This study investigates the estimation of the stress-strength reliability measure, ς = P(X < Y), assuming that both stress (X) and strength (Y) follow the new X-Lindley (NXL) distribution. The NXL distribution has gained attention in reliability and risk analysis due to its flexibility and long-tailed behavior. To mimic realistic life-testing scenarios, progressive Type-II censoring is employed. Three estimation approaches are compared: maximum likelihood estimation (MLE), Bayesian estimation via Markov Chain Monte Carlo (MCMC) with a gamma prior, and the Tierney–Kadane (TK) approximation using a secondorder Laplace method. A comprehensive Monte Carlo simulation with 10,000 replications is conducted to evaluate estimator performance in terms of mean squared error, coverage probabilities, and the average lengths of asymptotic confidence or credibility intervals at the 95% and 97.5% levels. The results highlight the efficiency and robustness of the MCMC-based Bayesian approach, particularly under higher censoring levels. |
