Statistical inference for the reliability of Burr-XII distribution under improved adaptive Type-II progressive censoring

We propose an improved adaptive Type-II progressive censoring scheme, which can effectively guarantee that the test time will not exceed a certain threshold time. And the adaptive Type-II progressive censoring scheme is its special case. Based on this censoring scheme, the parameters, reliability and hazard functions of Burr-XII distribution were estimated. Firstly, we obtain the estimators of parameters, reliability and hazard functions by using the maximum likelihood estimation method. Subsequently, the approximate confidence intervals of the above statistics are obtained by using the asymptotic normality properties of maximum likelihood estimation and the Bootstrap method. Furthermore, based on the square loss function and the LINEX loss function, the point estimators and approximate confidence intervals of parameters are derived by using Bayesian method. A real data is used to illustrate and validate the advantages of the proposed improved adaptive Type-II progressive censoring scheme. Finally, the Monte Carlo simulations are performed to compare the behavior of improved adaptive Type-II progressive censoring scheme with adaptive Type-II progressive censoring scheme for different evaluation methods.