Estimation of reliability of complex system with renewal based on element test results

The problem of confidence estimation of reliability of complex systems with network structure with repairable elements is considered. Estimation of reliability of a system is based on test results of its individual elements (subsystems). Existing methods for solving this problem are designed for relatively simple series-parallel structures consisting of elements with exponential distribution of time to failure. Solution of this problem is suggested for the more general model of “monotone structures” with independent renewable elements, as well as significantly more general case of “aging” system elements (with monotonically increasing function of failure rate). It is assumed that elements of the system are restored regardless of the state of other elements. In addition, the solution of this problem is obtained in the natural, from the practical point of view, asymptotic behavior for the case of high reliability (fast recovery) system elements.