Stress-Strength Reliability Estimation for Geometric-Exponential Model under Complete and Censored Sampling Using Classical and Modern Estimation Approaches

This paper addresses the estimation of the stress-strength reliability parameter, defined as R = P(X < Y ), within a model where the stress variable X follows a Geometric distribution and the strength variable Y follows an Exponential distribution. The analysis is conducted for two prevalent data scenarios in reliability studies: complete and right-censored sampling. We derive and compare the performance of several estimation methodologies. The classical Maximum Likelihood Estimator (MLE) serves as a baseline. Its performance is contrasted with modern robust techniques, including three distinct shrinkage estimators based on a constant weight factor, a modified Thompson-type factor, and the Mehta and Srinivasan formulation. A comprehensive Monte Carlo simulation study is designed to evaluate these estimators under various conditions of sample size, true reliability, and censoring proportions. The performance is assessed based on Bias and Mean Squared Error (MSE). The results consistently demonstrate that shrinkage estimators offer substantial improvements in MSE over the traditional MLE, particularly in small to moderate sample sizes and under heavy censoring, highlighting the practical benefits of regularization in this mixed discrete-continuous reliability context.