A novel Bayesian approach to reliability modeling: The benefits of uncertainty evaluation in the model selection procedure

Abstract

This paper proposes a different likelihood formulation within the Bayesian paradigm for parameter estimation of reliability models. Moreover, the assessment of the uncertainties associated with parameters, the goodness of fit, and the model prediction of reliability are included in a systematic framework for better aiding the model selection procedure. Two case studies are appraised to highlight the contributions of the proposed method and demonstrate the differences between the proposed Bayesian formulation and an existing Bayesian formulation.

Discrimination between accelerated life models via Approximate Bayesian Computation

“…Contrarily to the classical approaches, Santana et al 24 . proposed a novel Bayesian formulation based on the residuals evaluation to examine the benefits of the uncertainty evaluation in the model selection procedure.…”

“…These approaches require the estimation of the model parameters that maximize the likelihood function and an additional term to penalise overly complex models. The major limitation of these approaches is that they undertake separately the competing models regardless the uncertainties related to the parameters estimates which could lead to an inaccurate selection of the 'best' model as stated by Gupta et al 23 Contrarily to the classical approaches, Santana et al 24 proposed a novel Bayesian formulation based on the residuals evaluation to examine the benefits of the uncertainty evaluation in the model selection procedure. Other Bayesian approaches based on goodness of fit indices evaluation are used to discriminate between the competing models.…”