動態加權下貝氏逐次抽樣之研究

本文針對破壞性檢驗或高檢驗成本之產品檢驗進行研究，在考量檢驗成本及因抽樣誤差所造成之誤判損失成本情況下，建立一適當之數學分析模式。由於母體不良率未知，因此本文利用動態加權平均的概念對母體不良率進行估計，求得母體不良率之後驗機率，並建構一期望總損失成本函數，經由電腦數值模擬分析，找出使總損失成本最小化之最適抽樣檢驗個數。此外，再運用逐次抽樣檢驗方法，在每一逐次抽樣中，決定是否停止抽樣或繼續抽樣，據此建構出可使期望總損失成本最小化之逐次抽樣決策圖。本文列舉一數值範例進行驗證，並提出三點具體結論以供後續研究與實務應用之參考。

關鍵字

抽樣檢驗；逐次抽樣；貝氏估計法；動態加權平均

並列摘要

In this paper, we focus our attention on sample size for destructive inspection, and under the considerations of inspection cost and cost of sampling error. This paper built a mathematical model to determine the optimal sample size to minimize the total expected cost. Because the population defective rate is unknown, therefore this paper applied dynamic weighted average method to estimate the population parameter. We can find out the posterior probability density function for defective rate of population, and set up an expected total losses function to search for the optimal solution. Applying computerized numerical analysis method, we can find out the optimal sample size that minimizes the total losses. Furthermore, we used the concept of sequential sampling, then we draw a sample and inspect it in each sequential observation to determine whether to stop sampling and then making decision or not, and the decision chart for sequential sampling is constructed. Finally, three conclusions are drawn for future studies and practical applications.