Statistical inferences of reliability and order-restricted nano-droplet rebound by comparative kumaraswamy populations based on balanced joint progressive censoring

Abstract The rebounded nano-droplet ( RND ) is one of the important issues in creating defective coatings. The RND depends on many factors such as angle of droplet impact and velocity. Reliability model can be considered to determine the probability of surface defect under two impact angles in the RND data. In this paper, we have delved into the application of reliability and order-restricted ( ORe ) estimation methods for two Kumaraswamy populations in the RND data. The study kicks off by evaluating maximum likelihood and Bayesian estimates of the reliability parameter and order-restricted parameters in presence of balanced joint progressive censored data. Bayes estimations for reliability and ORe parameters under two different loss functions are investigated with the Metropolis-Hastings technique and Lindley’s approach. To evaluate order-restricted Bayesian estimates, ordered Beta-Gamma prior is considered. The asymptotic, Bootstrapping and Bayesian bounds are also computed. A thorough simulation analysis is demonstrated to assess the performance of the supplied approaches across various sample sizes. The usefulness of the techniques is illustrated using RND data to prove their versatility in practical applications.