Reliability Analysis for Repairable Multistate Two-Unit Series Systems When Repair Time Can Be Neglected

A model for two-unit series multistate Markov repairable systems with repair time omission is developed based on a model for single-unit multistate Markov repairable systems. In the model, each component has three states: perfect operation, minor failure, and complete failure. Repair time for a complete failure, if it is sufficiently short (no longer than a critical value), does not affect the system operation. The critical value is first supposed to be a constant, and then to be a nonnegative random variable. Some reliability indexes, such as the instantaneous availability, the steady-state availability, and the mean time to first failure, are given. Finally, some numerical examples are presented to illustrate the results obtained in the paper.