變異數不確定下計量型戴明抽樣檢驗模式之貝氏分析

Bayesian Analysis on the Deming’s Inspection Model by Variables under Normal Assumption with Unknown Variance

邵嘉瑀(Jia-Yu Shao)

指導教授 ： 徐旭昇

元智大學/工程學院/工業工程與管理學系/碩士(2002年)

摘要

由於產品的品質會直接影響企業獲得利潤及市場佔有率，實施檢驗計畫不僅可降低產品的不良率及減少損失成本；另一方面可提高產品的品質，建立商譽與增加產品在市場上的競爭力。
本論文提出一個計量型抽樣檢驗模式，適用於品質規格為一區間連續值的情況，以貝式決策分析方法為工具，最小損失成本為目標，來求得最佳抽樣檢驗計劃。研究模式假設情況是依據資料的分析，可以接受組件品質之測量值為常態分配，此分配之期望值是確定，但變異數是不確定，而對於檢驗資訊獲得組件品質變異數之驗前分配則採inverted gamma。研究模式考量組件之品質、檢驗成本以及組件裝配後可能發生產品失效成本，以辛普森3/8法則來計算數學模式中之積分值，並以Borland c++語言撰寫程式來執行模式之數學運算。最後，本研究對模式之相關參數做敏感度分析。並且在相同之條件下與計數型模式作比較。

關鍵字

貝氏決策分析 ； 計量型抽樣檢驗計劃 ； 計數型抽樣檢驗計劃

並列摘要

This thesis studies an extension of Deming’s model for inspection sampling in continuous distribution measurement. The model is useful when the quantitative measurements of components are normally distributed with known mean but unknown variance. We focus our attention on finding the optimal sample size that minimizes the expected total cost. The factors that influence the total cost include inspection cost, product failure cost, specification limits, lot size, and the uncertain variance. We develop a rectifying inspection model by variables that takes all those factors into consideration using the Bayesian method. Numerical analysis on how these factors influence the optimal sample size and the total cost of the model is presented. In addition, this model can be used to select the best supplier when the total cost of the product is the main concern of the producer. The results are also compared with the inspection model by attributes under the same probability distribution of the uncertain variance. The inspection model is encoded and it provides an alternative choice other than some inspection sampling plans by variables such as the ASQC Z1.9-1980 for the industry.

並列關鍵字

Bayesian Decision Analysis ； Sampling Plan by Variables ； Sampling Plan by Attributes

參考文獻

12.林世偉，「不可修復產品原料供應商之選擇─貝氏決策模式」，元智大學工業工程研究所碩士論文，1998年6月。

11.林鴻欽，「貝氏檢驗計劃之設計」，元智大學工業工程研究所碩士論文，1992年6月。

2.Barlow, R. E. and X. Zhang,” Bayesian Analysis of Inspection Sampling Procedures Discussed by Deming,” Journal of Statistical Planning and Inference, Vol.16, North-Holland, 1987.

5.Deming, W.E.,” Quality, Productivity, and Competitive Position,” Massachusetts Institute of Technology, Center for Advanced Engineering Study, Cambridge, MA, 1982.

6.Kaminsky, F. C. and K. R. Haberle,” Probability Distributions for the Deming Cost Models,” Journal of Quality Technology, Vol. 27, No. 4, pp.355-362, 1995.