
系統識別號 
U00260407201300562300 
論文名稱(中文) 
各種指數加權移動平均多變量管制圖偵測能力之比較研究

論文名稱(英文) 
A Comparative Study on the Detecting Performance for Various EWMAtype Multivariate Control Charts 
校院名稱 
成功大學 
系所名稱(中) 
統計學系碩博士班 
系所名稱(英) 
Department of Statistics 
學年度 
101 
學期 
2 
出版年 
102 
研究生(中文) 
錢柏維 
研究生(英文) 
BoWei Chien 
學號 
R26001100 
學位類別 
碩士 
語文別 
英文 
論文頁數 
47頁 
口試委員 
指導教授潘浙楠 口試委員鄭春生 口試委員溫敏杰 口試委員鄭順林

中文關鍵字 
同時監控平均與變異指數加權移動平均多變量管制圖
指數加權移動平均
平均連串長度

英文關鍵字 
EWMAtype multivariate control chart for simultaneously monitoring mean and variability
Multivariate exponentially weighted moving average (MEWMA)
Average run length (ARL)

學科別分類 

中文摘要 
在實際使用管制圖監控製程時，通常呈管制狀態下的製程參數為未知，因此在試用第一階段欲取得穩定狀態下之資料以估計製程參數，並以此估計量做為製程參數。由於多變量管制圖在監控製程之第二階段會受到第一階段樣本數大小的影響，故已有多位學者探討第一階段下多變量管制圖樣本數大小之決定與管制界線之制定。然而前大多數文獻中只著重於偵測平均數研究，尚未有學者針對各種同時監控平均與變異之指數加權移動平均(EWMA)之多變量管制圖進行比較研究。由於大多數同時監控平均與變異之指數加權移動平均多變量管制圖均建立在製程參數已知下。因此，本研究乃針對Chen et al. (2005)所提出的MaxMEWMA管制圖之缺點進行修正，並提出參數未知時，以統計估計量修正MaxMEWMA管制圖的RMaxMEWMA管制圖，再與其他學者所提出之指數加權移動平均多變量管制圖進行比較與分析。藉由模擬結果證實，當第一階段樣本的組數(m)較小時，本研究所提出之修正後的多變量(RMaxMEWMA)管制圖其平均連串長度在穩定與失控狀態下在大多數情況均優於現有的管制圖。

英文摘要 
When implementing a multivariate control chart, incontrol parameters of the process are usually unknown in practice. Thus, we need to estimate incontrol parameters using incontrol data set from Phase I analysis and replace these parameters with their estimates. Moreover, the detecting performance of multivariate control charts in Phase II is affected by number of samples in Phase I. Several authors have dealt with this problem for process mean, but most previous studies did not compare the effect of parameter estimates on the detecting performance of various EWMAtype multivariate control charts in Phase II for simultaneously monitoring mean and variability, and the test statistics of these EWMAtype multivariate control charts are established when parameters are known. In this paper, we propose a RMaxMEWMA control chart in which the unknown incontrol parameters are replaced by their estimates based on Chen’s MaxMEWMA control chart. Then, the detecting performances of our RMaxMEWMA and other EWMAtype multivariate control charts are compared. The simulation results show that RMaxMEWMA chart outperforms the other EWMAtype multivariate control charts in terms of incontrol and outofcontrol ARLs when number of samples is small.

論文目次 
Contents
1. Introduction: Motivation and Research Objectives 1
2. Mathematical notations and definitions 3
3. Review of the pertinent multivariate control charts 5
3.1. Combined EWMA Mchart and EWMA Vchart 6
3.2. MaxEWMA chart 8
3.3. Combined chart and chart 11
3.4. ELR control chart 13
4. Development of RMaxMEWMA Charts 16
5. Comparison of the detecting performance for RMaxMEWMA and Other
Multivariate Control Charts 20
5.1. Simulation procedure 20
5.2. Incontrol performance 23
5.3. Determining the minimum number of samples 31
5.4. Outofcontrol performance 36
6. Conclusions and Future works 43
References 45
List of Tables
Table 1. A summary of the characteristics for various multivariate EWMA control charts 15
Table 2. The upper control limit value that produces an overall incontrol ARL of 200 for various control charts under different p = 2, n=5 and λ=0.1, 0.2 when number of samples approaches infinity. 21
Table 3. The upper control limit value that produces an overall incontrol ARL of 200 for various control charts under different p (p = 3, 4), n=5 and λ=0.1, 0.2 when number of samples approaches infinity. 22
Table 4. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=2, n=5, λ=0.1. 25
Table 5. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=3, n=5, λ=0.1. 26
Table 6. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=4, n=5, λ=0.1. 27
Table 7. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=2, n=5, λ=0.2. 28
Table 8. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=3, n=5, λ=0.2. 29
Table 9. The simulation results of incontrol ARL and SDRL for the various multivariate control charts with p=4, n=5, λ=0.2. 30
Table 10. Minimum numbers of samples required for various multivariate control charts under p=2 35
Table 11. Minimum numbers of samples required for various multivariate control charts under p=3, 4 35
Table 12. The simulation results of outofcontrol ARL for the various multivariate control charts under m=300, p=2, n=5,λ=0.1 given the incontrol ARL=200 when number of samples approaches infinity 37
Table 13. The simulation results of outofcontrol ARL for the various multivariate control charts under m=300, p=2, n=5,λ=0.2 given the incontrol ARL=200 when number of samples approaches infinity 38
Table 14. The simulation results of outofcontrol ARL for the various multivariate control charts under m=300, p=3, n=5,λ=0.1 given the incontrol ARL=200 when number of samples approaches infinity 40
Table 15. The simulation results of outofcontrol ARL for the various multivariate control charts under m=300, p=3, n=5,λ=0.2 given the incontrol ARL=200 when number of samples approaches infinity 41
List of Figures
Figure 1. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts under p=2, n=5, . 31
Figure 2. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts under p=3, n=5, . 32
Figure 3. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts based on p=4, n=5, . 32
Figure 4. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts under p=2, n=5, . 33
Figure 5. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts under p=3, n=5, . 33
Figure 6. The relationship between incontrol ARLs and different numbers of samples (m) for various multivariate control charts under p=4, n=5, . 34

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