Optimal Process Mean and Quality Investment Settings Under the Single Rectifying Inspection Plan With Producer's Risk

單次選剔檢驗計畫考量生產者風險之最佳製程平均數與品質投資設定

10.6220/joq.202408_31(4).0001

Chung-Ho Chen(陳忠和)

process mean ； quality investment ； single rectifying sampling inspection plan ； producer's risk ； 製程平均數 ； 品質投資 ； 單次選剔檢驗計畫 ； 生產者風險

品質學報

31卷4期（2024 / 08 / 30）

223 - 232

英文;繁體中文

In this paper, the author proposes the joint determination of process mean and quality investment by considering the maximum of expected total profit per unit for single rectifying sampling inspection plan with producer's risk. The lower specification limit of product is considered and the quality characteristic is normally distributed. Model I with unknown process mean and known process standard deviation is addressed and the declining exponential reduction of process standard deviation is the function of quality investment. Model II with known process mean and known process standard deviation is considered and the declining exponential reduction of process mean and process standard deviation is the function of quality investment. This work is an extension of economic design for the parameters of sampling plan and statistical process control. Numerical example and sensitivity analysis of some parameters will be provided for illustration.

本研究考量具生產者風險的單次選剔檢驗計畫在單位產品平均利潤最大的情況下來獲取最佳製程平均數與品質投資設定，本研究基於常態品質特性並考量產品具規格下限。模式I係假設品質特性有未知的製程平均數與已知的製程標準差，而品質投資函數為製程標準差的指數遞減函數；至於模式II係假設品質特性有已知的製程平均數與已知的製程標準差，而品質投資函數分別為製程平均數與製程標準差的指數遞減函數。本研究為延伸的抽樣計畫參數與統計製程管制經濟設計方法，最後本研究將舉一數值例子並進行相關參數的敏感度分析加以說明。