  This paper presents a maintenance policy for a modular system formed by K
independent modules (n-subsystems) subjected to environmental conditions
(shocks). For the modeling of this complex system, the use of the
Matrix-Analytical Method (MAM) is proposed under a layered approach according
to its hierarchical structure. Thus, the operational state of the system (top
layer) depends on the states of the modules (middle layer), which in turn
depend on the states of their components (bottom layer). This allows a detailed
description of the system operation to plan maintenance actions appropriately
and optimally. We propose a hierarchical decision-based maintenance strategy
with periodic inspections as follows: at the time of the inspection, the
condition of the system is first evaluated. If intervention is necessary, the
modules are then checked to make individual decisions based on their states,
and so on. Replacement or repair will be carried out as appropriate. An
optimization problem is formulated as a function of the length of the
inspection period and the intervention cost incurred over the useful life of
the system. Our method shows the advantages, providing compact and
implementable expressions. The model is illustrated on a submarine Electrical
Control Unit (ECU).
