Checking policy for deteriorating multistate systems

In this article a multistate system under some checking policy is considered. The system has n+1 states: 0,1,...,n, and deteriorates gradually. State 0 is a normal (full capacity) state and states 1,...,n are considered unsatisfactory. Transition from state 0 to state 1 is considered a system failure. This failure can be detected only through checking, which entails a fixed cost c. The holding time in the undiscovered state i (i=1,...,n) results in cost di per unit of time. For such a system, the algorithm of determining optimum checking times is given.