Estimation and prediction of the inverted exponentiated Rayleigh distribution under adaptive progressive double Type-II hybrid censored data

In this paper, a new censoring scheme, namely adaptive progressive double Type-II hybrid censoring, is proposed. The unknown parameters are estimated using the maximum likelihood method. Approximate confidence intervals are constructed based on the asymptotic normality of the maximum likelihood estimation and the bootstrap method. Bayesian estimates of the unknown parameters are derived under symmetric and asymmetric loss functions using Lindley’s approximation method and Markov chain Monte Carlo techniques. The remaining useful life of the component is also predicted. Monte Carlo simulations are conducted to evaluate the finite-sample performance of the proposed inferential procedures. A real dataset is analyzed to illustrate the practical application of our proposed methods and their effectiveness.