多變異製程移動平均管制圖之統計經濟設計

Statistical-Economical Design of Moving-Average Control Charts with Multiple Assignable Causes

余豐榮(Fong-Jung Yu) ； 劉亮成(Liang-Cheng Liou) ； 黃開義(Kai-I Huang)

《科學與工程技術期刊》 3卷2期 (2007/06) Pp. 1-9

https://doi.org/10.7117/JSET.200706.0001

摘要

移動平均管制圖在偵測製程小變動時比Shewhart管制圖更有效率，使用上又比累積和管制圖簡單，因而在製程中也被考慮使用。管制圖之經濟設計可以降低管制圖之使用成本，然而經濟設計管制圖之統計特性並不理想。管制圖統計經濟設計模式，不僅可降低管制圖使用成本，並可使管制圖的型Ⅰ、型Ⅱ誤差在需求值以內，因而本研究乃探討製程多變異情況之移動平均管制圖統計經濟設計模型，以彌補純經濟設計之缺點，本統計經濟模式之建構，跨越僅以成本設計管制圖之生產者觀點，而可同時兼顧生產者與消費者需求。並以數值應用例說明模式之應用，數值應用例顯示，在增加些微成本下，確可兼顧型Ⅰ及型Ⅱ誤差需求。同時進行敏感度分析，以了解管制圖各參數之改變對管制圖產生的影響。

關鍵字

移動平均管制圖 ； 統計經濟設計 ； 敏感度分析

並列摘要

The economic design of a control chart insures that it has a lower cost in comparison with a Shewhart control chart. However, the economic design has certain weaknesses because it does not consider statistical properties such as type Ⅰ or type Ⅱ errors and average time to signal when selecting parameters for the chart. Considered by some to be simpler to implement than the CUSUM, a moving-average (MA) control chart is more effective than a Shewhart for detecting small process shifts. To improve the economic design, this research constructs a statistical-economic model to determine the optimal parameters of an MA control chart with multiple assignable causes. This completed model can meet the requirements of factories and customers. A numerical example is employed to demonstrate the function of the model. A numerical application also reveals that type Ⅰ and type Ⅱ errors can be considered simultaneously when there is a small increase in the cost of the control chart. Sensitivity analysis is also performed to determine the effects among parameters when implementing a statistical-economical model.

並列關鍵字

moving-average MA control chart ； statistical-economical design ； sensitivity analysis