Today, maintenance strategies and their analyses remain a worrying problem for companies. Our study, presented in this paper, shows that our indicator can provide help for expert decision (maintenance manager) in the context of condition-based maintenance. The paper deals with the proposition of using Hidden Markov Models to track and estimate the degradation of a system, according to observati...

We consider the estimation of the number of hidden states (the order) of a discrete-time finite-alphabet hidden Markov model (HMM). The estimators we investigate are related to code-based order estimators: penalized maximum-likelihood (ML) estimators and penalized versions of the mixture estimator introduced by Liu and Narayan. We prove strong consistency of those estimators without assuming an...

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

Markov chain model is widely applied in many fields, especially the field of prediction. The classical Discrete-time Markov chain(DTMC) is a widely used method for prediction. However, the classical DTMC model has some limitation when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain model is proposed by combining Dempster-...

We present a new improved parsimonious multivariate Markov chain model. Moreover, we find a new convergence condition with a new variability to improve the prediction accuracy and minimize the scale of the convergence condition. Numerical experiments illustrate that the new improved parsimonious multivariate Markov chain model with the new convergence condition of the new variability performs b...

The paper presents a quick and simpli ed aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter...

To evaluate and predict component-based software security, a two-dimensional model of software security is proposed by Stochastic Petri Net in this paper. In this approach, the software security is modeled by graphical presentation ability of Petri nets, and the quantitative prediction is provided by the evaluation capability of Stochastic Petri Net and the computing power of Markov chain. Each...

Introduction: One major problem in analyzing epidemic data is the lack of data and high dependency among the available data, which is due to the fact that the epidemic process is not directly observable. Methods: One method for epidemic data analysis to estimate the desired epidemic parameters, such as disease transmission rate and recovery rate, is data ...

We analyze the performance of the novel Markov chain stochastic modeling technique for derivation of effective equations for a set of essential variables. This technique is an empirical approach where the right-hand side of the essential variables is modeled by a Markov chain. We demonstrate that the Markov chain modeling approach performs well in a prototype model without scale separation betw...