Reliability Theory: Properties of Probability Distributions for Lifetimes of Systems of Components

The purpose of this paper is to make the concepts of reliability theory manageable even for those without an extensive mathematics background. This paper will break down the types of systems, explore the aspects of probability distributions which are important in reliability theory, as well as examine some concepts regarding the differences between system lifetimes and lifetimes of components. The goal of this paper is to allow the reader to gain an understanding of some of the key concepts explored in this theory, to provide examples for the reader to try, and to include proofs that have been broken down for clearer comprehension.