Reliability of semi-Markov systems in discrete time: modeling and estimation

Vlad Stefan Barbu (1) , Nikolaos Limnios (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

This chapter presents the reliability of discrete-time semi-Markov systems. After some basic definitions and notation, we obtain explicit forms for reliability indicators. We propose non-parametric estimators for reliability, availability, failure rate, mean hitting times and we study their asymptotic properties. Finally, we present a three state example with detailed calculations and numerical evaluations.

Mots clés: Empirical Estimator; Embed Markov Chain; Markov System; Failure Rate Function

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Vlad Stefan Barbu, Nikolaos Limnios. Reliability of semi-Markov systems in discrete time: modeling and estimation. Misra, K.B. Handbook on Performability Engineering, Springer, pp.369-380, 2008, 978-1-84800-131-2. ⟨10.1007/978-1-84800-131-2_24⟩. ⟨hal-00530335⟩