Discrete-Time Markov Chains in Reliability Analysis-Case Study
This paper presents reliability analysis drawn up for an industrial firm. The main goal of this paper is to estimate the probability of firms failure to satisfy an order to its industrial partners. The second aim is to quantify expected value of amount of manufactured products for specific time period. Discrete Markov chains- well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. The disadvantage of Markov chains is that the amount of computations usually increases rapidly with the amount of states. The Monte Carlo method was implemented to deal with the problem. Chebyshev’s inequality was applied to estimate sufficient number of simulations.
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- 1.Moura, M.C.: Semi Markov decision process for determining multiobjective optimal condition-based replacement policies. In: ESREL (2000)Google Scholar
- 2.Koutras, M.V.: On a Markov chain approach for the study of reliability structures. Journal of Applied Probability (1999)Google Scholar
- 3.Marek, I.: Algebraic Schwarz methods for the numerical solution of Markov chaos. Linear Algebra and Its Applications (2004)Google Scholar
- 4.Stewart, W.: Introduction to the Numerical Solution of Markov Chains, 1st edn., 538 p. Princeton (1994)Google Scholar
- 5.Dubi, A.: Monte Carlo Applications in Systems Engineering, 1st edn., 266 p. Wiley (2000)Google Scholar
- 6.Bernd, A.: Markov Chain Monte Carlo Simulations and Their Statistical Analysis, World Scientific, Singapore (2004)Google Scholar
- 7.Beck, J.L.: Bayesian Updating of Structural Models and Reliability using Markov Chain Monte Carlo Simulation. Journal of Engineering Mechanics (2001)Google Scholar