類別資料混合先驗分配之經驗貝氏製程監控技術

Abstract

在此篇論文中，首先對在製程控制下的先驗分配提出一個由兩個成份組成的混合先驗有母數族。然後在可以得到製程控制下所產生的某些類別資料時，提出一個經驗貝氏的方法。接著提出一個例子來解釋此經驗貝氏模型。為了建構模型，我們討論此經驗貝氏模型之配適度和簡化。利用概似比的方法，提出貝氏和經驗貝氏製程監控技術來作為本篇論文的主要目的。最後藉由平均連串長度來研究此製程監控技術的表現。

In the paper, first, a two-components mixture prior parametric family for the in-control prior distribution is proposed in a manufacturing process. Then an empirical Bayes approach is proposed when there are available in-control categorical data generated from the manufacturing process. As an illustration, an example of the proposed empirical Bayes model is introduced. For the purpose of model building, the goodness of fit and the simplification of the proposed model are discussed. Utilizing the likelihood ratio method, both Bayesian and empirical Bayes monitoring techniques are proposed as the main purpose of the paper. Finally, the performance of the proposed process monitoring scheme is studied in terms of the average run length to show the robustness of the methodology.