Statistical inference of R = P( Y < X) for Weibull distribution under Type-II progressively hybrid censored data

Type-II progressively hybrid censoring is a mixture of Type-II progressive and hybrid censoring schemes. In this paper, we consider the estimation ofR = P(Y < X) when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape parameter, and the data obtained from both distributions are Type-II progressively hybrid censored. Different methods for estimating R are applied. The maximum likelihood estimator and the approximate maximum likelihood estimator of R are proposed. The observed Fisher information matrix is computed and it is used to construct an asymptotic confidence interval for R. Also, two bootstrap confidence intervals are proposed. Bayes estimate ofRand the associated credible interval are also obtained under the assumption of independent suitable priors. Monte Carlo simulations are performed to compare the efficiency of the proposed estimators. One data analysis has been presented for illustrative purposes.