Control limit type policies are widely discussed in the
literature, particularly regarding the maintenance of deteriorating
systems. Previous studies deal mainly with stationary
deterioration processes, where costs and transition probabilities
depend only on the state of the system, regardless of its
cumulative age. In this paper, we consider a nonstationary
deterioration process, in which operation and maintenance
costs, as well as transition probabilities “deteriorate”
with both the system's state and its cumulative age.
We discuss conditions under which control limit policies
are optimal for such processes and compare them with those
used in the analysis of stationary models.
Two maintenance models are examined: in the first (as in
the majority of classic studies), the only maintenance
action allowed is the replacement of the system by a new
one. In this case, we show that the nonstationary results
are direct generalizations of their counterparts in stationary
models. We propose an efficient algorithm for finding the
optimal policy, utilizing its control limit form. In the
second model we also allow for repairs to better states
(without changing the age). In this case, the optimal policy
is shown to have the form of a 3-way control limit
rule. However, conditions analogous to those used
in the stationary problem do not suffice, so additional,
more restrictive ones are suggested and discussed.