本論文對單一觀測值建立監控製程變異之適應性多變量指數加權移動平均管制圖。
此一管制圖有助於針對製程變異提早發出警訊。並在模擬研究下, 我們利用數值分析法
找出不同條件下之最佳管制圖參數。相較於目前文獻中的方法, 數值分析的結果顯示,
本論文建議的管制圖可以有較佳的錯誤預警效果。

Based on an adaptive adjustment, this thesis provides a multivariate expo-
nentially weighted moving average control chart with individual observations.
This chart is used for monitoring shifts on process variances or correlation.
A computation procedure is give to determine the chart parameters. More-
over, some of these parameters are tabulated. Numerical results show that the
proposed variances or correlation with shorter average run lengths to alarm
out-of-control signals.

Contents
1 Introduction 1
2 Literature Review 6
3 The Adaptive MEWMA Control Chart 10
4 Numerical Study 16
5 Conclusions 42
List of Tables
4.1 The values of L for different combinations of r and v when p=2 and
ARL0=200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 The values of L for different combinations of r and v when p=2 and
ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 The values of L for different combinations of r and v when p=2 and
ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 The values of L for different combinations of r and v when p=3 and
ARL0=200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.5 The values of L for different combinations of r and v when p=3 and
ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.6 The values of L for different combinations of r and v when p=3 and
ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.7 The values of L for different combinations of r and v when p=5 and
ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.8 The values of L for different combinations of r and v when p=5 and
ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.9 The values of L for different combinations of r and v when p=10 and
ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.10 The values of L for different combinations of r and v when p=10 and
ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.11 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 29
4.12 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 30
4.13 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 31
4.14 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 32
4.15 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 33
4.16 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 34
4.17 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 35
4.18 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 36
4.19 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 37
4.20 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 38
4.21 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 39
4.22 Performance comparison for various multivariate control charts with p = 2. 40
4.23 Performance comparison for various multivariate control charts with p = 2
and only q shifts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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