Numerical simulation on the existence of fluctuation of instantaneous availability

This paper considers the fluctuation of the instantaneous availability by numerical methods for a one-unit repairable system. The choices of the failure rate and repair rate are linear or cubic increasing functions. For the equation of instantaneous availability composing of two convolutions, the following numerical methods are used: the composite Simpson formula and the trapezoidal formula. That is to say, the simulated curves of instantaneous availability under any condition are obtained. Through the simulated results, when the failure rate and repair rate are selected as increasing functions, the extremum of simulated curve exists so fluctuation exists. On the other hand, if parameters of increasing functions become smaller, the fluctuation weakens.