean and sample standard deviation ,which are the general estimator for process mean and standard deviation respectively,are not unitless and sometimes are not convenient summary statistics when hundreds of characteristics in a plant or supply base are considered. In many situations, capability indices can be used to relate the process mean and standard deviation to engineering
specifications that many include unilateral or bilateral tolerances with or without a target value. The resulting indices are unitless and provide a common and easily understood language for quantifying the performance of a process.

Various process capability indices have been applied to measure the process performance in Japan, U.S.A. and the other countries. In the applications of process capability indices, it is usually assumed that there is no correlation among the measurements within a sample, i.e., the measurements within a sample are independently distributed. However, in practice this assumption may not be tenable. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. The purposes of this project are:

(1)to investigate the effect correlation on the process capability indices, and
(2)To examine the uses of the process capability indices, along with their sampling properties and estimation procedures, when correlation within a sample exists.

目錄
頁次
中文摘要……………………………………………………………………i
英文摘要……………………………………………………………………ii
誌謝…………………………………………………………………………iii
目錄…………………………………………………………………………iv
表目錄………………………………………………………………………vi
圖目錄………………………………………………………………………viii

第一章 緒論…………………………………………………………………1
第二章 文獻回顧與探討……………………………………………………4
第三章 相關性製程能力指標Cp……………………………………………20
第四章 實例探討……………………………………………………………38
第五章 Cpk、Cpm和Cpmk的探討……………………………………………52
第六章 結論與未來研究方向………………………………………………64
參考文獻 ……………………………………………………………………66
附錄 …………………………………………………………………………69

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