Modulating Early-life Risk without Breaking Weibull Structure: An Odds-Based Weibull Model for Engineering Failure-Time Data

Abstract

The classical Weibull distribution lacks flexibility for nonlinear or early- life failure behaviors. We present a new three- parameter generalized Weibull (NGW) distribution using a probability- based generator. The NGW preserves the monotonic Weibull hazard structure by adding a parameter that controls for early- life hazard and cumulative curvature. We derive its key properties (density, survival, hazard, quantiles, moments), estímate the parameters using maximum likelihood and Bayesian methods, and perform simulations. Application to engineering failure data shows that the NGW offers a competitive fit compared to several Weibull- type extensions, with a parsimonious and analytically tractable structure.

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