On a new family of r-modified reliability systems

In this work, we focus on stochastic modeling for sustainable systems and introduce the family of r -modified reliability systems. This new family generalizes classical reliability systems studied in the literature by considering the components in the system to exhibit a kind of dependence that relaxes the component operating requirements and provides energy and resource efficiency. From a theoretical viewpoint, such a dependence is modeled with the use of a modified binary sequence. We then derive the reliability of two members of the family, i.e., the r -modified- k -out-of- n : F system and the r -modified-consecutive- k -out-of- n : F system, under different assumptions on the component reliabilities by using a variety of approaches, including Markov chains, combinatorial methods, and simple probabilistic arguments. We finally give some examples of real-life systems wherein the developed models and results are applicable and present the corresponding numerical results.