Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis

Abstract

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can be used in the studies of various applications of systems with dependent failures between their elements.

Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem

“…[1] and [2]), usefulness of generating functions in deriving polynomial time algorithms seems not to have been noticed before. Probability generating functions are also used to model Queuing System [3], redundant renewable system [4], waiting Time Problems [5]. A good review of application of Probability generating functions to Stochastic Polling systems is done by Vishnevsky [6].…”