International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2728 2020 2020 Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq Kawther Kawther 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 2024 68 79 10.54216/IJNS.240207 https://www.americaspg.com/articleinfo/21/show/2728