A Hierarchical Decision-Based Maintenance for a Complex Modular System Driven by the { MoMA} Algorithm
M. L. Gamiz, D. Montoro-Cazorla, M. C. Segovia-Garcia
TL;DR
The paper introduces a hierarchical, decision-based maintenance policy for complex modular systems with $K$ independent modules, where unit lifetimes follow PH distributions and module shocks follow MAPs. It leverages the Matrix-Analytic Method (MAM) and the MoMA algorithm to build a bottom-up, layered generator and to formulate a cost-minimization problem over inspection intervals $ au$, incorporating wear-out, shocks, and maintenance actions. Maintenance matrices ${f M}_i$ and cost matrices ${f C}_i$ enable state-aware module repair or replacement, with system-wide decisions derived from the consolidated states $U_1$, $U_2$, and $D$; the approach yields closed-form, implementable expressions and is illustrated on a submarine Electrical Control Unit (ECU). The numerical study demonstrates how inspection frequency and maintenance costs influence total life-cycle cost, showing the method’s potential for reliability planning in modular systems and its adaptability to other architectures. The work advances modular reliability modeling by coupling hierarchical state descriptions with a tractable maintenance-cost optimization framework grounded in MAP/PH representations.
Abstract
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).