A study on the types of fuzzy semi markov models and their fuzzy reliabilities

Abstract

The present work consists of five chapters. A brief summary of these chapters is given below. Chapter one of the thesis contains the introductory concepts and a survey of the literature. In chapter two, we define the homogeneous fuzzy semi-Markov model in which the system 1 is characterized in terms of possibility measures. In chapter three, we extend the definitions and results of chapter two to the non homogeneous case for which time itself has influence on the transition possibilities. We obtain the various fuzzy reliability measures (the system behavior is characterized in the context of possibility measures) of a system 1 using non homogeneous fuzzy semi-Markov model. And all the concepts are illustrated through real time example. In chapter four, we define the homogeneous fuzzy probabilistic semi-Markov model together with fuzzy state space in which the system 1 is characterized in terms of probability measures. In chapter five, we define non homogeneous fuzzy probabilistic semi-Markov model on the fuzzy probability space. We estimate the fuzzy reliability of a system 1 using non homogeneous fuzzy probabilistic semi Markov model in which the fuzziness in the transition probabilities are modeled as triangular fuzzy numbers on [0, 1] using n component method. In chapter six, we make the comparative study between the fuzzy reliabilities using the models non homogeneous unified fuzzy possibilistic Markov model and non homogeneous fuzzy probabilistic semi-Markov model. In addition to all the above concepts, we also estimate the waiting time distribution for all fuzzy semi-Markov models defined as fuzzy Weibull distribution. The parameters involved in the fuzzy Weibull distribution can be estimated using MATLAB software. In the final chapter, conclusions and future works are summarized. newline newline newline