Committee Chair

Gunasekera, Sumith

Committee Member

Weerasena, Lakmali; Saleh, Ossama; Qin, Hong

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, Rs;k = Pr(at least s of (X1;X2; :::;Xk) exceed Y) = Pr(Xks+1:k >Y) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley’s approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates - the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals - are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted.

Acknowledgments

This journey would not have been possible without the support of my family, professors and mentors, and friends. To my family, thank you for encouraging me in all of my pursuits, never giving up on me and inspiring me to follow my dreams. I am forever indebted and hope my work makes you proud. I must give special acknowledgment to my advisor, Dr. Sumith Gunasekera (Associate Professor of Statistics, Department of Mathematics) who I have been extremely fortunate to work with and has served as a mentor throughout my academic journey. For his advice, his encouragement and guidance, I am eternally grateful and humbled. In addition, I would like to acknowledge the entire faculty and staff in the Department of Mathematics at The University of Tennessee at Chattanooga. It has been an absolute privilege working alongside such a dedicated and generous group of people. I would like to give special thanks to my Thesis Committee. I owe a debt of gratitude to Dr. Ossama Saleh for his time and careful attention to detail. To Dr. Lakmali Weerasena, I thank her for her untiring support and guidance throughout my journey. To Dr. Hong Qin, I am grateful for the well needed critiques and feedback. I look up to them as the epitome of the researcher and teacher I strive to be in the future. I want to thank Dr. Michael Colvin (Professor of Mathematics & Interim Head, Department of Mathematics) and Dr. Andrew Ledoan (Associate Professor of Mathematics, and Associate Head for Graduate Studies & Research, Department of Mathematics) for their very valuable support and counsel over the years. To Ms. Heather Sirley Heinlein (Administrative Specialist, Department of Mathematics) and students in the Department of Mathematics, I give my most sincere thanks for their support and encouragement during my time at UTC. To my friends, thank you for supporting me throughout this entire journey. Special thanks to my Chattanooga friends: Joel, Nicole, Madeline and Chyniece. The debates, dinners, random musings on life, general help and friendship are all greatly appreciated. To you all I say thank you for being there when I needed a friend.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2019

Subject

Random variables; Reliability (Engineering)

Keyword

Chen distribution; Multicomponent system; Stress-strength; Progressively-censored data; Confidence intervals; Reliability estimation

Document Type

Masters theses

Extent

svii, 86 leaves

Language

English

Rights

Under copyright.

License

http://creativecommons.org/licenses/by-nc-nd/3.0/

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