第三代製程能力指標cpmk之近似不偏估計量績效分析

Performance Analysis of Approximately Unbiased Estimator of Process Capability Index cpmk

宋陵姈(Ling-Ling Sung)

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

製程能力指標時常被用來衡量製程的表現。Pearn et al. (1992) 提出第三世代的指標Cpmk，此指標可以被用來評斷製程能力是否符合規格需求，並且能透過其估計量去估計真實Cpmk的數值。然而，因其估計量為偏誤的估計量，所以Pearn (2015) 提出了Cpmk的不偏估計量，但在實務上的應用，製程母體的平均數及標準差都未知，無法直接使用不偏估計量作為估計量，因此我們對該不偏估計量中的參數ξ進行估計，產生其近似不偏估計量。本篇論文先行評估近似不偏估計量的表現並應用四種有母數拔靴法方法及數學分析法去建構Cpmk的95%信賴區間下界，並比較這五種方法所產生的信賴下界涵蓋率及平均值。

關鍵字

常態製程 ； 製程能力指標 ； 近似不偏估計量 ； 信賴區間下界 ； 有母數拔靴法

並列摘要

The process capability indices (PCIs) have been proposed to measure manufacturing performance. Pearn et al.(1992) proposed Third-generation capability index Cpmk which is used in judging whether a process meets the capability requirement, and we can use natural estimator to estimate the actual Cpmk. However, the estimator is biased, Pearn (2015) proposed the unbiased estimator. In practice, since the process parameters mean and deviation are unknown, we estimate the parameter ξ and use the approximately unbiased estimator to estimate the actual Cpmk. In this thesis, we measure the performance of the approximately unbiased estimator. Then, we apply four parametric bootstrap methods, and analytical method to construct 95% lower confidence bounds. In addition, we compare the coverage rates and mean of the lower confidence bounds among the five methods.

並列關鍵字

process capability index ； approximately unbiased estimator ； lower confidence bound ； parametric bootstrap method

參考文獻

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