ISSN 0146-4116, Automatic Control and Computer Sciences, 2013, Vol. 47, No. 6, pp. 342–351. © Allerton Press, Inc., 2013. Original Russian Text © V.V. Rykov, Tran Anh Nghia, 2013, published in Avtomatika i Vychislitel’naya Tekhnika, 2013, No. 6, pp. 73–85. 342 1. INTRODUCTION Most technical systems and biological objects operate in a changing environment, the changes being of both regular (seasons) and random nature; their frequency can be as well as commensurable with failure rates of the system or to be greater or less than it. The way that reliability of the system depends on these factors is of significant interest, given rapidly changing technical capabilities of the modern world. In the paper the influence of the environment variability to the stationary characteristics and the reliability func- tion is studied. There are a number of papers devoted to studying the behavior of queuing systems operating in a ran- dom environment. The paper of M. Eisen and M. Tainiter [1] was one of the first publications on this sub- ject, where they studied the M/M/1(ME) system (here and in the following ME denotes Markov environ- ment and means that the respective system operates in a random Markov environment), assuming that the environment can take two states only. The same system was studied in [2] and then generalized in [3] for an arbitrary finite number of states of the environment. M. Newts [4] used the matrix-analytical approach to study the behavior of single and multi server systems in a random environment. Then, the M/M/1(ME) and M/M/∞ (ME) models have been studied in [5, 6]. As for further research on the subject, the behavior of queuing systems has been spread out in different directions involving generalization of the input flow models, the queuing scheme, and the structure of the random environment. One can find a rather detailed overview of up-to-date publications in, for instance, [7, 8]. However, the reliability of systems operating in a random environment has received insufficient attention thus far. In this paper, we study the reliability of the binary Markov system operating in a random Markov environment. To shade the structural side of the issue and to avoid superfluous technical difficulties, we consider the simplest binary model of a cold redundancy system with only one repair device that operates in a random Markov environment with a finite number of states. Note that generalization for hot and warm redun- dancy system with several recovery devices does not entail any principal difficulties and only involves changing parameters of the model. Studying heterogeneous reliability systems operating in a random Markov environment implies extending significantly the phase space that describes the behavior of the system of random processes and, hence, applying more complicated computational algorithms and pro- cedures. Examples of how the model involved can be used to study a hybrid communication system are given in [9, 10]. The paper is structured as follows. The next section describes the model of the system involved and the random process of its operation. In the third and fourth sections, we give the Kolmogorov equations for probabilities of system states and the procedure of calculating stationary probabilities. The fifth section deals with calculating the reliability function for the system. Finally, the last section gives the results of numerical analysis of the model for a system of two elements n = 2 that operates in a random environment taking two possible states m = 2. We complete the work with the conclusions and references. On Reliability of Binary Systems in a Random Environment V. V. Rykov and Tran Anh Nghia Peoples’ Friendship University, ul. Miklukho-Maklaya 6, Moscow, 117198 Russia e-mail: vladimir_rykov@mail.ru, trananhnghiadhv@yahoo.com Received April 29, 2013; in final form, July 15, 2013 Abstract—The influence of random environments to technical systems reliability is studied. A Markov model of reliability of the system that operates in a random Markov environment is proposed. General relations for stationary and non-stationary Quality of Service (QoS) characteristics of such system are given. Numerical study and comparison for a cold backup system operating in stable and random two- state environments are performed. Keywords: reliability of the system, random environment, Markov process DOI: 10.3103/S0146411613060096