@article{Nashwan_2021, place={Iraq, Baghdad}, title={ Reliability and Failure Probability Functions of the m-Consecutive-k-out-of-n: F Linear and Circular Systems}, volume={18}, url={https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5023}, DOI={10.21123/bsj.2021.18.2.0430}, abstractNote={<p>The <em>m</em>-consecutive-<em>k</em>-out-of-<em>n</em>: F linear and circular system consists of <em>n</em> sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least <em>m</em> non-overlapping runs of consecutive-<em>k</em> failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly <em>m</em>-consecutive-<em>k</em>-out-of-<em>n</em>: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.</p>}, number={2}, journal={Baghdad Science Journal}, author={Nashwan, Imad I. H.}, year={2021}, month={Jun.}, pages={0430} }