在監控產品壽命的資料時，我們常以韋伯分佈來描述其失效時間。在現有
文獻中大多在探討如何個別監控韋伯分佈的形狀參數和尺度參數。在本文中我
們會利用兩個現有的舒華特管制圖的監控統計量，建構出能同時監控韋伯分佈
雙參數的 EWMA 管制圖及 AEWMA 管制圖，並且將變動抽樣區間的概念應用
到這兩個管制圖上，同時我們使用統計模擬的方式來評估管制圖效率的表現。
最後我們舉了一個碳纖維拉扯強度的資料來說明在實際上如何運用與執行我們
所提出的管制圖。

When monitoring the lifetime data of the products, we often use Weibull distribution to represent the failure time. There are a lot of literatures studying
how to monitor the shape parameter and the scale parameter, individually. In
this article, we use two existing charting statistics of Shewhart-type control charts
to develop the EWMA and AEWMA control charts for monitoring the shape
and scale parameters simultaneously. In addition, we propose the EWMA and
AEWMA control charts using the concept of varible sampling intervals. We use
simulation to evaluate the performance of our purposed control charts. Finally,
we use a breaking strength example from a carbon fiber process to demonstrate
the applicability of the proposed control schemes.

第一章 緒論 1
1.1 管制圖的簡介 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的與動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第二章 監控韋伯分佈的雙參數 3
2.1 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 監控韋伯分佈雙參數的 EWMA 管制圖 . . . . . . . . . . . . . . . . 4
2.2.1 固定抽樣區間管制圖 . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 變動抽樣區間管制圖 . . . . . . . . . . . . . . . . . . . . . . 6
2.3 調適的 EWMA 變動抽樣區間管制圖 . . . . . . . . . . . . . . . . . 8
第三章 管制圖的比較 12
3.1 管制界限與警戒界限 . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 管制界限 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.2 警戒界限 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 管制圖效率比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
第四章 實例分析 20
第五章 結論與後續研究 23
參考文獻 24
附表 26
附圖 46

[1] 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.
[2] Guo, B., Wang, B. X. and Xie, M. (2014).“ARL-unbiased control charts for
the monitoring of exponentially distributed characteristics based on type-II
censored samples.”Journal of Statistical Computation and Simulation, 84(12),
pp. 2734–2747.
[3] Haq A, Gulzar R, Khoo, M. B. C. (2018). “An efficient adaptive EWMA control chart for monitoring the process mean.”Quality and Reliability Engineering
International, 34(4), pp. 563-571.
[4] Haq A. (2018). “A new adaptive EWMA control chart for monitoring the
process dispersion.”Quality and Reliability Engineering International, 34(5),
pp. 846-857.
[5] Padgett, W. and Spurrier, J. D. (1990).“Shewhart-type charts for percentiles
of strength distributions.”Journal of Quality Technology, 22(4), pp. 283-288.
[6] Page, E. S. (1954).“Continuous inspection schemes.”Biometrics, 41(1/2), pp.
100-115.
[7] Pascual, F. (2010).“EWMA charts for the Weibull shape parameter.”Journal
of Quality Technology, 42(4), pp. 400–416.
[8] 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.
[9] Reynolds, M. R., Amin, R. W. and Arnold, J. C. (1990).“CUSUM charts with
variable sampling intervals.”Technometrics, 32(4), pp. 371-384.
[10] Roberts, S. W. (1959). “Control chart test based on geometric moving averages.”Technometrics, 1(3), pp. 234-250.
[11] Saccucci, M. S. and Lucas, J. M. (1990).“Exponentially weighted moving
average control schemes: properties and enhancements.”Technometrics, 32(1),
pp. 1-12.
[12] 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
[13] Zhang, C. W., Ye, Z. and Xie, M. (2017).“Monitoring the shape parameter of
a Weibull renewal process.”IISE Transactions, 49(8), pp. 800-813.