Estimation and optimal design for constant stress model under maximum ranked set sampling with unequal samples

This paper develops an optimal design for a constant stress model under Maximum Ranked Set Sampling with Unequal Samples (MaxRSSU) which is a novel approach to improve estimation efficiency in life test studies. The maximum likelihood and Bayesian methods are used to estimate model parameters and reliability characteristics. Subsequently, the asymptotic and highest posterior density intervals (HPD) are constructed for quantifying uncertainty quantification. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimators, followed by an application to real-life reliability data. Finally, optimal sample allocation plans are formulated under the MaxRSSU methodology with multiple optimality criteria by minimizing posterior variance. The studied design strategy emphasizes the benefit of MaxRSSU over the traditional simple random sampling technique, thus providing more efficient information for reliability engineering study.