aspg-21-2728-1791475504 20261008160504 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 2 Kawther F. Alhasan Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq Industry has developed greatly nowadays, and it has been accompanied by great complexity in machines and devices. Researches that seeks to obtain high efficiencies for these machines have emerged , such as reliability theory. Due to the verity and complexity of the machines, we resort to using the neutrosophic reliability that includes cases excluded from classical reliability. The aim of this paper is to define the neutrosophic parallel system and study neutrosophic methods of calculating the neutrosophic reliability, where the basic concept neutrosophic adjacency matrix of system are present by defined neutrosophic adjacency matrix of neutrosophic graph. Two methods for calculate the neutrosophic reliability are defined conformity to neutrosophic logic which are neutrosophic minimal path method and neutrosophic tracing method. some applications have been introduced. 2024 68 79 2728 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240207 https://www.americaspg.com/journal/21/article/2728 https://www.americaspg.com/storage/91714350154.pdf