Data Analysis and Related Applications, Volume 1

28Reliability of a Double Redundant System Under the Full Repair Scenario

For two probability distributions A(x) and B(x) in Rykov et al. (2020b), modified Laplace–Stieltjes transforms have been introduced. In terms of these transforms, the analytical expressions of the main reliability characteristics of a double redundant system with arbitrarily distributed life- and repair times of system components under the partial repair scenario have been found. In this chapter, we extend the investigation of the same model under the full repair scenario. The analytical expressions for the time-dependent and steady-state system probabilities as well as the system reliability function are presented in this chapter. The proposed approach and obtained analytical results also allow us to investigate the sensitivity of system reliability characteristics to the shape of system component life- and repair time distributions.

28.1. Introduction

Reliability of both simple and complex systems is a key issue in management, production and other areas of human activity. The redundancy technique is one of the most common methods for improving reliability (Ushakov 2013; Levitin et al. 2016). Duplication, for example, is of particular interest among researchers.

There are a lot of papers devoted to the study of redundant systems. Calculation of the reliability characteristics of such systems is not a trivial task, even for a simple double redundant structure but for arbitrarily distributed component ...