臺灣博碩士論文加值系統

在這篇論文中，發表了三種新型管制圖用於監控完全資料和型II設限資料的韋伯低百分位。通過把韋伯分佈轉換成最小極值分佈，Pascaul et al. (2017)發表了一種新型的EWMA管制圖，稱之為基於條件與輔助統計量的樞紐量的EWMA-SEV-Q管製圖。延伸這個想法來創建一種CUSUM管製圖，稱之為CUSUM-SEV-Q。也提供了關於監控統計量更深入的探討。此外，通過把韋伯分佈轉換為標準常態分佈，發表了EWMA和CUSUM管製圖，分別稱之為EWMA-YP和CUSUM-YP，用來監控完全資料的韋伯百分位。在完全資料，通過比較ARL，EWMA-YP和CUSUM-YP管製圖表現優於EWMA-SEV-Q和CUSUM-SEV-Q管製圖。在設限資料，EWMA-SEV-Q表現優於CUSUM-SEV-Q。兩個數值案例用來描繪所發表管制圖的實際應用。

In this paper, we propose three new control charts for monitoring the lower Weibull percentiles under complete data and Type-II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al. (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA-SEV-Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM-SEV-Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA-YP and CUSUM-YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA-YP and CUSUM-YP control charts perform better than the EWMA-SEV-Q and CUSUM-SEV-Q control charts in terms of average run length (ARL). In Type-II censoring, the EWMA-SEV-Q chart is slightly better than the CUSUM-SEV-Q chart in terms of ARL. Two numerical examples are used to illustrate the applications of the proposed control charts.

Table of content
摘要 i
Abstract ii
Acknowledgement iii
Table of content iv
List of figures v
List of tables vi
Chapter 1: Introduction 1
Chapter 2: Literature review 4
Chapter 3: Research methods 7
3.1 Existing control charts 7
3.1.1 Weibull percentiles 7
3.1.2 Existing control charts for complete data and Type-II censoring 9
3.2 Three new controls 14
3.2.1 A new control chart for complete data and Type-II censoring 14
3.2.2 Two new control charts for complete data 14
3.3 Computing the ARLs of the four control charts 16
3.4 Optimal design parameters for EWMA-SEV-Q and CUSUM-SEV-Q control charts 16
Chapter 4: Comparison study 20
4.1 Computation of control limits 20
4.2 ARL comparison 20
Chapter 5: Numerical examples 27
Chapter 6: Conclusion 27
References 33
Appendix 33

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