應用望想函數建構多變量管制圖

Abstract

現今許多產品功能複雜，需要多個品質特性才能衡量其品質之良窳。應用單變量管制圖(control chart)來監控具多個品質特性的產品時，需製作許多張管制圖來監控多個品質特性，不僅廢時且型一誤差會膨脹。Hotelling T^2管制圖可同時監控多個品質特性，但此管制圖在判斷哪個品質特性失控時，相當不便，尤其是品質個數很多時，此管制圖亦未考慮各品質的權重。因此，若能將多個品質特性整合成一個綜合指標，並考慮到各個品質的目標值及重要性，再製作一張管制圖來監控製程，當製程失控時即可快速找出造成製程失控之主要品質特性，以便立即改善，如此方能省下許多人力及時間。因此，本研究之主要目的是針對產品的多個品質特性和其重要程度，利用修正之望想函數(modified desirability function)公式將多個品質特性整合成一個綜合指標，再針對此綜合指標發展出一個管制圖來監控生產系統。本研究最後以模擬之半導體案例，來說明本研究方法確實有效可行。本研究所提出之方法來建構多品質管制圖(multivariable control chart)不僅可以節省建構多個單品質管制圖之人力成本，且可快速正確地找到需立即改善之重要品質。

Nowadays, the design of a product becomes complicated and needs more than one quality characteristic to measure the overall quality. Monitoring multi-response products with univariate control charts needs to construct many univariate control charts. It is not only wasting time but also increasing the type I error. Using Hotelling T^2 control charts to determine which quality characteristics are out of control is not easy especially when there are many quality characteristics. Therefore, the aim of this study is to integrate multiple quality characteristics into one composite index which comprehends the priority of each quality characteristic. Then a control chart is constructed to monitor the process for the composite index. It can easily be detected the main incontrollable quality characteristics when the situation occur out of control to save time and labour. Therefore, the main purpose of this study is to utilize the modified desirability function to integrate multiple responses into one composite index based on their priorities. Then a control chart is constructed for the composite index to monitor the system. Finally, a simulated case of a semiconductor is utilized to demonstrate the effectiveness of the proposed method. In order to save time and labour from constructing many univariate control charts of Hotelling T^2 control charts, industries can employ the proposed multivariate control charts to effectively monitor the product qualities.