Empirical Bayes Estimates Of Steady-state Availability In Exponential Distribution Model And Availability Of A Periodically Inspected System, Maintained Through No More Than H Imperfect Repair(s) Before A Perfect Repair Or A Replacement

This dissertation consists of three chapters, which is completed during my Master Degree of Science.Chapter One is a preface. It gives an introduction to the development and significance of reliability as well as the basic concept. It also introduces the background and main ideas of this dissertation.In Chapter Two, empirical Bayes procedure is used to estimate the steady-state availability in an exponential distribution model. The nonparametric polynomial density estimation of the unknown prior probability density function of the steady-state availability is considered. Examples are given to study whether a nonparametric polynomial density estimation of the prior density function with a higher degree gives a significantly better estimation.In Chapter Three, a periodically inspected system is discussed, which is maintained through no more than h imperfect repair(s) before being perfectly repaired or replaced. If a failure occurs between consecutive inspections, the system remains failed until the next inspection. And then the failed one is perfectly repaired or replaced with probability p and imperfectly repaired with probability l-p, where p is a fixed constant. The times required for imperfect repairs and perfect repairs or replacement are random. The repaired system is restored to operation at the next scheduled inspection time. The life time distributions of the system in new and imperfectly repaired states are arbitrary. The system availability function and the limiting average availability are also expressed in this chapter. Examples are given to investigate the relationship between the limiting average availability and the probability of perfectly repair or replacement and the number of imperfectly repair in a renewal cycle.