A model for a system subject to random shocks

Abstract

A Markovian stochastic model for a system subject to random shocks is introduced. It is assumed that the shock arriving according to a Poisson process decreases the state of the system by a random amount. It is further assumed that the system is repaired by a repairman arriving according to another Poisson process if the state when he arrives is below a threshold alpha. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t), if X(t) greater-than-or-equal-to alpha. The stationary case is also discussed.