Reliability of repairable multi-state two-phase mission systems with finite number of phase switches.

• A repairable multi-state two-phase mission system with finite number of phase switches is proposed. • The probability density function for the time to first failure of the two-phase mission system is presented. • Some reliability indexes, such as the point-wise and interval availabilities, are given. In this article, a repairable multi-state two-phase mission system with finite number of phase switches is considered. System states can be divided into a subset of working states and a subset of failed states, and the system can be repaired from the failed subset to the working subset. However, when the number of switches between two phases exceeds a specified integer, the system will be permanently damaged and cannot be repaired any more. The closed-form formulas of the probability density function of the time to first failure of the system, the point-wise availability, the interval availability and other reliability indexes are obtained by using the theory of aggregated stochastic processes. Finally, a detailed example of lithium-ion batteries is given to illustrate the proposed model and obtained results. [ABSTRACT FROM AUTHOR]