在給定先驗分配下最適計數值品質檢驗計畫之研究

A Study on Optimal Quality Inspection Plan of Attributes Under Given Prior Distribution

10.6220/joq.202308_30(4).0002

黃允成(Yun-Cheng Huang)；江旻倩(Min Qian Jiang)；張簡政利(Cheng-Li Chang Chien)

先驗機率 ； 最適抽樣個數 ； 最適容許不良品個數 ； priori probability ； optimal sample number ； optimal allowable number of defects

品質學報

30卷4期（2023 / 08 / 30）

281 - 308

繁體中文;英文

本研究應用統計理論建構進貨商之產品抽樣檢驗計畫決定機制，在母體不良率未知之情境下，分別採用連續均勻分配、貝他分配與常態分配為其先驗機率分配，樣本不良品個數則在各先驗機率下服從超幾何分配。以實務角度開發智慧型品質管制抽樣系統，並將多項成本之目標函數整合為單一指標，包含檢驗成本、外部損失成本與懲罰成本，以期望總品質成本最小化為目標，求解最適抽樣個數與最適容許不良品個數之組合。最後，透過模擬數據測試與分析，並進一步將各系統參數進行多變數之敏感度分析，以探討各系統參數對最適決策變數組合及期望總品質成本之影響。實證結果顯示，使用本研究所開發之智慧型品質管制抽樣系統，可找到使期望總品質成本最小化之最適抽樣個數與最適容許不良品個數之組合。

This study applies statistical theory to construct the decision mechanism of the product sampling inspection plan of the purchaser. In the context of unknown population defect rate, continuous uniform distribution, beta distribution, and normal allocation are used to allocate their priori probability. The number of defective products in the sample is subject to hypergeometric distribution at each prior probability. We will develop an intelligent quality management sampling system from a practical point of view and integrate the objective function of multiple costs to a single metric. It includes the inspection cost, external loss costs, and penalty costs, and targets the expected total quality cost minimization, to solve the combination of the optimal sampling number and the optimal allowable number of defects. In the end, through the simulation data test and analysis, and further analyze the sensitivity of each system parameter for multi-variable, we investigate the effect of various system parameters on the optimal decision-making variable combination and the expected total quality cost. Empirical results show that the intelligent quality management sampling system developed by this study can find the combination of the optimal sampling number and the optimal allowable number of defects in the situation of the expected total quality cost minimization.

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