Prognostic models based on statistical flowgraphs

Abstract

We present a framework for developing hierarchical models for predicting system health (e.g. probability of failure within a given mission duration), based on component‐level reliability and degradation models. Component models may be specified as parametric probability distributions or nonparametrically as empirical distribution functions. Flowgraph methods are then used to predict the system failure time distribution. We illustrate with an application to aircraft maintenance. Copyright © 2011 John Wiley & Sons, Ltd.

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

“…For this purpose we use an inversion algorithm called EULER, developed by Abate and Whitt [14], in the version provided by [4]. For parametric transforms of smooth distributions, EULER is remarkably accurate, typically with maximum absolute error on the order of 10 −8 or less.…”

“…In practical applications, these models were successfully used to model a variety of time-to-event data arising in multistate stochastic networks such as prediction of service degradation and failure in cellular telephone networks [2], prediction of cumulative seismic damage [3], maintenance and repair of aircraft [4] and various biomedical applications [5]. See [6] for an introductory book on Statistical Flowgraphs.…”

Deployment of Prognostics to Optimize Aircraft Maintenance - A Literature Review

“…Results show improvements on many levels, of which an im-Figure 2. Prognostics on different levels, adapted from (Collins & Huzurbazar, 2012).…”

A flowgraph model for bladder carcinoma

“…An account of the theory developed up to 2005 may be found in [ 12 ]. A recent contribution proposing a prognostic model is [ 15 ].…”

“…To recover the PDF we use a variant of the inversion algorithm EULER [ 15 ]. From this function we obtain the survival function (with regard to progression), that is shown in Figure 6 , jointly with the empirical survival function.…”