zbMATH — the first resource for mathematics

The first failure of a highly reliable system of two elevators. (English. Ukrainian original) Zbl 0958.60084
Theory Probab. Math. Stat. 59, 113-120 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 110-116 (1998).
Asymptotic of the distribution function of time to failure for a system of two lifts were investigated by A. N. Korlat, V. N. Kuznetsov, M. M. Novikov and A. F. Turbin [“Semi-Markov models of renewal systems and queueing systems” (1991; Zbl 0778.60064)]. In this paper an analogous limit theorem is proved by another method under more general conditions. A uniform limit theorem is formulated in this case. Upper estimates for distribution function of time to failure of a highly reliable system of two lifts are given. Highly reliable systems with protection were investigated by the author [Theory Probab. Math. Stat. 55, 121-128 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 117-124 (1996; Zbl 0923.60092)].

60K10 Applications of renewal theory (reliability, demand theory, etc.)
90B25 Reliability, availability, maintenance, inspection in operations research
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)