The reliability and performability of a repairable and degradable ATP system

In this paper, the reliability and performability analysis of a repairable and degradable ATP system (automatic train protection system) are discussed. The ATP system is composed of nine subsystems, five of which are duplicated and the other of which are simplex subsystems. When some subsystems with two fold fail, the ATP system can still operate. But its performance comes down. When one of the other subsystems fails, the system can´t operate again, which means the system is at fault. The ATP system is repairable if and only if the system is at fault. In addition, it is assumed that each unit´s lifetime of ATP system obeys exponential distribution and the distribution of the repair time is an arbitrary distribution. All the distributions of the above are mutually independent. The switches´ lifetimes follow three kind of cases: the first is that the switches can´t fail; the second is that the lifetimes distributions of switches are 0-1 distributions; and the third is that the distributions of switches´ lifetimes are exponential. By using the extended Markov renewal processes and probability theory, we obtain the ATP system´s reliability measures, such as reliability function R(t), system availability A(t), mean time to system first fault (MTFF) etc., and ATP system´s performability measures, such as system computation availability (or system mean computation ability at time t) Ac(t), and mean computation to system first fault (MCFF) etc