用核密度估計建構階段I管制圖之研究

Abstract

大多數階段II 監控表現的評估與比較，都是假設管制狀態下的 參數已知；但實際上，是由階段I 蒐集的資料來估計參數再提供給階 段II 使用。當階段I 的資料不完全來自管制狀態下，可能會導致參數估計得不準確，造成階段II 無法正確判斷製程是否失控。所以，本文的研究目的是針對階段I 樣本中有部分樣本來自製程發生平均數偏移的情況，提供一個新方法來估計管制狀態下的分配之平均數，稱之為核密度估計法。從模擬結果可發現，使用核密度估計法所建構的管制圖之表現比傳統方法來得好，尤其當平均數偏移程度較大時，有更佳的表現。

When evaluating and/or comparing control chart, usually it is assumed that the in-control values of the parameters are known. In practice, control limits in Phase II process monitoring are often constructed using the parameter estimates obtained from Phase I analysis. When the Phase I data are not all from the in-control state, the estimated parameters is systematically biased. Consequently, the effectiveness of the control chart constructed based on these estimates is doubtful in Phase II process monitoring. The purpose of this paper is to propose a new method to estimate the in-control process mean based on kernel density estimator (KDE). Simulation studies show that the performance of the control chart constructed with kernel density estimator is better than that of conventional two methods, especially when the mean shift is large.