Optimal maintenance model for a multistate deteriorating system: a geometric process approach

A monotone process model is introduced for a deteriorating system with k+1 states (k working states and one failure state). We prove that the model is equivalent to a geometric process model for a two-state system, in the sense that both systems have the same long-run average cost per unit time and the same optimal maintenance policy. Finally, an optimal maintenance policy for the deteriorating system is determined analytically.