隨著經濟不斷的發展與進步，商品市場的需求漸趨多元，廠商彼此之間的競爭愈來愈激烈，為了滿足客戶多元的需求，採用多等級製程的生產方式成為廠商製造產品的一種策略。Doganaksoy, Schmee, and Vandeven (1996)提出使用EWMA管制圖監控多等級產品製程的方法，利用合併資料之EWMA管制圖可以更快速地偵測出同時影響所有等級產品品質特性之非機遇因素是否發生。但是他們並沒有考慮到管制圖的經濟層面，因此本文主要探討如何由經濟觀點設計EWMA管制圖以監控生產多等級產品的製程。

本研究所探討之多等級產品製程可生產二個等級產品。在同時影響所有等級產品品質特性之非機遇因素不存在的情況下，我們擴展Banerjee and Rahim(1987)的更新理論方法，建立了二個獨立的EWMA經濟管制圖；另外我們還討論管制圖在統計層面的表現，即以平均連串長度(ARL)為統計上的限制式，仿照經濟設計的做法，建立了二個獨立的EWMA經濟統計管制圖，並和經濟設計的結果做比較。最後我們考慮同時影響所有等級產品品質特性之非機遇因素發生在製程的情況下，擴展更新理論方法建立三個EWMA經濟管制圖以追蹤此製程狀態，文末並以例子說明如何使用EWMA經濟管制圖以監控多等級產品製程。

在資料分析方面，本研究考慮32組製程與成本參數組合，透過最佳化技巧找出EWMA經濟及經濟統計管制圖之最低成本及最佳設計參數組合。再利用敏感度分析，我們可以得知重要的製程與成本參數為何。這些訊息可做為製程工程師決策參考之用。

With the progress of the economic of the world and the various demands of the consumers, there is a new strategy to product with multiple product grades. Doganaskoy, Schmee, and Vandeven(1996) had provided a method of using a combined exponentially weighted moving average (EWMA) control charts that allow speedy detection of assignable causes affecting all grades. But this control scheme is not designed from economic viewpoint. In this paper we will discuss how to construct an economic model for the EWMA control chart to monitor the process with multiple product grades.

We discuss the process with two product grades. We expand the renewal theory method proposed by Banaerjee and Rahim (1987) to construct two independent economic EWMA control charts to monitor the process with two product grades. Besides, we also present a statistically constrained economic model of the EWMA control chart, subject to statistical constraints on average run length (ARL). If the assignable cause affecting all grades does exist, we also construct the three economic EWMA control charts by expanding the renewal theory approach. Finally, we illustrate how to use the economic EWMA control chart to monitor the process.

In data analysis, 32 combinations of the cost and process parameters are considered. The minimum cost and the optimal design parameters of economical and economic statistical EWMA control charts are determined by using optimal techniques. Sensitivity analyses show the significant cost and process parameters.

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