A Study on the η-Sharing Change-point Weibull Model Explaining Shape-Parameter Transition in a Homogeneous Population

Purpose: Weibull probability plot slope transitions in accelerated life testing of electronic components are conventionally modeled with two-component mixture Weibull models presupposing a heterogeneous population. When the data come from a homogeneous lot, this assumption is inconsistent: the fit can look stable yet gives a systematically biased characteristic life η, because a two-subpopulation structure, prone to weight collapse, is forced onto a single lot. This study instead frames the slope transition as a mechanism-driven regime transition in time, not a population mixture.<br/>Methods: This study takes the engineering premise that η is a lot-level property set by process and material, while β reflects the dominant failure mechanism. The resulting four-parameter η -sharing change-point Weibull model(M3) is a nested sub-model of the five-parameter full piecewise Weibull model(M4). Parameters are estimated by profile maximum likelihood with a τ -grid search over the non-smooth change point.<br/>Results: Across three data-generating scenarios, M3 reaches 99.2% BIC selection at n = 1000 in the true-model scenario (S1). Here β and η are within 1%, while τ carries a larger bias (about -7%) that does not transfer to B₅₀ (-0.7%) or MTTF (0.1%), both within 1%. The η-gap supports η-sharing in simulation: from M4 fits, the gap collapses toward 0 for homogeneous-lot data (S1) but recovers the true separation in S3. Separately, the mixture weight-collapse rate, a stability check, stays below 5%.<br/>Conclusion: These results support M3 for homogeneous-lot accelerated life testing, while M4 remains suited to heterogeneous-population contexts such as transformer asset management, enabling context-dependent model selection.