X_bar與R管制圖之聯合經濟模式應用在未知自相關過程上

The Joint Economic Design of X_bar and R Control Charts for Unknown Autocorrelated Processes

廖家葦(Jia-Wei Liao)

指導教授 ： 陳慧芬

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2011年)

https://doi.org/10.6840/cycu201100617

摘要

本論文研究探討X_bar與R管制圖的聯合經濟設計模式，我們假設品質特性測量值是假設製程分配為未知且服從自我相關的時間序列模式，且在製程管制狀態下的時間服從韋柏分配。當我們在設計經濟統計管制圖時，必須決定四個設計參數：樣本數、抽樣得間隔時間、 X_bar管制圖的管制圖的上下限因子k1及R管制圖的管制圖的上下限因子k2，在經濟設計下，這四個參數必須滿足期望單位時間成本最低。
在實際製程裡，並不是只有一種原因會使不良品發產生，若單單只用X_bar管制圖來監控製程，在實際的產線上並是合理的，因為在製程中也可能會發生變異數偏移，因此要同時利用X_bar與R管制圖來監控整個製程。本論文方法的建立以Pao 的成本模式為架構，其假設在製程中有這兩個可歸屬原因，其互為獨立，也就是說此兩個可歸屬原因可同時發生。我們將品質特性測量指標假設為分配未知，在實驗中假設階段ㄧ資料的品質特性為相關性服從ARTA (autoregressive to anything) with empirical分配，以此來建立經濟管制圖。
我們提出敏感度分析來研究在不同的自相關性上、不同平均值偏移程度和變異數偏移程度及不同的韋柏的參數(λ1, λ2)，對經由模擬實驗估計最佳的設計參數，並探討幾個例子對設計參數的影響，最後進行敏感度分析。

關鍵字

經濟性設計 ； ARTA ； X_bar與R管制圖 ； 自相關性

並列摘要

This thesis consider the economic design of X_bar and R control chart assuming that the quality characteristic measurement are autocorrelated time series and the in control time is Weibull. When designing a control chart, we should determine four parameters: the sample size n, sampling interval h, control limit factor k1 for X_bar chart and control limit factor k2 for R chart. In economic design, four parameters to satisfy the expected cost per hour is minimized.
In the real world, manufacture process is not only one cause to produce the fail products. If we only use X/_bar chart to detect, it is not reasonable. Because variance may change during manufacture process. Therefore, both X_bar and R charts are employed to monitor the variation in the process parameters simultaneously. In this thesis, our cost model is based on the framework of the Pao’s model. The cost model assumes that the process is subject to two independent assignable causes. In the other words, the two assignable causes can occur simultaneously. We assume quality characteristics measurement are unknown distribution. In the experiment, we assume phase I data is ARTA (autoregressive to anything) process with empirical distribution and use this data to establish economic control chart.
We find optimal parameters form difference autocorrelated, level of mean shifts, level of variance shifts and Weibull scale parameters λ1 and λ2. And study perform the sensitivity analysis that effect on the four optimal design parameters (n, h, k1, k2).

並列關鍵字

Economic Design ； ARTA (autoregressive to anything) ； X_bar and R control chart ； autocorrelated

參考文獻

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