Abstract
The reliability modelling of redundant systems is an important step to estimate the ability of a system to meet the required specifications. Markov chains have characteristics making it very simple the graphic representation of this type of model. They however have the disadvantage of being quickly unworkable because of the size of the matrices to be manipulated when systems become complex in terms of number of components or states. This issue, known as of combinatorial explosion is discussed in this chapter. Two methods are proposed. The first one uses the concept of decoupling between phenomena driven by different dynamics. The second is based on a principle of iteration after cutting the model into classes of membership. Both are based on the principles of approximating the exact result by reducing the scale of the problem to be solved. A case study is eventually carried out, dealing with the reliability modelling and assessing of a mechatronic subsystem used for an Unmanned Aerial Vehicle flight control with a triple modular redundancy. Results are discussed.
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Notes
- 1.
It would be logical in such a case, to reverse the process decoupling but our intention here was to observe the behaviour of the iterative method when product calculations do not give satisfactory results. Let us note that the rates considered here are meaningless.
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Martin, C., Gonzalez-Prida, V., Pérès, F. (2015). Reliability Assessment of a Multi-Redundant Repairable Mechatronic System. In: Kadry, S., El Hami, A. (eds) Numerical Methods for Reliability and Safety Assessment. Springer, Cham. https://doi.org/10.1007/978-3-319-07167-1_14
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