A new approach and software support to reliability analysis of repairable complex systems

A new method of reliability analysis of complex systems and software supporting is suggested. It is based on modelling of their evolution by means of semi–Markov processes. The results are obtained under general assumptions concerning the distributions of failure and repair times of the system’s unit. We will consider a complex system S with repairable units. It consists from N, (N ≥ 1) units and has a definite functional structure. The failure time of the i–unit is a random variable (r.v.) α 1 with the following distribution function (d.f.) F (i) 1 (t) = P (α (i) 1 ≤ t), i = 1, N , and the repair time is a r.v. α 0 with d.f. F (i) 0 (t) = P (α (i) 0 ≤ t), i = 1, N . It is assumed that d.f. F (i) k , k = 0, 1, i = 1, N are absolutely continuous with respect to Lebesgue measure, and r.v. α k are independent in totality and have finite means (0 ≤ Eα k < ∞) The i–unit may be in one of the following states: operative, operative disconnected, under repair or disconnected under repair. The disconection of i–unit (or a totality of units) may be a result of total system’s failure or of some functional connected with it system’s unit and the i–unit does not belong to any efficient way. We will understand here under an efficient way a chain of functional connected units, whose functioning involves the system’s viability. When the system’s failure occurs all the remained operative units are disconnected. At this moment the repair of units under repair in system is done only. The disconnected units are included in system with that level of operation or repair which find theirs at the moment of disconnection c ©1994 by A.Corlat, S.Corlat