ESTIMATION OF RELIABILITY FOR MULTI- COMPONENT SYSTEMS USING EXPONENTIAL, GAMMA AND LINDLEY STRESS-STRENGTH DISTRIBUTIONS

Abstract

This paper deals with the stress vs. strength problem incorporating multi-component systems viz. standby redundancy. The models developed have been illustrated assuming that all the components in the system for both stress and strength are independent and follow different probability distributions viz. Exponential, Gamma and Lindley. Four different conditions for stress and strength have been considered for this investigation. 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 derived based on its stress- strength models. Then the corresponding system reliabilities Rn have been computed numerically and presented in tabular forms for different stress-strength distributions with different values of their parameters. Here we consider n<=3 for estimating the system reliability R₃.