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題名 | A Study on the Process Capability Index Cp for Correlated Data=相關性資料下製程能力指標Cp之研究 |
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作者 | 周昭宇; 江行全; 陳清信; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷期 | 23:2 1999.03[民88.03] |
頁次 | 頁319-329 |
分類號 | 440.8 |
關鍵詞 | 製程能力指標Cp; Process capability index; Correlation; Estimation; Hypothesis testing; Non-central chi-square distribution; |
語文 | 英文(English) |
中文摘要 | 統計方法的應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。製程能力指標為量化製程狀況之簡便 易懂的溝通語言。製程能力指標普遍應用於日本、美國和很多其他國家的工業界。在使用製 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常態隨機向量,可能來得更接近真實狀況。本文運用文獻 中的統計模式,對下列主題進行研究: (1)樣本裡的量測值存在著相關性對製程能力指標 Cp 的影響; (2)當樣本裡的量測值存在著相關性時,製程能力指標 Cp 的統計推論,包括估計與假設 檢定。 研究結果顯示:若忽略樣本裡量測值間的正相關效應,製程能力指標 Cp 將會被高估;然而 ,若忽略量測值間的負相關效應,則製程能力指標 Cp 將會被低估。 |
英文摘要 | Statistical techniques applied to industrial process control have been revitalized due in part to efforts by Demimg. One of these techniques is the analysis of process capability indices. Process capability 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 process performance in Japan, the 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 article are: (1) to investigate the effect correlation on the process capability index Cp, and (2) to present the uses of the process capability index Cp, along with its sampling property and estimation procedure, when correlation within a sample exists. From the study, it can be shown that the capability index Cp will be over-estimated if the effect of positive correlation is neglected, and that Cp will be under-estimated if the effect of negative correlation is ignored. |
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