International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/708 2020 2020 Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq Kawther F. Alhasan Department of Mathematics and Computer Science, Port Said University, Egypt A.A. Salama Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA Florentin Smarandache   Reliability is one of the most important indicators of the quality of any system or product, ranging from the simplest machines as a product in any factory to the most complex system, such as phone or aircraft or missile engines, etc. The accuracy of these products indicates their high reliability, and therefore the customer or business owner will have confidence in products and will request more quantity. To reach the highest level of accuracy for the reliability of any system, the corresponding data must be very accurate. For this purpose, we proposed to add accuracy to reliability by adding data that contains more pieces of information about a  specific product or problem. We introduced a new logic (Neutrosophic logic) of data instead of classical logic which gives us more accuracy of data that contain indeterminacy such as extremist, vague, and unclear data. We defined the neutrosophic reliability according to the modern neutrosophic logic by constructing a neutrosophic reliability function. We have used the type of series as an application of neutrosophic reliability and introduced some examples. Neutrosophic reliability theory can be applied in computer science and decision support systems.   2021 2021 52 61 10.54216/IJNS.150105 https://www.americaspg.com/articleinfo/21/show/708