應用品質損失函數於具多種可歸屬原因之平均值管制圖之經濟-統計性設計

Abstract

管制圖為統計製程管制(Statistical Process Control)中最重要的工具之一，其中最常被使用的管制圖為平均值管制圖，在使用平均值管制圖時必須先設定管制圖中三個參數(n、h、k)的值。目前已有中外文獻提出了適用於當製程中具有多種可歸屬原因的平均值管制圖之經濟性設計模式及經濟-統計性設計模式，藉由經濟性設計模式或經濟-統計性設計模式來設定最佳之(n、h、k)值。然而上述研究均未考慮到產品品質特性值之差異對顧客可能會造成不同的損失，因此，本研究應用田口之品質損失函數修正現有文獻所提出之經濟性設計模式或經濟-統計性設計模式之缺失，提出一個修正之經濟-統計性設計模式，並以基因演算法求解(n、h、k)的最佳設定值，最後再對本研究所提出之經濟-統計性設計模式中的參數進行敏感度分析。研究結果顯示如果品質損失是一個重要指標，則本研究所提出之經濟-統計性設計模式在單位時間的成本表現上較現有文獻所提出之方法為佳。在敏感度分析方面，製程平均值的單位偏移係數的改變對本研究所提出之經濟-統計性設計模式求解結果的影響最顯著。

Control Chart is one of the most important tools in statistical process control (SPC). Among many types of control charts, the most often used one is X bar chart. When using X bar chart, the values of sample size(n), sampling interval(h) and coefficient of control limit(k) must be determined. Some studies have developed the economic design and economic-statistical of X bar chart with multiple assignable causes in the process. The economic design or economic-statistical design can determine the optimal values of (n, h, k) with lowest cost. However, these methods did not consider that different values of a quality characteristic of a product may have different effects on customers’ loss. Therefore, this study proposes an revised economic-statistical design of X bar chart with multiple assignable causes in the process using Taguchi’s loss function. After constructing the economic-statistical design, genetic algorithm (GA) is utilized to determine the values of (n, h, k) in the proposed model and sensitivity analysis is carried out to study the effect of the parameters in the proposed model. The results showed that if quality loss is an important index, then the proposed economic-statistical design is better than the developed methods in previous studies in terms of total cost per unit time. Additionally, the most sensitive parameter of the proposed economic-statistical design is the amount of shift in means by certain assignable cause.