Estimation of Stress-Strength Reliability Based on the Exponential-Gamma Model: Theory and Applications
Joyshree Saharia
Department of Statistics, Assam University, Silchar-788011, Assam, India.
Jonali Gogoi *
Department of Statistics, Assam University, Silchar-788011, Assam, India.
*Author to whom correspondence should be addressed.
Abstract
The stress-strength reliability measure, defined as R = P(Y < X), is a widely used index in reliability analysis, representing the probability that a system’s strength exceeds the applied stress. This paper investigates the Exponential-Gamma stress-strength model, assuming the stress variable follows an exponential distribution while the strength variable follows a gamma distribution. Analytical expressions for the reliability function are derived and generalized to the case of standby redundant systems. Estimation of reliability is developed using maximum likelihood and uniformly minimum variance unbiased approaches, and both exact and asymptotic confidence intervals are obtained. A detailed Monte Carlo simulation study evaluates the finite-sample properties of the proposed estimators, highlighting the superior small-sample performance of the UMVUE and the asymptotic efficiency of the MLE. The practical usefulness of the model is demonstrated through real data applications, showing that the Exponential-Gamma framework provides an effective and tractable tool for modeling system reliability in applied settings.
Keywords: Stress-strength reliability, standby redundancy, maximum likelihood estimation, UMVUE, confidence intervals