Method for constructing GL‑models for consecutive k‑within‑m‑out‑of‑n systems

Abstract

The article is devoted to the method for constructing a GL‑model for fault‑tolerant multiprocessor systems. GL‑models are used to evaluate the reliability parameter of a system by performing statistical experiments based on its behavior in the failure flow. The paper considers consecutive‑k‑within‑m‑out‑of‑n systems – systems that fail when any k of m consecutive elements fail. Currently, no known method exists for constructing GL‑models for consecutive‑k‑within‑m‑out‑of‑n systems, despite their wide use and the fact that reliability evaluation using GL‑models is often simpler than analytical methods, especially for complex and heterogeneous systems. When additional failure conditions are introduced, GL‑models make it relatively easy to represent such changes, whereas analytical methods may require significant recalculations. Therefore, the purpose of this work is to describe a universal method for constructing GL‑models for consecutive‑k‑within‑m‑out‑of‑n systems. The construction of the GL‑model for the above‑mentioned system begins with creating submodels for each group of m elements with a one‑element shift. In the next step, all submodels are combined into one by connecting their graphs at a common vertex. Experimental results have confirmed that the model built using the proposed method accurately reflects the behavior of the given system in the failure flow..