非對稱規格製程能力指標Cpk"的近似不偏估計式之績效分析

Performance Analysis of the Approximately Unbiased Estimator of Process Capability Index Cpk"

陳孟薰(Meng-Hsun Chen)

指導教授 ： 彭文理

國立交通大學/管理學院/工業工程與管理系所/碩士(2018年)

摘要

製程能力指標被製造業廣廣泛用來量化製程之表現。Pearn 和 Chen (1998)提出製程能力指標Cpk的新推廣，稱為Cpk"，用以衡量非對稱規格區間下的製程能力。然而在Cpk"的不偏估計式內，存在一個未知的母體參數ξ。因此在此論文的第一部分我們對ξ進行估計，估計後便可以得到Cpk"的近似不偏估計式，並且我們針對Cpk"的近似不偏估計式進行績效分析。此論文的第二部分，我們使用電腦軟體MatLab 並且應用有母數複式抽樣法和數學分析法去建構信賴區間下界。再者，我們比較有母數複式抽樣法和數學分析法兩者信賴區間下界的涵蓋率及平均值。

關鍵字

製程能力指標 ； 非對稱規格區間 ； 不偏估計式 ； 近似不偏估計式 ； 有母數複式抽樣法 ； 信賴下界

並列摘要

The process capability indices (PCIs) are extensively used in the manufacturing industry to provide quantitative measures on process performance. For asymmetric tolerances processes, Pearn and Chen (1998) proposed a new generalization of process capability index Cpk, called Cpk". However, the unbiased estimator of Cpk" has unknown parameter ξ inside. In the first part of this thesis, we estimate the ξ to obtain the approximately unbiased estimator of Cpk" and analyze its performance. In the second part, we applied the parametric bootstrap method and analytical method to construct the lower confidence bound by MatLab computer programing. Furthermore, we compare the coverage rates and mean of lower confidence bound between the parametric bootstrap method and analytical method.

並列關鍵字

Process capability index ； asymmetric tolerances ； unbiased estimator ； approximately unbiased estimator ； parametric bootstrap ； lower confidence bound

參考文獻

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