The multi-stress-strength reliability of the form \(\ddot{R}=\, P[W<V<T]\) , when the strength (V) of the system is affected by two random stresses \(\left( W\ \text {and}\ T\right) ,\) has gained significant attention recently. In this study, we assume \(W,\ V,\) and T are independent random variables following an inverse Weibull distribution with a common scale parameter. We address the novel problem of estimating \(\ddot{R}\) under a Type-II progressive censoring (TII-PC) scheme incorporating binomial removals. Therefore, our aim is to examine parameter estimation and \(\ddot{R}\) under TII-PC, where the number of eliminated units at each failure time follows a binomial distribution. We derive parameter estimators and the multi-stress strength reliability function using maximum likelihood and Bayesian methods. The Metropolis-Hastings algorithm is employed for Bayesian estimation under symmetric and asymmetric loss functions. Asymptotic confidence intervals are determined using the Fisher information matrix and delta method, supplemented by bootstrap-t and bootstrap-p confidence intervals. Monte Carlo simulations have been conducted. These data are then used to compute the point and interval estimates and to compare the two approaches. Finally, the practical application of our methodology is demonstrated using three transformer insulation datasets corresponding to different voltage.
