Incorporating Covariates in Flowgraph Models: Applications to Recurrent Event Data

Abstract

Modeling recurrent event data is of current interest in statistics and engineering. This article proposes a framework for incorporating covariates in flowgraph models, with application to recurrent event data in systems reliability settings. A flowgraph is a generalized transition graph (GTG) originally developed to model total system waiting times for semi-Markov processes. The focus of flowgraph models is expanded by linking covariates into branch transition models, enriching the toolkit of available data analysis methods for complex stochastic systems. This article takes a Bayesian approach to the analysis of flowgraph models. Potential applications are not limited to engineering systems, but also extend to survival analysis.

Bayesian prediction for flowgraph models with covariates. An application to bladder carcinoma

“…The semi-Markov assumption is a more realistic framework in many situations, for example in the considered bladder carcinoma process. Moreover it is also possible to relax this assumption [7]. Therefore it is very interesting to facilitate handling of flowgraphs, and in particular the incorporation of covariates and the Bayesian approach in this context.…”

“…The inclusion of covariates in Flowgraph Models is very recent [7]. We perform it with a different approach in a simple way.…”

“…The general expression of the censored overall likelihood function is provided in [7] that in our flowgraph model and from the states 0 and 1 is the function L = L 0 L 1 , where L 0 and L 1 are computed as follows. Let S jk be the set of observation indices in transition j → k, and S j * the index set of observations censored in state j.…”

“…The incorporation of covariates in this methodology have been recent, just the work [7] extends previous flowgraph modeling to incorporate covariates. Our aim in this paper is to propose an easy way to perform a Bayesian approach with covariates.…”

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

“…Stochastic Flowgraphs [25] and Hidden Markov Models [35] (both based on the Maximum Likelihood Estimation method) have been proposed to estimate the unknown parameters of the stochastic model of the maintained component, when some field data are missing (e.g., [26], [43]). Fuzzy Logic ( [47]) has been applied to address the cases in which the lack of knowledge concerns both the degradation model of a component and its parameters (e.g., [1]- [3], [27]).…”