APPLICATION OF METHODS OF THE THEORY OF LIMIT THEOREMS TO PROBLEMS ON DETERMINING THE RELIABILITY OF COMPLEX SYSTEMS

摘要

We present two methods of solving one of the fundamental problems of reliability theory (1) for proportional and logistic, homogeneous and nonhomogeneous Poisson models of reliability growth in complex systems: 1. on the basis of estimates of convergence rates in limit theorems for special random sums; 2. on the basis of an analogue of the Bernstein inequality for Poisson random sums. We illustrate how to apply these methods by examples of specific models and obtain explicit expressions (19), (22), (29), (30), and (31) of the lower bound for the reliability level.