Reliability of unstructured systems with excess time

Abstract

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

Reliability analysis of a system with combined time reserve

“…Assuming formally that g = 0 in formula (6), we obtain the following expectation of the time (established in [3]) to failure of the system only with cumulative time reserve: …”

“…The average values of times of staying the system in its states are specified by the formulas In addition to the subset of states E + introduced above, we consider a subset of states E From formula (10), we obtain the stationary availability factor of the system with cumulative time reserve when g = 0 and obtain this factor for the system with instantly replenished time reserve [3] when t = 0, i.e., we have …”

“…Sources of this time reserve are interoperational accumulators, a throughput reserve, etc. In [3,4], systems with cumulative, instantly replenished, and gradually replenished time reserves were considered. In this article, we analyze the reliability of a system with combined time reserve that consists of cumulative and instantly replenished components.…”

“…In this article, we analyze the reliability of a system with combined time reserve that consists of cumulative and instantly replenished components. Here, as in [3,4], the apparatus of the theory of semi-Markov processes with a common phase state space is used [5]. A system S includes an object that is represented by one structural element and has a combined time reserve.…”