An Investigation of Some Characteristics of Univariate and Multivariate Control Charts


Maravelakis Petros
Supervisor: I. Panaretos
 

CHAPTER 1
INTRODUCTION

 

CHAPTER 2

UNIVARIATE AND MULTIVARIATE CONTROL CHARTS

2.1 Introduction
2.2 The fundamental characteristics of a control chart
2.3 Univariate Shewhart Control Charts

    2.3.1 Control charts for the mean for data in subgroups

    2.3.2 Control charts for the variability for data in subgroups

    2.3.3 Control charts for individual data

    2.3.4 Control charts for Attributes

2.4 Cumultive Sum (CUSUM) Control Charts

    2.4.1 Optimality for the CUSUM

    2.4.2 Average Run Length (ARL)

    2.4.3 Fast Initial Response (FIR)

    2.4.4 CUSUM control chart for process variability

2.5 Exponentially Weighted Moving Average (EWMA) Control Chart

    2.5.1 EWMA control chart for the mean

    2.5.2 EWMA control chart for process variability

2.6 Multivariate Shewhart Control Charts

    2.6.1 Control Charts for the Process Mean (n>1)

    2.6.2 Control Charts for the Process Mean (n=1)

    2.6.3 Control Charts for Process Dispersion

    2.6.4  Multiattributes Control Charts

2.7 Multivariate CUSUM and EWMA Control Charts

    2.7.1 CUSUM Type Control Charts

    2.7.2 Multivariate Exponentially Weighted Moving Average Charts

 

CHAPTER 3
ESTIMATION EFFECT IN CONTROL CHARTS

3.1 Introduction

3.2 Estimation Effect in Univariate and Multivariate Shewhart Charts

   3.2.1 The S (Three Sigma) Control Chart

   3.2.2 The S (Probability Limits) Control Chart

   3.2.3 The X Chart for Monitoring Process Dispersion

   3.2.4 Discusion

3.3 Estimation Effect in the EWMA Chart

   

CHAPTER 4
NON-NORMALITY IN CONTROL CHARTS

4.1 Introduction

4.2 Non-Normality in Univariate and Multivariate Shewhart Charts

4.3 Non-Normality in Univariate and Multivariate EWMA Charts

   4.3.1 The EWMA control charts for monitoring the process mean

    4.3.2 The EWMA control charts for monitoring the process dispersion

    4.3.3 Methods of evaluating control charts performance and their computation

    4.3.4 Results

    4.3.5 Discussion

 

CHAPTER 5
IDENTIFICATION OF THE OUT OF CONTROL VARIABLE WHEN A MULTIVARIATE CONTROL CHART SIGNALS

5.1 Introduction

5.2 The Use of Univariate Control Charts

    5.2.1 Univariate Control Charts with Standard Contrlo Limits

    5.2.2 Using Univariate Contrlo Charts with Bonferroni Control Limits

    5.2.3 Hayter and Tsui's Interpretation Method

5.3 Using an Elliptical Control Region

5.4 Using T2 Decomposition

    5.4.1 Mason, Tracy and Young's T2 Decomposition

    5.4.2 Mason, Tracy and Young's Out-of-Control Variable Selection Algorithm

    5.4.3 Doganaksoy, Faltin and Tucker's Out-of-Control Variable Selection Algorithm

    5.4.4 Murphy's Out-o-Control Variable Forward Selection Algorithm

    5.4.5 Chua and Montgomery's Out-of-Control Variable Selection Method

    5.4.6 Roy's Interpretation Algorithm

    5.4.7 Timm's Interpretation Algorithm

    5.4.8 Contributors to a Multivariate SPC Chart Signal

    5.4.9 Cause-Selecting Control Chart

    5.4.10 Hawkin's Interpretation Method

    5.4.11 Minimax Control Chart

5.5 Using Principal Components

    5.5.1 Jackson's Approach

    5.5.2 Bivariate Control Chart for Paired Measuements

    5.5.3 Kourti's and MacGregor's Approach

5.6 New Method

    5.6.1 Covariance matrix with positive correlations

    5.6.2 Covariance matrix with positive and negative correlations

    5.6.3 Illustrative examples

    5.6.4 Further Investigation

    5.6.5 A Comparison

    5.6.6 A Graphical Technique

5.7 Graphical Techniques

    5.7.1 Multivariate Profile Charts

    5.7.2 Dynamic Biplots

 

CHAPTER 6
MEASUREMENT ERROR EFFECT IN CONTROL CHARTS

6.1 Introduction

6.2 Shewhart Control Charts and Measurement Error

    6.2.1 Measurement error effect on the joined X-R and X-S control charts

    6.2.2 Model with Covariates

6.3 EWMA Charts and Measurement Error

    6.3.1 The EWMA Chart Using Covariates

    6.3.2 Multiple measurements

    6.3.3 Linearly increasing variance

    6.3.4 ARL computations

    6.3.5 Effect of the measurement error

  

CHAPTER 7
CONCLUSIONS

REFERENCES