具有多項異常原因之 X-bar管制圖經濟設計

Abstract

本論文主要研究製程異常原因發生為多項異常原因之 X ̅ 管制圖經濟設計。研究中製程生產方式分為斷續工件生產及連續流動生產兩種；製程失效機構則考慮指數分配與韋氏分配兩種。根據生產方式及製程失效機構，在論文中共提出二項研究主題：(1)連續流動生產且製程失效機構屬指數分配之 X ̅ 管制圖經濟設計，(2)斷續生產且製程失效機構屬韋氏分配之 X ̅ 管制圖經濟設計。 對於這兩種經濟設計模式，我們利用抽樣方法和成本結構來建構損失成本函數，並在損失成本最小化下來找尋最佳的 (樣本大小)， (抽樣間隔時間)， (管制界限係數)。由於經濟設計模式進行敏感度研究，可以提供管理者或工程師了解輸入參數對模式的影響。因此，我們也將對最佳的 , , 值進行敏感度分析，藉此分析來了解時間參數或成本參數的變動後，對於最佳 , , 值之影響。最後，我們有提供數值結果並討論之。 除此之外，我們將對多項異常原因下僅一個異常發生之模式和多項異常原因下有二個異常發生之模式進行比較分析，藉由數值結果可以得知考慮多項異常原因下有二個異常發生之模式對於降低品質成本和增加其在斷續生產之競爭力是有一個有用的方法。

In this dissertation, we analyze the economic design of -control charts and extend the model for the case of multiple assignable causes to allow for the second occurrence of an assignable cause following the first occurrence. In addition, two process failure mechanisms are investigated in different manufacturing environments. One is the Exponential failure mechanism in a continuous flow process and another is the Weibull failure mechanism in a discrete part process. For those two models, the expected loss-cost functions are established by the sampling scheme and cost structure. Optimal values of the economic design parameters including the sampling size( ), the sampling intervals ( ) and control limit coefficient ( ) are determined by minimizing loss-cost functions. Because of sensitivity investigation on the model with critical input parameters may provide some answers for the model analyst. A sensitivity analysis is provided to discuss how the model can be affected by the time parameters or cost parameters in the investigated model. For illustration purpose, numerical results are also presented. Subsequently, we perform comparative analysis between the model that once an assignable cause occurs, no further assignable causes will occur and the modified model that allow for the second occurrence of an assignable cause following the first occurrence. Our numerical investigations showed that a modified model should be helpful in reducing the quality cost and increasing competitiveness in a discrete part process.