第二階段自我相關一般線性輪廓的監控方法

Phase II monitoring schemes for autocorrelated general linear profiles

賴韻如(Yun-Ju Lai)

指導教授 ： 王藝華

淡江大學/商管學院/統計學系碩士班/碩士(2017年)

https://doi.org/10.6846/TKU.2017.00516

摘要

近年來，有些產品品質的好壞或製程是否穩定不再只是利用產品或製程的品質特徵是否滿足某個品質特徵的分配來判斷，而是藉由資料是否滿足某個函數關係來判斷，這種類型的資料稱為輪廓資料，而監控此種資料的過程則稱為輪廓監控。在過去的文獻中，通常假設製程的觀察值在不同時間之下具有相同且彼此獨立的常態分配，但是許多設備或系統的連續性製程會使得模型的隨機誤差項具有相關性。因此在本文中，考慮在第二階段一般線性輪廓模型，且輪廓間具有一階自我相關時，我們提出新的監控方法並與舊有的方法做比較。由模擬的結果可以得到，本文提出的 MEWMA (multivariate exponentially weighted moving average) 監控方法比舊有的方法好。最後會透過一個例子來說明如何實際應用本文所提出的監控方法。

關鍵字

第二階段 ； MEWMA管制圖 ； 輪廓監控 ； 一階自我相關

並列摘要

Recently, for some applications, the quality of a process or product cannot be represented by a distribution of a quality characteristic but better characterized and summarized by a functional relationship. This kind of data is called a profile. Profile monitoring is to check the stability of this relationship over time. In the
literature, it is often assumed that the error terms of models are independent and identically normally distributed. However, in some applications, there is an autocorrelation between the error terms due to continuous processes. Thus, general linear profiles with a first
order autocorrelation between profiles in Phase II are considered in this study. We propose new monitor schemes for this profile data and compare with existing monitor schemes. By the simulation results, our proposed MEWMA (multivariate exponentially weighted moving average) scheme has better performance than the existing monitor schemes. Finally, an example is used to illustrate the applicability of the proposed scheme.

並列關鍵字

Phase II ； MEWMA control chart ； Profile monitoring ； First order autocorrelation

參考文獻

黃婉瑄 (2015). 第二階段自我相關線性輪廓的監控方法. 淡江大學統計所碩士學位論文.

Amiri, A., Jensen, W. A., and Kazemzadeh, R. B. (2010). A Case Study on Monitoring Polynomial Profiles in the Automotive Industry. Quality and Reliability Engineering

International, 26, pp. 509-520.

Amiri, A., Koosha, M., Azhdari, A., and Wang, G. (2015). Phase I monitoring of generalized linear model-based regression profiles. Journal of Statistical Computation and Simulation, 85, pp. 2839-2859.

Cano, J., Moguerza, J. M., Psarakis, S., and Yannacopoulos, A. N. (2015). Using statistical shape theory for the monitoring of nonlinear profiles. Applied Stochastic Models in Business and Industry, 31, pp. 160-177.