MoMA Algorithm: A Bottom-Up Modeling Procedure for a Modular System under Environmental Conditions Gámiz Pérez, María Luz Segovia García, María del Carmen Pérez Ocón, Rafael Modular systems Markovian arrival process Phase-type distribution Shock models Reliability analysis Maintenance Matrix-analytic methods The functioning of complex systems relies on subsystems (modules) that in turn are composed of multiple units. In this paper, we focus on modular systems that might fail due to wear on their units or environmental conditions (shocks). The lifetimes of the units follow a phase-type distribution, while shocks follow a Markovian Arrival Process. The use of Matrix-Analytic methods and a bottom-up approach for constructing the system generator is proposed. The use of modular structures, as well as its implementation by the Modular Matrix-Analytic (MoMA) algorithm, make our methodology flexible in adapting to physical changes in the system, e.g., incorporation of new modules into the current model. After the model for the system is built, the modules are seen as a ‘black box’, i.e., only the contribution of the module as a whole to system performance is considered. However, if required, our method is able to keep track of the events within the module, making it possible to identify the state of individual units. Compact expressions for different reliability measures are obtained with the proposed description, optimal maintenance strategies based on critical operative states are suggested, and a numerical application based on a k-out-of-n structure is developed. 2022-11-03T11:01:40Z 2022-11-03T11:01:40Z 2022-09-27 journal article Gámiz, M.L... [et al.]. MoMA Algorithm: A Bottom-UpModeling Procedure for a Modular System under Environmental Conditions. Mathematics 2022, 10, 3521. [https://doi.org/10.3390/math10193521] https://hdl.handle.net/10481/77730 10.3390/math10193521 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI