An Economic-Statistical Design of (average)x Control Charts with Multiple Assignable Causes

多重失效平均值管制圖經濟統計設計

余豐榮(Fong-Jung Yu)；鄒慶士(Ching-Shih Tsou)；黃開義(Kai-I Huang)；Zhang Wu

統計製程管制 ； 平均值管制圖 ； 多重失效 ； 經濟設計 ； 統計經濟設計 ； SPC ； (average)x control chart ； multiple assignable causes ； economic design ； economic-statistical design

品質學報

17卷4期（2010 / 08 / 31）

327 - 338

英文

Duncan於1956年首先提出平均值管制圖經濟設計並證實經濟設計管制圖比傳統修華特管制圖有較低之品質成本。之後，有多位學者以成本之角度來探討管制圖之設計。經濟設計管制圖並未考量管制圖之統計特性，如型一或型二誤差及錯誤訊號平均出現之時間等。爲改善此一現象，單一失效之管制圖統計經濟設計已經被提出。然而，在實際製程中，通常有機械問題、材料變異、人爲錯誤等多重失效存在。爲較符合實際應用需求，本研究延伸單一失效爲多重失效，以建立平均值管制圖統計經濟設計模式。同時以數值案例說明模式之應用，並比較經濟設計與統計經濟設計之成本差異，且執行敏感度分析以了解設計參數對管制圖成本之影響。

Duncan first proposed the economic design of (average)x control charts in 1956 to control normal process means and ensure that an economic design control chart actually lowers the cost, compared with a Shewhart control chart. Many authors have studied the control charts from economic viewpoint from then on. An economic design does not consider the statistical properties, such as type I or type II error and average time to signal (ATS). To improve these issues, an economicstatistical design of control charts has been developed under the consideration of one assignable cause. However, there are multiple assignable causes in the real practice such as machine problem, material deviation, human errors, etc. In order to have a real application, this research will extend the original research from single to multiple assignable causes to establish an economic-statistical model of (average)x control chart. A numerical example is used to illustrate the performance of the proposed model and to compare the lost cost between the pure economic and economic-statistical control chart design. A sensitivity analysis is also conducted in this numerical example.

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