應用基因演算法於相依性累積合格品數管制圖之多目標統計設計

The application of genetic algorithm to the statistical design with multi-objective of cumulative count of conforming chart

陳琬昕(Wan-Hsin Chen)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/碩士(2011年)

摘要

近年來，計數值管制圖之發展著重於事件時間間隔管制圖(time-between-events, TBE 管制圖) 之研究，此種管制圖特別適用於不合格率或缺點率很低的高產出製程。TBE 管制圖因其統計特性之需求，一般皆採用機率界限。本研究所使用之累積合格品數管制圖 (cumulative counts of conforming chart, CCC 管制圖) 為 TBE 管制圖的一種，用以監控高產出製程的不合格率變化。而 CCC-r 管制圖為 CCC 管制圖之延伸，可有效提高管制圖偵測製程偏移之靈敏度。過去研究大多僅探討獨立性之高產出製程，但在實際製程中，產品間通常存在相依性，故學者提出相依性 CCC-r 管制圖。然而，此管制圖具有 ARL-biased 之缺點，且當製程處於統計管制外時，其平均連串長度相當高，使管制圖無法快速發出製程異常之警訊。且當相依程度愈大則要選擇 r 愈大之管制圖，造成使用上的不便。
本研究考慮三種統計特性，將管制圖之統計設計轉換為最佳化搜尋問題。由於機率界限並不像傳統 k 倍標準差界限容易求得，在此情況下若又要符合統計特性則更難以計算，故本研究以基因演算法尋找符合統計特性之最佳管制界限。過去之統計設計大多為單一目標最佳化，而本研究則是採用多目標最佳化設計，並提出將多目標式納入基因演算法中存活篩選的求解過程之方法。本研究分別以平均連串長度與平均檢驗個數作為績效評估指標，研究結果顯示統計設計可有效提升相依性 CCC-r 管制圖之偵測績效，同時也突破原本相依性之限制範圍，提供一個更有效率的管制方法來監控高產出製程。

關鍵字

累積合格品數管制圖 ； 基因演算法 ； 多目標統計設計

並列摘要

Time-between-events charts (TBE charts) are suitable in monitoring a high-yield process. The Cumulative Count of Conforming chart (CCC chart), one of the TBE chart, is studied in this research. The CCC-r chart is an extension and improvement of the CCC chart. Generally, it is assumed that the production process follows an independent and identically distributed Bernoulli pattern. However, the production of the conforming item may be serially dependent in practical manufacturing. The serially dependent CCC-r chart was developed to monitor processes with high quality and serial dependence. However, average run length (ARL) of this chart is too long to alarm in time that the process is out-of-control. Moreover, this chart shows an ARL-biased property. In this study, we propose statistical designs to derive modified control limit for the serially dependent CCC-r chart that can decrease ARL when process is out-of-control and produce ARL-unbiased performance.
We consider three statistical criteria transformed into multi-objective optimizations to improve the performance of the serially dependent CCC-r chart. The purpose of this study is to investigate how to choose values of probability limits with multi-objective optimization using genetic algorithm (GA) in order that the serially dependent CCC-r chart meets the statistical criteria in different statistical designs. ARL and average number inspected (ANI) are used to evaluate the chart’s performance in different designs. The control schemes proposed in this study provide more effective alternatives for monitoring the modern manufacturing production processes, especially in high-yield processes.

並列關鍵字

CCC-r chart ； genetic algorithm ； multi-objective statistic design

參考文獻

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