statistical process adjustment methods for quality control in short-run manufacturing

250 Pages·2002·2.06 MB·English

The Pennsylvania State University
The Graduate School
Department of Industrial and Manufacturing Engineering
STATISTICAL PROCESS ADJUSTMENT METHODS FOR
QUALITY CONTROL IN SHORT-RUN MANUFACTURING
A Thesis in
Industrial Engineering
by
Rong Pan
(cid:13)c 2002 Rong Pan
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2002
We approve the thesis of Rong Pan.
Date of Signature
Enrique del Castillo
Associate Professor of Industrial and Manufacturing Engineering
Thesis Adviser
Chair of Committee
Richard A. Wysk
Professor of Industrial and Manufacturing Engineering
Leonhard Chair, Department of Industrial and Manufacturing Engineering
M. Jeya Chandra
Professor of Industrial and Manufacturing Engineering
Bruce G. Lindsay
Professor of Statistics
Distinguished Professor, Department of Statistics
Richard J. Koubek
Professor of Industrial and Manufacturing Engineering
Head of the Harold and Inge Marcus Department of
Industrial and Manufacturing Engineering
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Abstract
Process adjustment techniques based on the feedback control principle have be-
come popular among quality control researchers and practitioners, due to the recent
interest on integrating Statistical Process Control (SPC) and Engineering Process Con-
trol (EPC) techniques. Traditionally, quality engineers, who are more familiar with
SPC methods, avoid using process adjustment methods because of process tampering
concerns. This has resulted in very few systematic studies on how to apply process
adjustment strategies for continuous quality improvement. Most of the work in this
area concentrates on chemical processes which typically have long production runs. This
thesis focuses on studying sequential adjustment methods, closely related to well-known
Stochastic Approximation procedures, for the purpose of quality control of a short-run
manufacturing process.
First, the problem of adjusting a machine that starts production after a defective
setup operation is considered. A general solution based on a Kalman Filter estimator
is presented. This solution unifies some well-known process adjustment rules, and is
a particular case of Linear Quadratic (LQ) control methods. In essence, this solution
calls for a sequential adjustment strategy which recursively calculates the value of an
adjustable variable according to the prior knowledge of this variable and the most recent
observation from the process.
Next, the integration of sequential adjustments with SPC control charts are in-
vestigated for controlling an abrupt step-type process disturbance on a manufacturing
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process. The performance of this type of integrated methods depends on the sensitivity
of the control chart to detect shifts in the process mean, on the accuracy of the initial
estimate of shift size, and on the number of sequential adjustments that are made. It is
foundthatsequentialadjustmentsaresuperiortosingleadjustmentstrategiesforalmost
all types of process shifts and shift sizes considered. A combined CUSUM chart plus
sequential adjustments approach has better performance than other methods when the
shift size is not very large.
If there are different costs associated with a higher-than-target quality character-
istic compared to a lower-than-target quality characteristic, that is, an asymmetric cost
function, the adjustment rule needs to be modified to avoid the quality characteristic
falling into the higher cost side. For this case, a sequential adjustment rule with an
additional bias term is proposed. A method to determine these bias terms is developed.
Furthermore, the effect of process measurement and adjustment costs on the decision of
whether or not to apply adjustment actions at each sampling instant is investigated. A
modified Silver-Meal scheduling algorithm is found to be good at providing robust and
close-to-optimal adjustment schedules for this problem.
Finally, methods for identifying and fine-tuning a manufacturing system oper-
ating in closed-loop are studied. When a process is operated under a linear feedback
control rule, the cross-correlation function between the process input and output has
no information on the process transfer function, and open-loop system identification
techniques cannot be used. In this research, it is shown that under certain general as-
sumptions on the controller and process disturbance structure, it is possible to identify
the process disturbance models from data obtained under closed-loop operation. After
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identification, it is proposed to tune the controller to a near-optimal setting according to
a performance criterion that considers both the variance of the output and the variance
of the adjustments.
In summary, a collection of mathematical models for short-run manufacturing
processes are proposed and studied systematically in this thesis. It is demonstrated that
by implementing proper adjustment strategies the stability of the process can be better
maintained; thus, significant economic benefits obtained from the consistent quality of
products will be achieved. This research contributes directly to the quality improvement
program of the manufacturing industry and to the field of applied statistics.
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Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Identification of the Problems under Study. . . . . . . . . . . . . . . 3
1.2.1 Process monitoring . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Process adjustment . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 An example: a modified Deming’s funnel. . . . . . . . . . . . 7
1.2.4 Cost considerations . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.5 Closed-loop processes . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Research Objectives and Contributions . . . . . . . . . . . . . . . . . 12
1.4 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 2. Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Control Charts for IID Processes and Autocorrelated Processes . . . 17
2.1.1 Performance of control charts on an i.i.d. process . . . . . . . 17
2.1.2 Change-point detection in an autocorrelated process . . . . . 20
2.1.2.1 Control charts on process residuals . . . . . . . . . . 22
vii
2.1.2.2 Conventional control charts with modified control
limits . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Process Adjustment Techniques and Stochastic Approximation . . . 26
2.2.1 Grubbs’ harmonic rule . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Integration of SPC and EPC . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Modified Adjustment Rules under Some Special Cost Considerations 35
2.5 Closed-loop Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 3. An Unifying View of Some Process Adjustments Methods and Their
Small-Sample Performance . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1 A Kalman Filter Model for Process Adjustment . . . . . . . . . . . . 43
3.2 Small-sample Performance of Process Adjustment Rules . . . . . . . 54
3.2.1 Performance indices for small samples . . . . . . . . . . . . . 54
3.2.2 Performance for an unknown constant setup offset . . . . . . 55
3.2.3 Performance when the setup offset is a random variable . . . 61
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 4. IntegrationofSequentialProcessAdjustmentsandSPCControlCharts 70
4.1 Process Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Control Charts and Adjustment Methods . . . . . . . . . . . . . . . 74
4.3 Integration of Control Charts and Sequential Adjustments for IID
Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.1 An improved integrated SPC/EPC method . . . . . . . . . . 84
4.3.2 Cost justification . . . . . . . . . . . . . . . . . . . . . . . . . 87
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4.4 Integrated SPC/EPC Methods for Autocorrelated Processes . . . . . 93
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 5. SequentialAdjustmentMethodsforAsymmetricOff-targetQualityCost
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.1 Asymmetric Cost Models . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 A Biased Feedback Adjustment Rule . . . . . . . . . . . . . . . . . . 108
5.3 Formulae for the Optimal Target and the Sequence of Bias Term . . 112
5.4 An Application to a Real Machining Process. . . . . . . . . . . . . . 117
5.4.1 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 132
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Chapter 6. Process Adjustments with Significant Measurement and Adjustment
Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.1 Cost Model and Sample-Average Adjustment Procedure . . . . . . . 139
6.2 Algorithmic and Heuristic Methods for Optimal Adjustment Schedule 143
6.3 Comparison of Numerical Results . . . . . . . . . . . . . . . . . . . . 147
6.3.1 The case when the process variance (σ ) is unknown . . . . . 152
ε
6.3.2 The case when a biased initial estimate of the offset is used . 156
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Chapter 7. Identification and Fine-Tuning of Closed-Loop Processes . . . . . . . 162
7.1 Process Model and Disturbance Dynamics . . . . . . . . . . . . . . . 163
7.2 Process Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
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7.2.1 ARMA modelling of process observations from closed-loop data 165
7.2.2 Stationarity of ARMA(2,q) process . . . . . . . . . . . . . . . 169
7.2.3 Techniques for identification of ARMA processes . . . . . . . 174
7.3 Tuning the Controller . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.4 Example: A Simulated Controlled Process with Real Disturbance Data 179
7.4.1 Including the cost of adjustments . . . . . . . . . . . . . . . . 183
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Chapter 8. Research Contributions and Future Work . . . . . . . . . . . . . . . 185
8.1 Research Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Appendix A. The Linear Quadratic Setup Adjustment Problem . . . . . . . . . 196
Appendix B. AdditionalTablesonthePerformanceofDifferentAdjustmentSchemes
for Autocorrelation Processes . . . . . . . . . . . . . . . . . . . . . . 198
•
Appendix C. Equivalence Between Minimization of the AIEC criterion and Min-
•
imization of Each E(C ) . . . . . . . . . . . . . . . . . . . . . . . . . 203
t
c
Appendix D. Minimization of E(C ) for the Asymmetric Constant Cost Function 206
t
c
Appendix E. Minimization of E(C ) for the Asymmetric Quadratic Cost Function 209
t
Appendix F. Variance of an ARMA(2,q) Process, where q ≤ 2. . . . . . . . . . . 215
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
x
List of Tables
2.1 ARL values for a Shewhart chart, EWMA chart, CUSUM chart and
CUSUM-Shewhart chart . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Shift size estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Scenarios of interested adjusting schemes . . . . . . . . . . . . . . . . . 58
3.2 AISDperformanceofKalmanFilteradjustingscheme,Grubbs’harmonic
rule and Integral controller . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1 Six methods of integrating control charts and sequential adjustments . . 77
4.2 Performance of SPC/EPC integrated adjustment schemes and EWMA
scheme when varying the probability of a shift . . . . . . . . . . . . . . 83
4.3 ARLs of CUSUM and CUSUM-Shewhart charts. . . . . . . . . . . . . . 85
4.4 Optimal number of adjustments . . . . . . . . . . . . . . . . . . . . . . . 92
4.5 Run-length distributions of CUSUM charts with modified control limits
for AR(1) processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6 Run-length distributions of CUSUM charts with modified control limits
for MA(1) processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 PerformanceofintegratedSPC/EPCadjustmentschemesandanEWMA
adjustment scheme on an AR(1) process with φ = 0.2 . . . . . . . . . . 98
4.8 PerformanceofintegratedSPC/EPCadjustmentschemesandanEWMA
adjustment scheme on an AR(1) process with φ = 0.05 . . . . . . . . . . 99