A Dynamic Analysis of a Class of Deteriorating Systems

This paper considers a model for the maintenance of a deteriorating system with a discrete state space. At discrete points in time a sequence of maintenance decisions is to be made. These decisions are either to leave the system in its present state, or by performing maintenance to place it in a "higher state." Between maintenance visits the behavior of the system is described by a stationary Markov matrix. For a maintenance cost c\cdotz (where z is the number of states by which the system is improved) and a convex one-period operating cost L(\cdot) a class of transition matrices is found which lead to simple maintenance policies. It is also shown that the restrictions on the transition matrix are not only sufficient but "almost necessary" if the result is to hold for all possible choices of L(\cdot).