Abstract
We consider a Bernoulli process where the success probability changes with respect to a Markov chain. Such a model represents an interesting application of stochastic processes where the parameters are not constants; rather, they are stochastic processes themselves due to their dependence on a randomly changing environment. The model operates in a random environment depicted by a Markov chain so that the probability of success at each trial depends on the state of the environment. We will concentrate, in particular, on applications in reliability theory to motivate our model. The analysis will focus on transient as well as long-term behaviour of various processes involved.
Similar content being viewed by others
References
Çmlar E (1975) Introduction to stochastic processes. Prentice-Hall, New Jersey
Cmlar E, Özekici S (1987) Reliability of complex devices in random environments. Probability in the Engineering and Informational Sciences 1:97–115
Howard RA (1971) Dynamic probabilistic systems. Wiley, New York
Lefèvre C, Mihaud X (1990) On the association of the lifelengths of components subjected to a stochastic environment. Advances in Applied Probability 22:961–964
Özekici S (1996) Complex systems in random environments. In: Özekici S (Ed.) Reliability and maintenance of complex systems. Springer, Berlin
Özekici S (1995) Optimal maintenance policies in random environments. European Journal of Operational Research 82:283–294
Singpurwalla ND, Youngren MA (1993) Multivariate distributions induced by dynamic environments. Scandinavian Journal of Statistics 20:251–261
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Özekici, S. Markov modulated Bernoulli process. Mathematical Methods of Operations Research 45, 311–324 (1997). https://doi.org/10.1007/BF01194782
Issue Date:
DOI: https://doi.org/10.1007/BF01194782