A rule-based approach for establishing states in a Markov process applied to maintenance modelling

Abstract

The deterioration of technical systems can often be classified into discrete states, and the transitions between these states can be modelled using a Markov process. Instead of using an exponential distribution, it may be more realistic to assume that a general probability distribution describes the sojourn time in one of these states. The resultant model is a semi-Markov process, which may be difficult to treat analytically. This paper therefore presents an approach where the sojourn times in these states are gamma distributed and where the gamma distribution is transformed into a Markov process with a sequence of states that have exponentially distributed sojourn times. This means that the gamma distribution is approximated by a Markov process, which simplifies maintenance modelling. The approach presented is based on a simple rule such that it can easily be implemented in a maintenance model. It is shown that the approach yields good results compared with available alternatives.

Bayesian Estimation of Remaining Useful Life for Wind Turbine Blades

“…This assumption can be relaxed by using a semi-Markov model, where the time in each state does not have to be exponential distributed. To model this using a Bayesian network, each 'physical' state is divided into several virtual states, to obtain another sojourn time distribution for the physical state, and the time spent in each virtual state is still exponentially distributed [21]. Dynamic Bayesian networks can also be applied for deterioration modelling based on physical models as shown in Equation (1) is still exponentially distributed [21].…”

“…To model this using a Bayesian network, each 'physical' state is divided into several virtual states, to obtain another sojourn time distribution for the physical state, and the time spent in each virtual state is still exponentially distributed [21]. Dynamic Bayesian networks can also be applied for deterioration modelling based on physical models as shown in Equation (1) is still exponentially distributed [21]. Dynamic Bayesian networks can also be applied for deterioration modelling based on physical models as shown in Equation (1) [22].…”

Expected impact quantification–based reliability assessment methodology for Chilean copper smelting process: A case study

“…The traditional reliability analyses that are based on logical and probabilistic modeling contribute to the improved key performance indicators (KPIs) of a system, 4 which directly influence optimal operation designs. 5 However, many alternatives are available for system reliability analyses that employ analytical techniques, such as Markov models, 6 Poisson models, 7 universal generating function (UGF) and decision diagram. 8 This systematic study is based on techniques such as reliability block diagrams (RBDs), 9,10 fault trees (FTs), 11 reliability graphics (RGs), 12 and Petri nets (PNs); 13 these techniques can be used to determine logical relationships that underlie the behavior or dynamics of a process.…”

Availability Analysis of Repairable Mechanical Systems Using Analytical Semi-Markov Approach

“…Semi-Markov process (SMP) models, which are capable of handling nonexponential distributions, are more appropriate for the availability modeling and analysis of the repairable mechanical systems. However, the SMP model is difficult to treat analytically (Welte 2009) and there is no general and exact method for its solution. In this regard, some attempts have been made by converting the SMP model to a Markov model by approximations of nonexponential distributions to exponential distribution for ease of solution.…”

“…In this regard, some attempts have been made by converting the SMP model to a Markov model by approximations of nonexponential distributions to exponential distribution for ease of solution. The semi-Markov model with a gamma distribution is approximated by a Markov process (Welte 2009), whereas Weibull distribution is approximated to an exponential distribution (M. Xie et al 2000). A transient solution of minimal SMP associated with Markov renewal processes with finite state space has also been attempted (Liminios 1993).…”