The Process Capability Index C_(pk) of the Weibull Distribution

Weibull分配下的C_(pk)製程能力指標

江俊佑(Jyun-You Chiang)；王帥(Shuai Wang)；秦燕(Yan Qin)；鄭茜(Xi Zheng)

The process capability indices ； Maximum likelihood estimate ； The Weibull distribution ； The Logistic distribution ； 製程能力指標 ； 極大似然估計 ； Weibull分配 ； Logistic分配

中國統計學報

58卷4期（2020 / 12 / 01）

312 - 326

英文

The process capability index is a simple method to quantify manufacturing capabilities. The traditional process capability index (PCI) requires data to follow normal distribution, but this assumption is not reasonable in practical applications. In this paper, we consider the problem of calculating the process capability index C_(pk) when the random variable follows the Weibull distribution. Monte Carlo simulation studies are conducted to evaluate the performance of the proposed capability index C_(pk). The results show that our proposed PCI results are very close to the target value and can obtain other additional process improvement information. Finally, the proposed method is applied to two data set.

製程能力指標是量化製造能力的一種簡單方法。傳統的製程能力指標要求資料服從常態分配，但這種假設在實際應用中可能無法滿足這個要求。本文研究了隨機變數服從Weibull分配時，過程能力指數C_(pk)的估計方法。經由蒙地卡羅模擬研究評估所提出的製程能力指數C_(pk)的表現，其結果表明，我們提出的C_(pk)結果與目標值非常接近，並且可以獲得其他額外的製程改進方向或訊息。最後，我們將該本篇提出的方法應用於兩個實際的問題中。

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