A Modified Weibull Distribution for Reliability Analysis: Transformation‐Based Model With Applications to Heavy Trail and Non‐Monotonic Behaviour Failure Data

In this paper, a transformation‐based generalisation of the classical Weibull distribution, called the modified Weibull distribution (MWD), is proposed to model complex reliability behaviour, including heavy‐tailed failure behaviour, and non‐monotonic, including bathtub‐shaped, hazard rates. The model also includes one more and physically interpretable parameter, the Safety Degradation Factor β, which controls the intensity of degradation by a transformation of failure‐time. Derivations of closed‐form expressions for important reliability functions and statistical properties are obtained. The estimation of the parameters is investigated using conventional likelihood‐based techniques. The proposed model is tested on several benchmark lifetime datasets and demonstrated to fit better than classical Weibull‐based models. The MWD is an effective framework for the reliability analysis of safety‐critical systems due to its analytical tractability, interpretability, and empirical performance.