Inference for Maximum Ranked Set Sampling with Unequal Samples from the Burr Type-III Model with Cycle Effects

This paper explores statistical inferences for the maximum ranked set sampling with unequal samples (MaxRSSU) from the Burr Type-III distribution. Under the assumption that the differences between different multiple MaxRSSU cycles are non-ignorable, classical likelihood and Bayesian approaches are employed for estimation of the model parameters and reliability indices. By taking into account the multiple-cycle effect, the maximum likelihood estimators for the parameters of the Burr Type-III distribution are established, along with an analysis of their existence and uniqueness. Furthermore, approximate confidence intervals are constructed based on asymptotic theory. In addition, a hierarchical Bayesian framework is conducted for analysis, and a Monte Carlo sampling method is proposed for complex posterior computation. Extensive simulation studies are carried out for evaluating the performance of the proposed methods, and a further two real-data examples are also provided for illustration. The numerical results indicate that the proposed methods work satisfactorily and the hierarchical Bayesian approach appears more appealing when the uncertainty cycle effect is involved.