A STUDY ON PROCESS VARIABILITY USING CUSUM AND
FUZZY CONTROL CHARTS
Thesis submitted to the
Bharathidasan University, Tiruchirappalli in partial fulfillment of the requirements
for the award of the degree of
DOCTOR OF PHILOSOPHY IN STATISTICS
by
R. VARADHARAJAN
Assistant Professor in Statistics
School of Management Studies
Vels University, Pallavaram,
Chennai - 600117
Under the Supervision of
Dr. A. PANDURANGAN
Prof. and Head, Department of Computer Applications,
SRM Valliammai Engineering College,
Kattankulathur, Chennai- 603203
BHARATHIDASAN UNIVERSITY
TIRUCHIRAPPALLI-620 024
OCTOBER – 2011
ABBREVIATIONS USED
1.
ARL -
Average Run Length
2. CL
-
Central Limit/Central Line
3. CS
-
Conventional Shewhart
4. CSSc -
Conventional Sampling Scheme
5. DFA
-
Direct Fuzzy Approach
6. FIR
-
First Initial Response
7. FPC
-
Fuzzy Process Capability
8. FPCI -
Fuzzy Process Capability Index
9. FSI
-
Fixed Sampling Interval
10. FSS
-
Fixed Sample Size
11. LCL
-
Lower Control Limit
12. LSL
-
Lower Specification Limits
13. MC
-
Markov Chain
14. MDSS -
Markov Dependent Sample Size
15. MDSSc-
Markov Dependent Sampling Scheme
16. PCA
-
Process Capability Analysis
17. PCIs
-
Process Capability Indices
18. SLs
-
Specification Limits
19. SPC
-
Statistical Process Control
20. SQC
-
Statistical Quality Control
21. SS
-
Standard Shewhart
22. TFN
-
Trapezoidal Fuzzy Number
23. TPM -
Transition Probability Matrix
24. UCL -
Upper Control Limit
25. USL
-
Upper Specification Limits
26. VSI
-
Variable Sampling Interval
27. VSSI -
Variable Sample Size and Sampling Interval
28. VSS
Variable Sample Size
-
ACKNOWLEDGEMENT
It gives me much pleasure to record my gratitude for those who helped me in one
way or other in completing this research work.
I place my sincere and heartfull
thanks
to my
Guide and Supervisor
Dr.A.Pandurangan, MSc.,M.Phil.,PGDCA.,MBA.,Ph.D., Professor & Head,, Department of
Computer Applications, SRM Valliammai Engineering College, Chennai, who is my source
of inspiration in carrying out this research work and a role model for my career.
I thank the Dr.M.Balasubramanian, B.Tech (Hons)., M.E., Ph.D., Principal of
Valliammai Engineering College, Chennai for having permitted me to do my research work
in the Department of Computer Applications and make use of the resources in the college.
I am very much grateful to Mr.S.Stanley Sagayaraj MSc.,M.Phil.,MCA.,M.E., who
has encouraged and helped me to complete the thesis.
I dedicated my thesis work to my beloved parents who provide the basic of my life
and supported me in every thing.
I thank my wife Ms. D.Sudha, BCA., B.Ed., who has encouraged and supported me
to complete the thesis. I wish to acknowledge the affection shown by my brother,
R.Manikandan, B.E., my daughter V.Thanushri, and my friends who supported and
encouraged me throughout my research work.
R. VARADHARAJAN
DECLARATION BY THE CANDIDATE
I do hereby declare that this work on “A STUDY ON PROCESS VARIABILITY
USING CUSUM AND FUZZY CONTROL CHARTS”, has been originally carried out
by me under the guidance and supervision of Dr.A.Pandurangan, Research Advisor, working
as Prof. and Head, Department of Computer Applications, SRM Valliammai Engineering
College, Chennai. This work has not been submitted elsewhere either in whole or in part for
the award of any other degree, diploma, associateship, fellowship or any other similar title
by any University.
Place: Chennai
Date:
(R.Varadharajan)
CONTENTS
Chapter
No.
Description
Page
No.
1
Introduction
1
2
Review of Literature
9
3
Standardized CUSUM Control Chart
15
4
Standardized CUSUM Median Control Chart
29
5
Fuzzy Multinomial Control Chart With Variable Sample Size
39
6
Construction of Fuzzy Control Charts Using Trapezoidal Fuzzy
Number
52
7
Summary of Findings and Concluding Remarks
80
References