Statistical Analysis of Alpha Power Inverse Weibull Distribution under Hybrid Censored Scheme with Applications to Ball Bearings Technology and Biomedical Data

Abstract

Applications in medical technology have a massive contribution to the treatment of patients. One of the attractive tools is ball bearings. These balls support the load of the application as well as minimize friction between the surfaces. If a heavy load is applied to a ball bearing, there is the risk that the balls may be damaged and cause the bearing to fail earlier. Hence, we aim to study the model of the failure times of ball bearings. A hybrid Type-II censoring scheme is recommended to minimize the experimental time and cost where the components are following alpha power inverse Weibull distribution. A ball bearing is one example; the other is the resistance of guinea pigs exposed to dosages of virulent tubercle bacilli. We use different estimation methods to obtain point and interval estimates of the unknown parameters of the distribution; consequently, estimating statistical functions such as the hazard rate and the survival functions are observed. The maximum likelihood method and the maximum product spacing methods are used, in addition to the Bayesian estimation method, in which symmetric and asymmetric loss functions are utilized. Interval estimators are obtained for the unknown parameters using three different criteria: approximate, credible, and bootstrap confidence intervals. The performance of the parameters’ estimation is accomplished via simulation analysis and numerical methods such as Newton–Raphson and Monte Carlo Markov chains. Finally, results and conclusions support the suitability of alpha power inverse Weibull distribution under a hybrid Type-II censoring scheme for modeling real biomedical data.