Estimation of the Change Point of a Gamma Process by Using the S Control Chart and MLE

使用S管制圖及MLE法以估計GAMMA製程改變點之研究

10.29977/JCIIE.200605.0004

邵曰仁(Yuehjen E. Shao)；侯家鼎(Chia-Ding Hou)；王雪如(Hsueh-Ju Wang)

改變點 ； gamma製程 ； 最大概似估計 ； 蒙地卡羅 ； S管制圖 ； change point ； gamma process ； maximum likelihood estimation ； Monte Carlo ； S chart

工業工程學刊

23卷3期（2006 / 05 / 01）

207 - 214

英文

製程人員向來是持續地改善製程，而改善製程的必要步驟之一，即是有效地辨識出製程產生干擾時的改變點或啓始點。不同於傳統常態製程假設，本文探討當製程服從Gamma分配時，如何使用S管制圖及最大概似估計法，以估計此gamma製程的改變點，本文將應用蒙地卡羅技術以決定S管制圖之管制上下限；同時，本文將展示研究方法之優異成果。

The process personnel always seeks the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. Different from the traditional normally distributed assumption for a process, this study considers a process which follows a gamma distribution. This study proposes an effective approach to estimate the change point of a gamma process. The proposed approach combines the commonly used S control chart with the maximum likelihood (ML) technique. This study applies the Monte Carlo technique to determine the upper and lower control limits for a gamma process when the S control chart is used to monitor a gamma process. The fruitful results with the use of the proposed approach are also demonstrated.

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