Estimation of Multi Component Systems Reliability in Stress-Strength Models

Abstract

In a system with standby redundancy, there are a number of components only one of which works at a time and the other remain as standbys. When an impact of stress exceeds the strength of the active component, for the first time, it fails and another from standbys, if there is any, is activated and faces the impact of stresses, not necessarily identical as faced by the preceding component and the system fails when all the components have failed. Sriwastav and Kakaty (1981) assumed that the components stress-strengths are similarly distributed. However, in general the stress distributions will be different from the strength distributions not only in parameter values but also in forms, because stresses are independent of strengths and the two are governed by different physical conditions. Assume the components in the system for both stress and strength are independent and follow different probability distributions viz. Exponential, Gamma, Lindley. Different conditions for stress and strength were considered. Under these assumptions the reliabilities of the system have been obtained with the help of the particular forms of density functions of n-standby system when all stress-strengths are random variables. The expressions for the marginal reliabilities R(1), R(2), R(3) etc. have been obtained based on its stress-strength models. Results obtained by J. Gogoi and M. Bohra are particular case presentations.

Estimating Reliability for Frechet (3+1) Cascade Model

“…There are many papers that have dealt with this topic, such as: Khan and Jan [13] derived the reliability of a multi-component system when the factors follow the Burr distribution. Khaleel [9] found the reliability of a model of one component that has strength and is subjected to four stresses.…”