Contributions to some areas in reliability theory.

Abstract

This work consists of some contributions to several areas in reliability theory. Chapter 1 is a short summary of the results obtained in this work with a brief overview of related areas. In Chapter 2, a model for k-out-of-n systems with n dependent components is studied. Sufficiency conditions on the conditional failure rate functions are given which imply that the first failure time of such a system is IFR (increasing failure rate). This result contains an earlier result of Esary and Proschan (1963) as a special case. Chapter 3 focuses on the block replacement policy, one of the most popular maintenance policies. Several new results which connect the properties of the block replacement policy with the properties of the corresponding renewal function and the excess lifetime are obtained. Some applications and relationships between these new results and some well known results are included. Chapter 4 deals with a model for discrete dependent maintenance reliability systems (DDMRS). We identify the conditions on the discrete conditional transition probabilities under which the two performance sequences associated with two DDMRS's are comparable in stochastic ordering. Further results and applications are discussed. In Chapter 5, several results on the properties of first failure times of some discrete dependent reliability systems (with or without maintenance) are presented.