Direct unavailability computation of a maintained highly reliable system

The paper presents a new analytical algorithm which is able to carry out exact reliability quantification of highly reliable systems with maintenance (both preventive and corrective). A directed acyclic graph is used as a system representation. The algorithm allows highly reliable and maintained input components to be taken into account. A new model of a repairable component undergoing hidden failures, i.e. a model when a failure is identified only at special deterministically assigned times, is analytically deduced within the paper. All considered models are implemented into the new algorithm. The algorithm is based on a special new procedure which permits only summarization between two or more non-negative numbers that can be very different. If the summarization of very small positive numbers transformed into the machine code is performed effectively, there is no error at the operation. Unavailability quantification is demonstrated on a test system from references and on its highly reliable modifications. Improvement of the reliability quantification by the new method in comparison to the simulation method is demonstrated on real reliability problem from practice, i.e. the decision-making problem related to reliability of the supply of electric power to consumers