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... shown in the figure Fig.1, the ABC-NS algorithm starts, as the rejected sampling (RS) algorithm, by generating N particles (parameters vector) from the prior distribution satisfying the constraint Δ(u, u * ) ≤ 1 . Each particle stands out by its e i = Δ i (u, u * ). ...

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... This has been reported by Bonassi et al. 42 To overcome this shortcoming and alleviate the computational burden, an ABC algorithm based on an elegant ellipsoidal Nested Sampling technique (ABC-NS) and a re-weighting scheme introduced in Ref. 43 is used. It promises drastic speedups compared to other variants 43 and provides a good alternative for parameter estimation as shown in Ref. 44 Additionally, it has been demonstrated that the ABC-NS can mitigate the effects of model misspecification through an appropriate choice of the distance function which can be tailored according to the user's interest. ...
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Accelerated life testing (ALT) is widely used in high‐reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood‐based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood‐based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.