Reliability Interval Estimation for a System Model with Element Duplication in Different Subsystems

Abstract

The problem was considered of estimating reliability for a complex system model with element duplication of various subsystems and ensuring possibility of additional redundancy in a more flexible dynamic (or 'sliding') mode in each of the subsystems, which significantly increases reliability of the system in general. For the system considered, general model and analytical expressions were obtained in regard to the main reliability indicators, i.e., probability of the system failure-free operation (reliability function) for a given time and mean time of the system failure-free operation. On the basis of these analytical expressions, the lower confidence limit for the system reliability function was found in a situation, where the element reliability parameters were unknown, and only results of testing the system elements for reliability were provided. It was shown that the system resource function was convex in the reliability parameters vector of the system separate elements various types. Based on this, the lower confidence boundary construction for the system reliability function was reduced to the problem of finding the convex function extremum on a confidence set in the system element parameter space. In this case, labor consumption of the corresponding computational procedure increases linearly with an increase in the problem dimension. Numerical examples of calculating the lower confidence boundary for the system reliability function were provided