A Simple Repairable System with Warning Device

الملخص EN

This paper considers a simple repairable system with a warning device which can signalan alarm when the system is not in good condition and a repairman who can have delayed-multiplevacations.

By using Markov renewal process theory and theprobability analysis method, the system is first described into a group of integrodifferentialequations.

Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution,are studied by using the strongly continuous semigroup theory or C0 semigroup theory and thespectrum theory.

The reliability indices and some applications (such as the comparisons of some indexes andprofit of systems with and without warning device) as well as numerical examples are presented at the end of the paper.