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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.

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.