Sampling Design of Group Decision with Uniform Random Censoring

均勻隨機設限下之集體決策的抽樣設計

10.6338/JDA.200812_3(6).0004

林玉彬(Yu-Pin Lin)

指數分配 ； 抽樣計劃 ； 多項式損失函數 ； 集體決策 ； 均勻隨機設限 ； Exponential Distribution ； Sampling Plan ； Polynomial Loss Function ； Group Decision ； Uniform Random Censoring

Journal of Data Analysis

3卷6期（2008 / 12 / 01）

47 - 63

英文

產品的品質不僅影響市場的銷售，也影響著企業的形象和利潤。對於抽樣計劃中，決策者對於有關參數之事前分配多採共軛事前分配，對此確實解決不少問題。但從企業經營須不斷提升的觀點而言，為提昇決策品質而採「集體決策」，為一可行的方法。因為決策時，若能整合更多專家的意見，對決策品質的提昇必有所助益。本研究利用均勻設限資料下的貝氏抽樣設計模型，將其引入集體決策的觀念，決策者根據以往的經驗或對未來的預測，即其對產品的特性，有事先的認知，則此決策群由K個專家所組成，則整合此K個專家之認知後，可獲得有關此抽樣計劃中所涉及之參數之事前分配，進而利用貝氏統計分析法，推演出具有事後分配觀點的決策準則，亦即推導出允收或拒收該產品的決策準則，並據以推導出其最佳抽樣大小、決策準則的檢測風險成本模型。最後利用數值分析法，求其最適解。

Quality control of products is essential to the manufacturers since it directly affects the market sale and the profits of the manufacturers. Decision-makers assume that the prior distribution of parameters is conjugate prior distribution. From this point of view, it is effective and efficient to make a ”group decision” for running a business. Based on the above requirement, we derive the sampling inspection plan with the group decision under the Bayesian framework. Assuming one decision group is composed of k experts, and the parameters involved in the sampling inspection plans are random variables. Using a suitable loss function, a Bayesian variable sampling plan is derived. Then, we calculate Bayes risk values related to our loss function and we obtain the most optimal sample size n. Then we try to understand the decision-making behavior under minimum Bayes risk by simulating the related decision.

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