Order-restricted inferences for the inverted exponentiated Rayleigh populations under two sample balanced progressive censoring scheme

By using additional information, researchers can effectively improve the accuracy of the estimate and enhance the efficiency and effectiveness of life testing processes. Order-restricted estimation is a useful methodology in engineering since it increases efficiency. In this paper, a balanced joint progressive censoring (BJPC) plan is utilized to overcome the order-restricted estimation issues associated with the inverted exponentiated Rayleigh (IERayleigh) populations. The flexibility of this distribution ensures a better fit to empirical data, leading to more accurate inferences. Using the maximum likelihood and Bayesian estimation approaches accomplishes estimating the unknown parameter. The MCMC technique is presented to gain Bayesian estimates based on appropriate priors. Different interval estimates are also built. A numerical example is provided for methodology elucidation purposes. Furthermore, we explore real engineering data to show how suggested approaches can be practically applied in research.