  In this paper, a condition-based imperfect maintenance model based on
piecewise deterministic Markov process (PDMP) is constructed. The degradation
of the system includes two types: natural degradation and random shocks. The
natural degradation is deterministic and can be nonlinear. The damage increment
caused by a random shock follows a certain distribution, and its parameters are
related to the degradation state. Maintenance methods include corrective
maintenance and imperfect maintenance. Imperfect maintenance reduces the
degradation degree of the system according to a random proportion. The
maintenance action is delayed, and the system will suffer natural degradations
and random shocks while waiting for maintenance. At each inspection time, the
decision-maker needs to make a choice among planning no maintenance, imperfect
maintenance and perfect maintenance, so as to minimize the total discounted
cost of the system. The impulse optimal control theory of PDMP is used to
determine the optimal maintenance strategy. A numerical study dealing with
component coating maintenance problem is presented. Relationship with optimal
threshold strategy is discussed. Sensitivity analyses on the influences of
discount factor, observation interval and maintenance cost to the discounted
cost and optimal actions are presented.
