從經濟觀點設計X-bar管制圖--製程失效機構屬韋氏分配(Weibull)

The Design of X-bar Control Chart from Economic Viewpoint--With a Weibull Distributed Failure Mechanism

楊義明(Yang Yit-Ming)

指導教授 ： 陳雲岫博士

元智大學/工程學院/工業工程與管理學系/博士(2001年)

摘要

摘要
本論文在探討製程失效機構屬韋氏分配之管制圖經濟設計，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 ; 製程異常原因之發生則考慮單一異常原因與多項異常原因兩項。根據生產方式及異常原因發生之時機，在論文中共提出三項研究主題 : (1) 斷續生產 管制圖之經濟設計，(2) 連續流動生產 管制圖之經濟設計，及(3) 個別值移動平均值管制圖之經濟設計。當製程失效機構屬韋氏分配時，其失效率會隨生產時間愈長而愈大，導致抽樣頻率也隨製程之生產時間愈長而增加，故本研究所推導出之經濟設計模式，具有可變動之抽樣間隔時間。論文中根據不同之成本因素、時間因素與韋氏分配參數，在損失成本最小化下，可求得最佳化經濟設計參數，包括樣本大小( )，變動抽樣間隔時間( ) 及管制界限寬度( )。
本研究所進行之分析涵蓋三項 : (1) 改變不同之韋氏分配參數( 為尺度(scale) 參數， 為形狀 (shape) 參數)探討損失成本之變化，得到在相同失效時間下， 愈大損失成本愈小 ; 在 固定下， 愈大損失成本愈大 ; 及在 固定下， 愈大損失成本愈大。(2) 在相同失效成本下，比較單一異常原因與多項異常原因之經濟設計模式，得到 =1下(指數分配) 單一異常原因與多項異常原因之損失成本並無顯著差異，但隨著 愈大，單一異常原因之損失成本則比多項異常原因大的多。(3) 成本因素與時間因素改變，對損失成本影響之敏感度分析，其中管制狀態下與非管制狀態下之生產成本對損失成本具有高敏感度，而消除異常原因之成本、尋找false alarm 之成本與時間則具有相當低之敏感性。
目前管制圖之經濟設計，因具有複雜之數學模式且因各項時間、成本參數值不易估計等因素，在實務上較少使用，但是只要改善生產環境，將經濟設計方法逐步簡化，其次加強使用著瞭解經濟設計之價值，未來在電腦程式及套裝軟體之製作與使用下，簡化使用者之運用步驟，相信管制圖之經濟設計將可成為未來製程管制之新趨勢。

關鍵字

管制圖經濟設計 ； 韋氏衝擊模式 ； 異常原因 ； 斷續工件生產 ； 連續流動生產

並列摘要

Abstract
We consider an economic design of control charts with a Weibull distributed process failure mechanism in a process when there are possible single assignable cause or multiple assignable causes。There are three different topics considered in this thesis: (1) economic design of control charts in a discrete part process，(2) economic design of control charts in a continuous flow process，and (3) economic design of single observation in a moving average control chart。When the process failure mechanism follows a Weibull model having a increasing failure rate，the sampling frequency is tendency to be increased with the age of the system。 A cost model based on the variable sampling intervals，as opposed to fixed sampling intervals， is formulated and analyzed。 Optimal values of the economic design parameters including the sampling size ( )，the variable sampling intervals ( ) and control limit width ( ) are determined by minimizing loss-cost model based on the varieties of combinations of cost factors and Weibull parameters。The performance of the loss-cost with various Weibull parameters is studies，comparisons between a multiplicity-causes model and a single-cause model are performed under both having same time to failure，a sensitivity analysis is performed to illustrate the effects of incorrectly estimating the cost factors of the proposed models。
There are three major discovery from the numerical and sensitivity analysis。(1) Based on the same mean failure times，higher value of shape parameter ( ) results lower loss-cost。If shape parameter is fixed，larger scale parameter ( ) gives larger loss-cost，vice verso，if scale parameter is fixed，larger shape parameter gives larger loss- cost。(2) Based on the same loss cost，there is no significant difference between single assignable cause and multiple assignable cause model when =1 ( that is exponential distribution )，while as increases，loss cost increases in the single assignable cause model than in the multiple assignable cause model。(3) Loss cost will be affected significantly on the production cost either in control state or out of control state ; However，there is litter affection on the loss cost and time on the costs in discovering and removing causes and finding false alarms。
In practice，the application of economic design is still not popular due to the complex of the mathematical models，difficult to determine the cost parameters and hard to measure time factors。If we can improve production environment，simplify economic design model，enhance the value of usage of economic design and provide friendly interfaces between economic design commercial softwares and users，then economic design of control charts can play an important role in the process control in future time。

並列關鍵字

Economic Design of Control Chart ； Weibull Shock Model ； Assignable Cause ； Discrete Part Process ； Continuous Flow Process

參考文獻

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