In this paper, we assessed the reliability of a paper plant using the weibull distribution and a hexadecagonal fuzzy number. Many difficulties in life have ambiguity, uncertainty, impreciseness, and so on, thus we must understand these phenomena. The paper factory under study is a complicated system comprised of numerous subsystems. Based on the Boolean function approach, the mathematical model was created. In this study, we will employ a hexadecagonal fuzzy Weibull lifetime distribution, in which the lifespan parameters are assumed to be fuzzy due to data ambiguity and inaccuracy. Expressions for fuzzy reliability, fuzzy mean time to failure, fuzzy hazard function, and their α-cut have been addressed when the system follows the hexadecagonal fuzzy weibull lifetime distribution. An examination of the numbers is offered at the end to highlight the system’s fuzzy reliability characteristics.