Reliability Estimation for the Inverse Weibull Distribution Under Adaptive Type-II Progressive Hybrid Censoring: Comparative Study

The aim of this study is to investigate different methods estimating the stress-strength reliability parameter, $\theta =P(Y<X)$, when strength (X) and stress (Y) are independent random variables taken from inverse Weibull distribution (IWD), with same shape parameter scale parameters. Based on Adaptive Type-II Hybrid progressive censored samples, we employ classical Bayesian approaches. In approach, use maximum likelihood estimator (MLE), approximate (AMLE), least squares (LSE). contrast, approach utilizes symmetric asymmetric loss functions. Due absence explicit forms for Bayes estimators, propose using Lindley's approximation method computing estimators. We compare these estimators extensive simulations two criteria: bias mean square error (MSE). Finally, real-life data examples provided illustrations.