Inference for Upper Record Ranked Set Sampling from Kies Model with k-Cycle Effect

This study investigates statistical inference for upper record ranked set sampling (URRSS) data from the Kies distribution. In multiple-cycle URRSS settings where the heterogeneity across cycles is non-ignorable, both classical and Bayesian approaches are adopted to estimate the unknown model parameters and associated reliability metrics. Likelihood-based point and interval estimates are derived for these parameters and reliability indices, and the existence and uniqueness of the maximum likelihood estimators for the Kies distribution parameters are rigorously established. Moreover, a hierarchical Bayesian framework is developed to accommodate cycle-specific variability, with a Metropolis–Hastings algorithm embedded within a Gibbs sampler proposed to facilitate posterior computation in complex scenarios. The performance of the suggested methods is assessed through extensive simulation studies, supplemented by two real-world data applications that demonstrate their practical utility. Numerical results show that the proposed estimators perform well overall, with the hierarchical Bayesian approach showing a particular advantage when uncertainty about the cycle effect is present.