A Comparative Study Using Generalized Power Akshaya Lifetime Distribution Under Joint Progressive Type‐II Censoring: Theory and Applications

ABSTRACT The estimate of model parameters under a combined Type‐II progressive censoring strategy for two independent samples with different scale and shape parameters that follow the Generalized Power Akshaya distribution (GP‐Akshaya‐D) is the subject of this research. Taking into account both informative priors, Maximum Likelihood Estimators (MLEs) are calculated and compared with Bayesian estimates generated using the importance sampling approach. The squared error loss function is used to evaluate the estimators. To assess the effectiveness and stability of the suggested techniques under various sample sizes and censoring schemes, a thorough simulation study is carried out. The findings show that Bayesian estimation works better than MLE in terms of generating more accurate and stable parameter estimates, especially under informative priors. Three genuine datasets are used to illustrate the proposed model's practical applicability. The suggested model's flexibility and usefulness for real‐world reliability analysis are confirmed by applying it to three actual datasets about carbon fiber tensile strength.