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Abstract
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Recent studies have introduced various models for reliability analysis of time-to-failure and competing risk (CR) datasets, but their empirical application does not match with certain CR problems, this is because some CR data require model based on cause-specific hazard rate function (HRF) or a model that can adequately describe data with complex non-monotone patterns. To overcome these limitations, we introduce a robust CR model constructed by a minimum variable following Dhillon or Burr-XII failures. The resulting model known as the Burr-XII Dhillon (BXIID) model, is designed to handle not only conventional monotone or bathtub-shaped failure but complex non-monotone datasets. Its HRF can manifest various shapes consisting of inverted bathtub-shaped, mod ified bathtub-shaped, and inverted roller coaster-shaped (increasing-decreasing-increasing-decreasing), among others. Some structural and reliability properties of the proposed model are explored. Furthermore, the reciprocal relationship between HRF and mean residual life is illustrated using the proposed model. In addition to employing the maximum likelihood approach for parameter estimation, we implement Bayesian inference for the BXIID model using the Hamiltonian Monte Carlo framework for improved computational efficiency and robust parameter inference. We evaluate the adequacy of the BXIID model using three competing risk datasets characterized with complex non-monotone structure. Besides existence model selection measures, we also adopt the recently unveiled Bridge criterion. The results highlight the flexibility of the proposed model over its competing candidates and also demonstrate the robustness of the Bayesian method over the conventional approach.
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