An Exponential GWMA Control Chart for Monitoring Interarrival Time

指數廣泛加權移動平均管制圖用於偵測稀有事件發生的間隔時間

10.6697/TBPJ.201212_6(1).0001

邱文智(Wen-Chih Chiu)；邱添彥(Tien-Yen Chiu)

指數加權移動平均 ； 廣泛加權移動平均 ； 管制圖 ； 田口損失函數 ； Exponential EWMA ； GWMA ； Control Charts ； Taguchi's Loss Function

臺灣企業績效學刊

6卷1期（2012 / 12 / 01）

1 - 25

英文

本文提出指數廣泛加權移動平均（exponential generally weighted moving average，指數GWMA）管制圖及指數雙重廣泛加權移動平均（exponential double GWMA，指數DGWMA）管制圖用於偵測稀有事件發生的間隔時間。指數GWMA管制圖乃管制指數分配的指數加權移動平均（exponentially weighted moving average，EWMA）管制圖的延伸。經由大量的模擬程序得到單邊指數GWMA及DGWMA管制圖的連串長度平均數及標準差（the average and the standard deviation of run lengths，ARL及SDRL），以用來選擇指數GWMA及DGWMA管制圖適當的設計參數及管制界限常數。基於以ARL為統計績效評估的基準及以田口損失函數（Taguchi's loss function）為整體經濟績效衡量的基準，顯示指數GWMA及DGWMA管制圖之績效比其他管制圖如Shewhart、EWMA及累積和（CUSUM）等指數管制圖為佳。

This study develops exponential generally weighted moving average (exponential GWMA) and exponential double GWMA (exponential DGWMA) control charts for monitoring the interarrival times of rare events. The exponential GWMA chart is an extension of the exponential EWMA chart. Via an extensive simulation procedure, the average and standard deviation of run lengths (ARL and SDRL) of one-sided exponential GWMA and DGWMA charts are obtained and employed to select the appropriate design parameters and control limit constant of exponential GWMA and DGWMA charts. Based on the statistical performance evaluated by the ARL criterion and the overall economical performance measured by Taguchi's loss function, the exponential GWMA and DGWMA charts are proven to be superior to other control charts, including exponential Shewhart-type, EWMA, and CUSUM charts.

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