Availability and reliability analysis of a retrial system with warm standbys and second optional repair service

Abstract

This article deals with availability and reliability characteristics for a repairable fault-tolerant system with warm standbys and second optional repair service. The failure times of primary components and warm standby ones are assumed to be exponentially distributed, and the failed components can be repaired by a repairman. For each failed component, the repairman provides two phases of repair service. All the failed components need the first essential repair, whereas only part of them demand the second optional repair. By using Markov theory and solving Matrix equation satisfied by the steady-state probabilities of the system, we present the steady-state availability of the system. By using Laplace transform method, we obtain the reliability function and the mean time to first failure of the system. Numerical examples are given to make research of the effect of the system parameters on the reliability function, steady-state availability and MTTF.

Keywords:

• Retrial system
• warm standby
• second optional service
• reliability problem

Additional information

Funding

This work was supported in part by the Natural Science Foundation of Anhui Higher Education Institutions of China (NO. KJ2020A0530), the Fuyang Municipal Government-Fuyang Normal University Horizontal Cooperation Projects in 2017 (NO. XDHXTD201709), the building of Brand Speciality Projects of Fuyang Normal University (NO. 2019PPZY01), Program for Science Research of Fuyang Normal University (NO. 2020FSKJ14).