A Random Shock Model for a Linearly Deteriorating System

  • Lee, Ji-Yeon (Department of Statistics, Yeungnam University, Kyongsan 712-749) ;
  • Lee, Eui-Young (Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784)
  • Published : 1995.12.01

Abstract

A random shock model for a linearly deteriorating system is introduced. The system deteriorating linearly with time is subject to random shocks which arrive according to a Poisson process and decrease the state of the system by a random amount. The system is repaired by a repairmen arriving according to another Poisson process if the state when he arrives is below a threshold. 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) is over the threshold. The stationary case is briefly discussed.

Keywords

References

  1. Probability in the Engineering and Informational Sciences v.1 An Inventory with Constant Demand and Poisson Restocking Baxter,L.A.;Lee,E.Y.
  2. Journal of the Applied Probability v.30 A Model for a System Subject to Random Shocks Lee,E.Y.;Lee,J.
  3. Acta Mathematica Academiae Scientiarum Hungaricae v.8 On Certain Sojourn Time Problems in the Theory of Stochastic Processes Takacs,L.