在可靠度分析的領域中，許多電子與機械產品時常使用韋伯分佈來描述其
失效時間。在過去有許多監控韋伯分佈參數的相關管制圖研究，本文的主要目
的則是希望利用無母數管制圖來對韋伯迴歸模型製程做監控。我們利用Zou,
Wang 和Tsung (2012) 所提出的空間秩EWMA 管制圖來對製程做監控，並透
過統計模擬將其監控效率與傳統的多變量EWMA 管制圖做比較。同時我們也
討論如何對製程的改變點做估計，來找出製程剛開始失控的時間點，以及如何
進行各個製程參數是否偏移的診斷。最後我們舉了一個絕緣材料的實際例子來
展示如何將兩個管制圖運用在監控韋伯迴歸模型製程上。

In the domain of reliability analysis, many electronic and mechanical products
often use the Weibull distribution to describe their failure times. In the past, there
are a lot of research related to control charts that monitor the Weibull distribution
parameters. The main purpose of this article is to use a nonparametric control
chart to monitor the Weibull regression model process. We use the spatial rank
EWMA chart proposed by Zou, Wang and Tsung (2012) to monitor the process
and compare its efficiency with that of the traditional multivariate EWMA chart.
At the same time, we also discuss how to estimate the process change point and
identify which parameters have changed in the process when an out-of-control
signal has been triggered by the control chart. Finally, we use an example from
a insulating material process to demonstrate the applicability of the control chart
for monitoring Weibull regression model process.

參考文獻
[1] Faraz, A., Saniga, E. M. and Heuchenne, C. (2015).“Shewhart control charts for monitoring reliability with Weibull lifetimes.”Quality and Reliability Engineering International, 31(8), pp. 1565-1574.
[2] Guo, B. and Wang, B. X. (2014).“Control charts for monitoring the Weibull shape parameter based on type-II censored sample.”Quality and Reliability Engineering International, 30(1), pp. 13-24.
[3] Lowry, C. A., Woodall, W. H. , Champ, C. W. and Rigdon, S. E. (1992).“A multivariate exponentially weighted moving average control chart.”Technometrics, 34(1), pp. 46-53
[4] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data., John Wiley and Sons Inc.
[5] Pascual, F. (2010).“EWMA charts for the Weibull shape parameter.”Journal of Quality Technology, 42(4), pp. 400–416.
[6] Pascual, F. and Li, S. (2012).“Monitoring the Weibull shape parameter by control charts for the sample range of type II censored data.”Quality and Reliability Engineering International, 28(2), pp. 233-246.
[7] Pascual, F., Yang, S. and Ye, M. (2017).“Monitoring Weibull quantiles by EWMA charts based on a pivotal quantity conditioned on ancillary statistics.” Quality and Reliability Engineering International, 33(1), pp. 103-119.
[8] Shewart, W. A. (1924)“. Some application of statistical methods to the analysis of physical and engineering data.”Bell System Technical Journal, 3(1), pp. 43-87.
[9] Zou, C. , Wang, Z. and Tsung, F. (2012).“A spatial rank-based multivariate EWMA control chart.”Naval Research Logistics, 59, pp. 91-110.