A quantitative lower estimate for the expectation of the first failure moment of a high reliable system with protection in a nonstationary regime. (English. Ukrainian original) Zbl 0985.60079

Kushnir, O. O.

Theory Probab. Math. Stat. 61, 95-100 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 91-96 (2000).

Quantitative lower estimation for the expectation of mean time to failure of a higher-reliable system with protection over upper estimation of the distribution function of this time in the case of existence of moments of second order of the initial distribution functions is obtained. In the previous paper [ibid. 55, 121-128 (1997); resp. ibid. 55, 117-124 (1996; Zbl 0923.60092)] the author obtained limit theorems on the exponential asymptotic of the distribution function of the mean time to failure of the system with protection using the method of summing up and analysis of integral equations. The present paper uses this method.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60K05	Renewal theory
60K10	Applications of renewal theory (reliability, demand theory, etc.)
60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)

Keywords:

higher-reliable system with protection; non-stationary regime; mean time to failure; lower estimation

Citations:

Zbl 0923.60092