Approximate instantaneous availability and its error analysis

The one-unit repairable system is studied in this paper, whose lifetime, repair time and repair-delayed time are all supposed to be random variables with general distributions. The instantaneous availability satisfying a second type Volterra integral equation which is solved by a successive approximation approach in this paper, and then the approximate instantaneous availability is obtained. Furthermore, the physical meaning of the approximate instantaneous availability and its error function are both analyzed. Then we get the conclusion that the approximate instantaneous availability can be used to substitute the real one to some extent, whose validity is verified by some numerical examples finally.