Bayesian and Non-Bayesian Inference for Discrete Model Based on Censored Samples with Optimal Test Plan

In reliability and lifetime studies, it is often impractical to observe the failure times of all units in a sample, particularly when the process is timeconsuming or expensive. Type II censoring addresses this by terminating the experiment after a predetermined number of failures from a total sample of size. The Discrete Alpha Power Extended Inverted Weibull distribution is particularly suitable for modeling such censored discrete lifetime data. Its flexible shape parameters allow it to capture a wide range of failure behaviors, including over-dispersion, which is common in censored datasets. In this context, the likelihood function and estimation procedures (maximum likelihood and Bayesian) explicitly account for the censoring, ensuring unbiased parameter estimates and reliable predictive inferences. Consequently, the Discrete Alpha Power Extended Inverted Weibull distribution provides a practical and statistically robust framework for analyzing discrete lifetimes under type II censoring.OPEN ACCESS Received: 28/07/2025 Accepted: 19/09/2025 Published: 23/01/2026