MoMA Algorithm: A Bottom-Up Modeling Procedure for a Modular System under Environmental Conditions

María Luz Gámiz, Delia Montoro-Cazorla (), María del Carmen Segovia-García and Rafael Pérez-Ocón
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María Luz Gámiz: Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain
Delia Montoro-Cazorla: Department of Statistics and Operational Research, University of Jaén, 23071 Jaen, Spain
María del Carmen Segovia-García: Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain
Rafael Pérez-Ocón: Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 19, 1-19

Abstract: 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.

Keywords: modular systems; Markovian arrival process; phase-type distributions; shock models; reliability analysis; maintenance; Matrix-Analytic methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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