Statistical inferences of Rs;k = Pr(Xk-s+1:k > Y ) for general class of exponentiated inverted exponential distribution with progressively type-II censored samples with uniformly distributed random removal
Gao, Cuilan; Saleh, Ossama; Dhamshala, Prakash
College of Arts and Sciences
University of Tennessee at Chattanooga
Place of Publication
The problem of statistical inference of the reliability parameter Pr(Xk-s+1:k > Y ) of an s-out-of-k : G system with strength components X1,X2,…,Xk subjected to a common stress Y when X and Y are independent two-parameter general class of exponentiated inverted exponential (GCEIE) progressively type-II right censored data with uniformly random removal random variables, are discussed. We use p-value as a basis for hypothesis testing. There are no exact or approximate inferential procedures for reliability of a multicomponent stress-strength model from the GCEIE based on the progressively type-II right censored data with random or fixed removals available in the literature. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed.
This thesis could not have been written without the support and friendship found at The University of Tennessee at Chattanooga and elsewhere. The love of my family and friends provided substantial inspiration and was my driving force. It has been a long journey and completing this work is definitely a high point in my academic career. I could not have come this far without the assistance of my family and friends and I want to express my deepest appreciation to them. I was extremely fortunate to gain a mentor in Dr. Sumith Gunasekera (Associate Professor, Dept. of Mathematics). I truly feel blessed to have worked with him. Without his belief in me I could not have developed confidence in my abilities as a Statistician and for that I am eternally grateful. It is astonishing to think how much influence one man has had on my academic career and I will never forget the valuable lessons he has taught me. In addition, the entire faculty and staff in the Dept. of Mathematics at The University of Tennessee at Chattanooga are the most dedicated and generous people that I have ever met and I feel honored to have worked with them. Their guidance has served me well and I owe them my heartfelt appreciation. My committee members deserve a special note of praise, for they have watched over me since my first days as a graduate student. Some have even been watching throughout my undergraduate career here as well. I wish to thank Dr. Cuilan Gao (Assistant Professor, Dept. of Mathematics), Dr. Ossama Saleh (Professor, Dept. of Mathematics), and Dr. Prakash Dhamshala (Professor, Dept. of Mechanical Engineering) for providing numerous hours of advice and critiques. Their examples, as researchers and as teachers, continue to serve as guidelines for my academic career. I want to thank Dr. Lucas Van der Merwe (Professor of Mathematics & Interim Head, Dept. of Mathematics) and Dr. Francesco Barioli (Associate Professor & Graduate Coordinator, Dept. ofMathematics) for their very valuable support, advice, mentoring over the years. Students in the Department of Mathematics also deserve my sincerest thanks. Their friendship and assistance have meant more to me than I could ever express. They have gone above and beyond to help me throughout my time as a graduate student. Finally, I wish to thank my family and friends. The people I have met while at the University of Tennessee at Chattanooga have become my closest and dearest friends, and counselors, and to all of you I give my love and thanks. I am especially thankful to Jimmy, Ashleigh, and Katie for their kind support, friendship and cooperation to help making my time as a student a success. My beloved parents have always believed in me and helped me reach my goals. Their support forged my desire to achieve all that I could in life. I owe them everything and wish I could show them just how much I love and appreciate them. Finally, I would like to dedicate this work to my beloved mom and dad. I hope that this work makes both of them proud.
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.
Reliability (Engineering); Risk assessment -- Mathematical models
xviii, 111 leaves
Fisher, Aaron J., "Statistical inferences of Rs;k = Pr(Xk-s+1:k > Y ) for general class of exponentiated inverted exponential distribution with progressively type-II censored samples with uniformly distributed random removal" (2016). Masters Theses and Doctoral Dissertations.