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.

This paper aims to estimate the stress-strength reliability parameter R = P(Y < X), considering the two different cases of stress strength parameters, when the strength ‘X’ follows exponentiated inverse power Lindley distribution ,extended inverse Lindley and Stress ‘Y’ follows inverse power Lindley distribution and inverse Lindley distribution. The method of maximum likelihood estimation is used to obtain the reliability estimators. Illustrations are provided using R programming.

No abstract

The term “Stress-Strength reliability” means , where a system or an equipment with random strength X is subjected to random stress Y in a way that system breaks down, if the stress surpasses the strength. In this paper, a system is considered with standby redundancy, and it is presumed that the distinct components in the system for both stress and strength variables are independent and have different probability distributions viz. M- Transformed Exponential, Exponential, Gamma and Lindley. The expressions for the marginal reliabilities  etc. based on its stress-strength models are obtained.

A quick method for estimating Mishra's  generalized geometric series distribution is suggested. The variance of the estimator is obtained and using this method a study on goodness of fit is done.