Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8251Research ArticleResearch of the Reliability of a Homogeneous Redundant Warm Standby System in a Random EnvironmentTranAnh NghiaProbability Theory and Mathematical Statistics Departmenttrananhnghiadhv@yahoo.comPeoples’ Friendship University of Russia150120141304208092016Copyright © 2014,2014This paper investigates the inﬂuence of randomness of the environment on the reliability of work of technical systems and extends research of the previous paper to the case of the warm redundant standby. A short review of the papers devoted to the queueing systems operating in random environments is cited. A general Markov model of the reliability of a system operating in Markov random environment is proposed. Diﬀerential equations for the time dependent state probabilities of such a system and appropriate formulas for the stationary and non-stationary its reliability characteristics is given. An expression for the moment generation function and appropriate moments of the system life time are given. For the purpose of inﬂuence of environmental variability on the system reliability characteristics some parameter c is introdeced, which indicates the inﬂuence of variability on the intensity of failures and recoveries of elements in diﬀerent states of the environment. With using a specially developed software module in the environment MATLAB the numerical study and comparison of the reliability characteristics of the warm redundancy two-units system, operating in a stable and random environments with two states are conducted. Results of the numerical investigation, presented in the form of tables and graphs show both similarities and diﬀerences in the systems in a random and stable environments.reliability systemsrandom environmentsstationary and non-stationary system reliability characteristicsнадёжность системслучайная средастационарные и нестационарные характеристики надёжности системы