容許區間建構的 c 管制圖

Abstract

傳統的 c 管制圖通常是根據卜瓦松分佈的信賴區間來建構的管制圖。當監控分佈的參數已知時，現有的 c 管制圖有令人滿意的監控結果，然而，當此參數未知時，現有的 c 管制圖則會遭遇到型一誤差過大的缺點。我們在這研究論文中，提出利用卜瓦松分佈的容許區間來建構 c 管制圖。藉由統計模擬和實際資料的分析顯示，新的 c 管制圖在許多情況都優於現有的 c 管制圖。

In the previous studies, c charts are usually constructed by confidence intervals for the mean of a poisson distribution. When the mean is known, the existing c charts may lead to a satisfactory result, However, when the mean is unknown, the existing c charts suffer the drawback of large type I error. In this study, c charts based on tolerance intervals for the poisson distribution are proposed. A numerical study shows the proposed c charts outperform the existing ones.