Burr III Scaled Inverse Odds Ratio‐Weibull Distribution for Modeling Asymmetric Medical and Engineering Data

This article introduces the novel five‐parameter Burr III Scaled Inverse Odds Ratio‐Weibull (B‐SIOR‐W) distribution, a flexible extension of the classical two‐parameter Weibull model, specifically engineered to model asymmetric data prevalent in medical and engineering domains. We present a comprehensive analysis of its statistical properties, including moments, the moment generating function, entropy, and order statistics, with parameters estimated using Maximum Likelihood Estimation (MLE), confirmed for efficiency and consistency via a robust simulation study. The B‐SIOR‐W distribution's competitive advantage is conclusively demonstrated against the parent and competing models using two diverse real‐world datasets: COVID‐19 mortality rates (Canada) and active repair times for an airborne communication transceiver, which constitutes the primary findings. This enhanced modeling precision is highly significant in domains like public health epidemiology and reliability engineering, where accurate risk assessment and prediction are critical. Furthermore, we illustrate its practical utility by designing a Group Acceptance Sampling Plan (GASP), leveraging the estimates from the COVID‐19 data to provide actionable insights for product quality specification and control.