Standard Article

Reliability Indices

  1. Flavio Frattini1,
  2. Antonio Bovenzi1,
  3. Javier Alonso2,
  4. Kishor Trivedi2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470400531.eorms1063

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Frattini, F., Bovenzi, A., Alonso, J. and Trivedi, K. 2013. Reliability Indices. Wiley Encyclopedia of Operations Research and Management Science. 1–21.

Author Information

  1. 1

    Università degli Studi di Napoli Federico II, Dipartimento di Informatica e Sistemistica, Naples, Italy

  2. 2

    Duke University, Department of Electrical and Computer Engineering, Durham, North Carolina

Publication History

  1. Published Online: 15 JAN 2013


Modern complex systems are expected to be reliable and to provide certain levels of performance during operation. Hence definition and evaluation of reliability and performability indices become necessary. State-space models, such as continuous time Markov chains, are often used because of their capacity of handling different failure/repair behaviors, such as imperfect coverage, correlated failures, and repair dependencies. However time-dependent rates associated to events and particular repair strategies make computation of indices harder. In such cases, nonhomogeneous continuous time Markov chains, semi-Markov processes, Markov regenerative processes (MRGPs), or phase-type approximation can be used. In this article, by means of a simple example, we show how to compute the reliability of such systems with three techniques: piecewise constant approximation, phase type expansion, and simulation.


  • reliability;
  • performability;
  • Markov models;
  • non-Markovian models