由對稱型分位向量建造品質管制圖及Bootstrap方法在分位向量之應用

Abstract

由於樣本的對稱型分為向量具有變異數較小之有效性性質, 我們將這 個分位向 量應用在品質管制圖上。我們並用模擬分析來證明用樣本對稱 型分位向量來辨別分 配是否有改變的效果是比一般的分位向量來得好。 接著我們考慮在實務上如何在一般的分位向量和對稱型分位向量之間做選 取。 我們建議使用Bootstrap這個技巧, 在一般分位向量和對稱型分位 向量兩者間選取 近似變異數較小者, 並和理論值加以比較, 證明 Bootstrap這個選取技巧是可行的。 Due to the efficiency of the symmetric sample quantile, we apply the symmetric sample quantile for constructing the control chart, where we prove that in detection of distributional shift, the one based on the symmetric sample quantile performed relatively more efficient than the one based ordinary sample quantile. Then we consider the problem of selecting the one from the ordinary sample quantile and the symmetric sample quantile. We propose the bootstrapping technique selecting the one with smaller estimator of asymptotic variance. We also compare the result through this technique with the theoretic correct one. This shows that bootstrapping technique is applicable.