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DUS-Transformed Quadratic Hazard Distribution: Identifiability, Likelihood Asymptotic, and Physics-Informed Neural Network Estimation |
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PP: 1199-1224 |
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doi:10.18576/jsap/150503
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Author(s) |
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Amin M. Elfeky,
Mohammad A. Tashtoush,
Essa Melfi Aldosari,
Mohamed Sayed Abdellatif,
Hasanain Jalil Alsaedi,
Adel S. Hussain,
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Abstract |
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| Many transformation-based generalizations are suggested for survival/reliability data with non-monotone risk
pattern without any formal inferential assurances being given, while hazard-based lifetime models must be able to cope with such risk patterns. A short parsimonious distribution called DUS–Quadratic Hazard (DUS–QH) distribution, which is obtained by the Dinesh–Umesh–Sanjay (DUS) transformation of a generalized polynomial quadratic failure-rate baseline, is introduced. We define properness and derive closed-form characteristics of reliability functions (density, survival, hazard and cumulative hazard) and demonstrate that the model can reproduce increasing, decreasing and unimodal hazard functions, as well as bathtub-shaped hazard functions. Importantly, we show parameter identifiability, and confirm the local (practical) identifiability numerically with a sensitivity (Jacobian) matrix analysis. We derive likelihood-based inferences that are explicitly Fisher information structured and asymptotically normally distributed and, alongside the maximum likelihood estimator, we present Physics-Informed Neural Network (PINN) estimator that incorporates the model-implied constraints in a differentiable optimization framework for estimation. A Monte Carlo simulation with various sample sizes analyzes bias and error measures for seventeen classical estimators and PINN, showing that spacing-based procedures and PINN have good recovery in moderate samples and nonlinear interactions of parameters. Two real reliability datasets (windshield service time for aircraft and breaking stress for carbon-fiber) are presented to illustrate practical performance, and information criteria, Kolmogorov–Smirnov, and other goodness-of-fit measures, and diagnostic plots also show that DUS–QH can give competitive and often better fit than the standard alternatives. We also provide computational time comparisons between
PINN and MLE and explore the scalability to enable reproducible deployment for applied reliability analysis. |
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