雙重廣泛加權移動平均管制圖用於偵測卜瓦松分配觀測值

Monitoring Poisson Observations Using Double GWMA Control Charts

10.6697/TBPJ.201006_3(2).0002

邱文智(Wen-Chih Chiu)；邱添彥(Tien-Yen Chiu)

EWMA ； GWMA ； 平均連串長度ARL ； 卜瓦松分配 ； EWMA ； GWMA ； average run length ARL ； Poisson distributions

臺灣企業績效學刊

3卷2期（2010 / 06 / 01）

183 - 206

繁體中文

本文提出一新的管制圖，名為「卜瓦松雙重廣泛加權移動平均(Poisson double generally weighted moving average, PDGWMA)管制圖」，用於偵測卜瓦松分配觀測值。使用模擬程序，評估PDGWMA管制圖的統計績效並與舒華特(Shewhart)c、卜瓦松EWMA(PEWMA)、卜瓦松GWMA(PGWMA)、卜瓦松雙重EWMA(PDEWMA)等管制圖比較，顯示PDGWMA管制圖在大部分情況比其他管制圖在製程平均數出現偏移時能更快的偵測出信號來。PDEWMA管制圖是PDGWMA管制圖的特例；以及PDGWMA管制圖的下管制界限通常是正的，可改善c管制圖下管制界限可能為零且沒作用之缺點。因此，PDGWMA管制圖不但在品質變壞（平均數向上偏移）時可易偵測出，品質改善（平均數向下偏移）時也同樣可易偵測出，此點對一個先進的生產系統是很重要的。

This article develops a novel control chart called ”Poisson double GWMA (PDGWMA) chart” for monitoring Poisson-distributed processes. Using simulation, the statistical performance of PDGWMA chart is evaluated and compared with those of other control charts including Shewhart c, Poisson EWMA, Poisson GWMA and Poisson double EWMA (PDEWMA). It is showed that this chart is always more sensitive than other control charts in detecting an out-of-control signal. The PDGWMA chart is a generalized model for which the PDEWMA chart is a special case, and its lower control limit is usually positive, while that of c chart is zero and can’t function. Consequently, not only the quality deterioration (upward shift) but also the quality improvement (downward shift) can be detected agilely, which is important to a modern advanced system.

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