A Stochastic Hybrid Systems framework for analysis of Markov reward models

作者：Dhople S V^*; De Ville L; Dominguez Garcia A D

来源：Reliability Engineering & System Safety, 2014, 123: 158-170.

DOI：10.1016/j.ress.2013.10.011

• Markov availability models
• Markov reliability models
• Reward models
• Performability analysis
• Stochastic hybrid systems

In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: (i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and (ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application Of the framework to performability analysis via analytical and numerical examples.

• 出版日期2014-3