Estimation Methods of Reliability Characteristics Based on Multiple Interval Type I Censored Samples Using Inverted Exponentiated Rayleigh Distribution

The reliability (or survival) function plays a key role in analysing the ageing and lifetime characteristics of engineering systems. This paper focuses on estimating the model parameters, reliability function (RF), hazard rate function (HF) and mean time to failure (M(t)) of the Inverted Exponentiated Rayleigh Distribution (IERD) under a multiple interval Type‐I censoring scheme (MITICS). Three estimation methods are considered: maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation. In the Bayesian framework, estimates are obtained using both the likelihood and product spacing approaches under squared error loss function (SELF). Gamma priors are assumed for the model parameters. Alongside point estimates, we construct approximate confidence intervals (CIs) for RF, HF and M(t) using classical techniques, and compare them with highest posterior density (HPD) credible intervals obtained from Bayesian analysis. Bayesian computations are carried out using a Markov Chain Monte Carlo (MCMC) method, with a Gibbs sampler combined with the Metropolis–Hastings algorithm. We assess the performance of the proposed estimators in terms of bias, mean squared error, average interval width, and coverage probability through an extensive Monte Carlo simulation study. Further, using several optimality criteria, the optimum MITICS design is suggested. Finally, the practical applicability and robustness of the developed methods are illustrated through the analysis of two empirical data sets drawn from reliability studies.