On Non-Homogeneous Markov Reward Model to Availability and Importance Analysis for CNC Machine Tools

This paper exploits the Markov reward method to availability and importance evaluation for CNC machine tools. The presented paper regards CNC machine tools as a multi-state system that state transitions process caused by elements and subsystem’s failures and corresponding maintenance activities during the lifetime. Simultaneously, considering the time-varying characteristics of the failure rates of subsystems, the non-homogeneous Markov reward model is introduced for evaluation of availability and subsystem importance identification for aging multi-state CNC machine tools under minimal repair. Corresponding procedures for the failure rates, state transition matrix, and reward matrix definition are suggested for the availability and importance measures. A numerical example is presented in order to illustrate the approach.

Reliability measures for a new general system using fuzzy non-homogenous Markov reward model under d-degradation levels

PurposeIn this paper, new procedures for a fuzzy Markov reward model are introduced to find the reliability measures.Design/methodology/approachIt is supposed that the introduced system consisted of n identical units connected in parallel and each unit has m different types of failures. Also, each unit of the system is allowed to have d levels of degradation from a working state to complete failure. Non-homogeneous Markov reward model is used to construct the system of differential equations of the model. Procedures are proposed to obtain reliability measures of the model under considering that the failure and repair rates of the systems unit are fuzzy. An application is constructed to analyze a system of 2-unit, and results are shown graphically.FindingsNon-homogeneous Markov reward model is used to construct the system of differential equations of the model.Originality/valueAll papers in literature assumed Markov reward model with deterministic parameters. In this paper, a generalization of classical Markov reward model is introduced.

An Improved Stochastic Model for Cybersecurity Risk Assessment

Most of the existing solutions in cybersecurity analysis has been centered on identifying threats and vulnerabilities, and also providing suitable defense mechanisms to improve the robustness of the cyberspace network. These solutions lack effective capabilities to countermeasure the effect of risks and perform long-term prediction. In this paper, an improved risk assessment model for cyberspace security that will effectively predict and mitigate the consequences of risk was developed. Real-time vulnerabilities of a selected network were scanned and analysed and the ease of vulnerability exploitability was assessed. A Risk Assessment Model was formulated using the synergy of Absorbing Markov Chain and Markov Reward Model. The model was utilized to analyse cybersecurity state of the selected network. The proposed model was simulated using R- Statistical Package, and its performance was evaluated by benchmarking with an existing model, using Reliability and Availability as metrics. The result showed that the proposed model has higher reliability and availability over the existing model. This implied that there is a significant improvement in the assessment of security situations in a cyberspace network.

A Symbolic Approach to the Analysis of Multi-Formalism Markov Reward Models

When modelling large systems, modularity is an important concept, as it aids modellers to master the complexity of their model. Moreover, employing different modelling formalisms within the same modelling project has the potential to ease the description of various parts or aspects of the overall system. In the area of performability modelling, formalisms such as stochastic reward nets, stochastic process algebras, stochastic automata, or stochastic UML state charts are often used, and several of these may be employed within one modelling project. This chapter presents an approach for efficiently constructing a symbolic representation in the form of a zero-suppressed Binary Decision Diagram (BDD), which represents the Markov Reward Model underlying a multi-formalism high-level model. In this approach, the interaction between the submodels may be established either by the sharing of state variables or by the synchronisation of common activities. It is shown that the Decision Diagram data structure and the associated algorithms enable highly efficient state space generation and different forms of analysis of the underlying Markov Reward Model (e.g. calculation of reward measures or asserting non-functional system properties by means of model checking techniques).

A NON-HOMOGENEOUS SEMI-MARKOV REWARD MODEL FOR THE CREDIT SPREAD COMPUTATION

In this paper, we present a model to describe the evolution of the yield spread by considering the rating evaluation as the determinant of credit spreads. The underlying rating migration process is assumed to be a non-homogeneous discrete time semi-Markov process. We calculate the total sum of mean basis points paid within any given time interval. From this information we show how it is possible to extract the time evolution of expected interest rates and discount factors.