Mathematical model of control of restorable system with latent failures has been built. Failures are assumed to be detected after control execution only. Stationary characteristics of system operation reliability and efficiency have been defined. The problem of control execution periodicity optimization has been solved. The model of control has been built by means of apparatus of semi-Markovian processes with a discrete-continuous field of states.
Time redundancy is a method of increasing the reliability and efficiency of the operation of systems for various purposes, in particular, energy systems. A system with time redundancy is given additional time (a time reserve) for restoring characteristics. In this paper, based on the theory of semi-Markov processes with a common phase space of states, a semi-Markov model of a two-component system with a component-wise instantly replenished time reserve is constructed. The stationary reliability characteristics of the system under consideration are determined.
Time redundancy provides one of the techniques for increasing reliability of systems. Systems with excess time may spend some time restoring their characteristics while continuing uninterrupted operation [1][2][3][10][11][12][13][14]. We study the class of systems with excess time using the apparatus of the theory of semi-Markov processes with a general phase space. Explicit expressions are derived for the nonstationary characteristics of the systems~ SYSTEMS WITH INSTANTANEOUSLY RENEWABLE EXCESS TIME Consider a system S which includes a processor consisting of a single structural element and is characterized by an instantaneously renewable excess time. The time to failure of the processor is a random variable (r.v.) c~ with the distribution function (d.f.) F(t); the repair time is a r.v, ~ with the d.f. G(t). The excess time in the system is a r.v. r with the d.f. R(t).The system S fails when the time to repair the processor after a current fault exceeds the excess time ~" (/~ > r); the system again becomes operational when the processor is repaired. We assume that the r.v.s c~,/3, ~-are independent and have ffmite means; the d.f.s F(t), G(t) have densities f(t), g(t); 0 < P(~ < ~') < 1. Such a system is described in [1][2][3].To describe the operation of the system S, as in [I, 3], we def'me a semi-Markov process (SMP) ~(t) with the following states: e o -the processor is repaired and starts operating; e 1 -the processor is faulty and its repairhas begun; e 2 -the system has failed.The semi-Markov kernel of the Markov renewal process (MRP) that describes the operation of the system S has the form t t.
0-ol
7t ( t) ffi f "R ( t -x) g ( t -x) ~o ( x) dx + R ( t) G ( t).o.
By [4], the system (1) has a unique solution in the class of functions bounded on any fmiteqnterval. Substituting the second equation in the first, we obtain
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.