CONTRIBUTIONS TO STATISTICAL METHODS OF PROCESS MONITORING AND ADJUSTMENT VIJAY KUMAR BUTTE A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 ACKNOWLEDGEMENTS First and foremost, I want to thank my advisor Professor Tang Loon Ching. I consider it as an honor to be his student. I thank him for his time and insightful guidance. His enthusiasm for research has been motivational for me during my PhD pursuit. He has positively influenced me in many ways. I admire him as a human being and continue to take him as my role model. I am deeply indebted to all Department of Industrial & Systems Engineering faculty members who imparted precious knowledge through teaching and discussions. I also would like to express my appreciation to all my past teachers. I would like to thank my lab mates in Simulation lab and friends from other labs for their support and friendship. I would like to thank support staff from ISE, librarians and support staff from other departments who helped in one or other way. My deepest gratitude goes to my parents for their love and support throughout my life. I am indebted to my mother and my father for their care and love. I have no suitable word that can fully describe their sacrifices and everlasting love to me. I also would like to thank my brothers for all the emotional support and valuable friendship. I would like to thank all my friends for the jolly company and cherishable memories. I would like to convey my earnest gratefulness to National University of Singapore for offering an ideal environment for my research. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS . ii  SUMMARY . v  LIST OF FIGURES . vii  LIST OF TABLES xi  Chapter . 1  INTRODUCTION 1  1.1 INTRODUCTION 1  1.2 STATISTICAL PROCESS ADJUSTMENT 2  1.2.1 Feedback Adjustment for Processes with Measurement Delay . 3  1.2.2 Multivariate Statistical Process Adjustment Integrating Monitoring & Control 5  1.2.3 Process Adjustment under Disturbance Uncertainty . 6  1.3 STATISTICAL PROCESS MONITORING 7  1.3.1 Multivariate Statistical Process Monitoring . 8  1.3.2 Profile Monitoring . 10  1.4 THESIS STRUCTURE . 13  Chapter . 15  ENGINEERING PROCESS CONTROL: A REVIEW 15  2.1 INTRODUCTION 15  2.1.1 Process control in product and process industries . 15  2.1.2 Need for Complementing EPC-SPC 17  2.1.3 Early Arguments against Process Adjustments and Contradictions . 19  2.2 STOCHASTIC MODELS 21  2.2.1 Time Series Modeling for Process Disturbances . 21  2.2.2 Stochastic Model Building . 24  2.2.3 ARIMA (0 1): Integrated Moving Average 26  i 2.3 OPTIMAL FEEDBACK CONTROLLERS . 28  2.3.1 Economic Aspects of EPC . 34  2.3.2 Bounded Feedback Adjustment . 36  2.3.3 Bounded Feedback Adjustment Short Production Runs . 36  2.4 SETUP ADJUSTMENT PROBLEM . 38  2.5 RUN TO RUN PROCESS CONTROL 40  2.5.1 EWMA Controllers 40  2.5.2 Double EWMA Controllers . 44  2.5.3 Run To Run Control For Short Production Runs 47  2.5.4 Related Research 48  2.6 SPC AND EPC AS COMPLEMENTARY TOOLS 49  Chapter . 52  FEEDBACK ADJUSTMENT FOR PROCESS WITH MEASUREMENT DELAY 52  3.1 INTRODUCTION 52  3.2 EPC FOR PROCESS WITH MEASUREMENT DELAY . 54  3.2.1 Unbounded Feedback Adjustment For Process With Measurement Delay . 56  3.2.2 Bounded Feedback Adjustment For Process With Measurement Delay . 56  3.2.3 Evaluation Of Average Adjustment Interval (AAI) And Mean Square Deviation (MSD) 57  3.3 BOUNDED ADJUSTMENT SCHEMES AND DISCUSSION 62  3.4 ILLUSTRATION : BOUNDED FEEDBACK ADJUSTMENT FOR A PROCESS WITH MEASUREMENT DELAY OF TWO PERIOD 73  3.5 CONCLUSION . 75  Chapter . 76  MULTIVARIATE STATISTICAL PROCESS ADJUSTMENT INTEGRATING MONITORING AND CONTROL . 76  4.1 INTRODUCTION 76  4.2 MULTIVARIATE PROCESS ADJUSTMENT . 77  4.3 MULTIVARIATE STATISTICAL PROCESS ADJUSTMENT 78  4.4 PARAMETER SELECTION – MULTIVARIATE STATISTICAL PROCESS ADJUSTMENT 81  4.5 ECONOMIC ASPECT OF PROCESS ADJUSTMENT 83  ii 4.6 MULTIVARIATE DISTURBANCE MODEL –PARAMETER ESTIMATOIN . 90  4.7 PERFORMANCE ANALYSIS 91  4.8 CONCLUSION . 95  CHAPTER 96  PROCESS ADJUSTMENT UNDER DISTURBANCE UNCERTAINTY 96  5.1 INTRODUCTION 96  5.2 PROCESS CONTROL UNDER DISTURBANCE UNCERTAINTY 97  5.2.1 Run Disturbance Distribution for Known Initial State 99  5.2.2 Run Disturbance Distribution for Unknown Initial State 100  5.2.3 Control Strategy under Uncertain Disturbances 102  5.3 ILLUSTRATIVE EXAMPLE 104  5.3.1 Process with Known Initial State . 105  5.3.2 Process with Unknown Initial State . 105  5.4 DISTURBANCE PARAMETER IMPACT AND ANALYSES 106  5.5 PARAMETER ESTIMATION TRANSITION MATRIX . 110  5.6 CONCLUSION . 113  Chapter . 114  MULTIVARIATE CHARTING TECHNIQUES: A REVIEW AND A LINE-COLUMN APPROACH . 114  6.1 INTRODUCTION 114  6.2 GRAPHICAL DISPLAYS FOR MULTIVARIATE QUALITY CONTROL . 116  6.3 LINE-COLUMN MULTIVARIATE CONTROL CHARTS . 121  6.3.1 Line-Column T-Square Control Chart . 122  6.3.2 Comparison and Discussion . 130  6.3.3 Line-Column MCUSUM & MEWMA Control Charts . 132  6.4 CONCLUSION . 134  Chapter . 135  CONTROL CHARTS FOR GENERAL PROFILE MONITORING BASED ON FISHER’S CENTRAL AND NONCENTRAL F-DISTRIBUTIONS . 135  iii 7.1 INTRODUCTION 135  7.2 FISHER’S F CONTROL CHARTS . 136  7.3 PERFORMANCE EVALUATIONS 141  7.4 PERFORMANCE COMPARISION 157  7.5 CHI-SQUARE CONTROL CHARTS FOR PROFILE MONITORING . 160  7.6 IMPLEMENTATION OF PROFILE MONITORING SCHEMES . 161  7.7 PHASE I ANALYSIS PROFILE CONTROL CHARTS . 164  7.8 PROFILE MONITORING UNDER AUTOCORRELATION 165  7.9 ILLUSTRATIVE APPLICATION: SEMICONDUCTOR MANUFACTURING WET ETCHING PROCESS . 166  7.10 CONCLUSION . 170  Chapter . 171  CONCLUSION . 171  REFERENCES 175  iv SUMMARY Statistical methods of process improvement have found numerous valuable applications in manufacturing and non-manufacturing processes. This thesis contributes to statistical process monitoring and process adjustment methods for quality control and quality improvement of industrial processes. One of the problems associated with process adjustment in product industry is unavailability of in-situ data. The delay in measurement is due to the time taken to measure the process quality characteristic, queue at metrology machines, multistage processes etc. The process adjustment strategies for processes with measurement delay are discussed in Chapter 3. It is crucial to consider the economic aspect of process adjustment such as adjustment costs and off target costs. The bounded and unbounded feedback adjustment methods are proposed. The adjustment schemes as a compromise between increase in process variance and adjustment costs are given. The processes experience various types of disturbances depending on the prevailing production environment. Intermittent process disturbances are one of the commonly experienced types of disturbances. The process operates under stable conditions and is affected intermittently by disturbances. The multivariate process adjustment method under such disturbances is considered in Chapter 4. It is proposed to integrate recursive estimation and the multivariate exponentially weighted moving average control chart. The process is monitored on the multivariate exponentially weighted moving average control chart. Once a shift in process is detected, the shift size is recursively estimated and process is adjusted sequentially. Unlike other multivariate controllers, this method does not actuate the process adjustment every period. Hence, suitable for processes where adjustment at every run is not desirable. v Another problem encountered in practice is the uncertainty in process disturbance distribution. The uncertainty may be attributed to several upstream machines, raw material variability, several suppliers and changing process conditions. The process adjustment under uncertain disturbance distribution is considered in Chapter 5. The process adjustment strategies for processes with known and unknown initial state under symmetric and asymmetric off target costs are given. Multivariate process monitoring methods have found several valuable applications in industry. One of the crucial needs of multivariate process monitoring methods is an efficient graphical display of the process. A chart which simultaneously displays the information about individual variables and its multivariate description yet remains easily interpretable. A novel graphical representation of multivariate control charts integrating line and column charts is discussed in Chapter 6. The proposed method efficiently displays the process information and is easier & economical for practical implementation. The proposed graphical display assists in identifying the components of multivariate process that have caused the out of control signal. In some processes it is desirable to monitor the relationship between a response variable and a set of explanatory variables. This relationship is referred to as profile. The profile monitoring control charts based on Fisher’s central and non-central F-distributions are proposed in Chapter 7. The proposed control charts perform better than the existing methods in detection of shift in profile variation and perform competitively in detecting the shift in profile parameters. The run length performances of the proposed charts are obtained analytically and generalized to various cases. The proposed monitoring method is very well-suited for practical implementation. vi LIST OF FIGURES Figure 2.1 Stationary and nonstationary time series Figure 2.2 Uncontrolled process Figure 2.3 Differenced time series Figure 2.4 Autocorrelation function (5% significance limits) Figure 2.5 Partial autocorrelation function (5% significance limits) Figure 2.6 MMSE controlled process Figure 2.7 MMSE robustness to suboptimal smoothing constant Figure 2.8 Uncontrolled and EWMA controlled process Figure 2.9 Single EWMA and dEWMA controlled process with deterministic drift Figure 3.1 Process adjustment schemes (no delay) Figure 3.2 Process adjustment schemes (1 period delay) Figure 3.3 Process adjustment schemes (2 periods delay) Figure 3.4 Process adjustment schemes (3 periods delay) Figure 3.5 Effect of measurement delay on AAI (   0.4 ) Figure 3.6 Effect of measurement delay on ISD (   0.4 ) Figure 3.7 EPC with measurement delay: Unadjusted and bounded adjusted process Figure 3.8 EPC with measurement delay: Bounded and unbounded process adjustment Figure 4.1 Effect of signal run and adjustment cost on adjustment decision N=50, 0.005, 0.025, Figure 4.2 Effect of signal run and off-target cost on adjustment decision N=50, 0.005, 10, vii Figure 4.3 Effect of signal run and 10, 0.025, 0.005, on adjustment decision N=50, Figure 4.4 Effect of signal run and adjustment cost on adjustment decision N=25, 0.005, 0.025, Figure 4.5 Effect of signal run and off-target cost on adjustment decision N=25, 0.005, 10, Figure 4.6 Effect of signal run and trace on adjustment decision N=25, 10, 0.025, 0.005, Figure 4.7 Effect of Adjustment cost/ off target cost ration on adjustment decision Figure 4.8 Ceramic substrate layout and hybrid microcircuits Figure 4.9 Performance comparison MEWMA and MVSPAD: Shift size = N(1,1) Figure 4.10 Performance comparison MEWMA and MVSPAD: Shift size = N(2,1) Figure 4.11 Performance comparison MEWMA and MVSPAD: Shift size = N(3,1) Figure 5.1 Process with uncertain disturbance distribution: Known initial state Figure 5.2 Process with uncertain disturbance distribution: Unknown initial state Figure 6.1 Polyplot Figure 6.2 Starplot Figure 6.3 Line graph Figure 6.4 Multiprofile chart Figure 6.5 Line-Column T control chart Figure 6.6 Polyplot chart: Illustration Figure 6.7 Line graphs: Illustration Figure 6.8 Multiprofile chart: Illustration viii REFERENCES 1. 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IIE Transaction, 38, 1093-1103. 190 [...]... proposed process adjustment method needs to be adopted 1.3 STATISTICAL PROCESS MONITORING The objective of a process is to produce products on target but the process is being affected by numerous factors that induce variation in the process This causes the products to deviate from target The variation in the process is due to random causes and special causes The aim in statistical process monitoring is to. .. proposed profile monitoring for lumber manufacturing The other aspects of profile monitoring have been monitoring of shapes and surfaces Jensen and Birch (2009) discussed nonlinear profile monitoring using nonlinear mixed model Yeh et al (2009) discussed profile monitoring under binary responses using logistic regression model and illustrated with an example A good review of profile monitoring was... aspects of statistical process adjustment In Chapter 3, feedback adjustment for process with measurement delay is discussed It is followed by Chapter 4 discussing on multivariate statistical process adjustment strategy by integrating multivariate process monitoring and adjustment methods In Chapter 5 process adjustment under disturbance uncertainty is discussed In the context of process monitoring, ... on profile monitoring In terms of applications, Kang and Albin (2000) discussed profile monitoring in the context of calibration in semiconductor manufacturing Walker and Wright (2002) discussed the vertical density of engineered wood boards with respect to depth Chang and Gan (2006) discussed monitoring of relationship between measurement processes to assure their accuracy Staudhammer, Maness and Kozak... safety, reduced inventory, reduced customer complaints, reduced call drops and improved efficiency Statistical process monitoring and process adjustment methods have definitely helped in improving the quality of processes The modern manufacturing processes are increasing in complexity and reducing in process margin Hence, a continuous effort from academia is needed to develop better methods to address the... (2004) and Woodall (2007) Profile monitoring has found several applications beyond manufacturing processes Woodall (2006) proposed profile monitoring application in public health surveillance to detect clusters of increased disease rate over time Jiang et al (2007) considered profile monitoring in context of change in the customer time series over time 12 Among the proposed linear profile monitoring methods. .. arising out of these manufacturing processes This will help industries to produce better quality products 1 using minimum resources, thus benefiting society Aligning with these efforts, this thesis contributes to the statistical process monitoring and process adjustment methods for quality and performance improvement 1.2 STATISTICAL PROCESS ADJUSTMENT Statistical process control (SPC) is widely used to keep... Engineering process control (EPC) is used in process control of continuous production processes EPC is a collection of techniques to manipulate the adjustable variable of the 15 process to keep the output of the process as close to target as possible The aim of engineering process control is to provide an instantaneous response, counteracting changes in the balance of a process and apply corrective action to. .. if the process is being affected by a special cause If the process is being affected by random causes alone the process is continued If the process is being affected by a special cause then the process needs to be stopped and the sources of the special cause need to be identified and removed Control charts are the most commonly used statistical process monitoring tools which signal when the process. .. wait for long time to observe out of control point and take control action 3 In a few processes the state of statistical control may be an ideal case and difficult to achieve In some processes it is difficult to tell if the process is in statistical control In such cases, it would be beneficial to have mild control with process adjustment 4 Process adjustment alone is not suited to eliminate special . CONTRIBUTIONS TO STATISTICAL METHODS OF PROCESS MONITORING AND ADJUSTMENT VIJAY KUMAR BUTTE A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR. CONTROL CHARTS FOR PROFILE MONITORING 160 7.6 IMPLEMENTATION OF PROFILE MONITORING SCHEMES 161 7.7 PHASE I ANALYSIS PROFILE CONTROL CHARTS 164 7.8 PROFILE MONITORING UNDER AUTOCORRELATION 165 7.9. methods of process improvement have found numerous valuable applications in manufacturing and non-manufacturing processes. This thesis contributes to statistical process monitoring and process adjustment