Inference of P(X > Y) for the Burr-XII model under generalized progressive hybrid censored data with binomial removals

In this paper, we studied the estimation of R=P(X>Y)$$ R=P\left(X>Y\right) $$ based on the Burr-XII distribution under the generalized progressive hybrid censoring scheme. This censoring scheme has become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T$$ T $$. In this progressive censoring plan, amount of units withdrawn at each failure is assumed to be random and subject to the binomial distributions. Inferences of R$$ R $$ are obtained under equal shape parameters and different shape parameters, respectively. Maximum likelihood (MLE) and the Bayesian estimation methods are used. We obtain the MLEs of the parameters using Newton-Raphson (NR) and expectation maximization (EM) methods, respectively. In the Bayesian section, Lindley's approximation and Markov Chain Monte Carlo (MCMC) method with Metropolis-Hasting algorithm are used. Simulation studies are used to evaluate the performance of the proposed estimators and two real-data examples are provided to exemplify the theoretical outcomes.

Automated summary

This paper investigates the estimation of R=P(X>Y)$$ R=P\left(X>Y\right) $$ based on the Burr-XII distribution under the generalized progressive hybrid censoring scheme. The inferences of R$$ R $$ are obtained using maximum likelihood and Bayesian estimation methods. Simulation studies evaluate the performance of the proposed estimators, and real-data examples illustrate the theoretical outcomes.