Doctor of philosophy in statistics



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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 logo
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





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