Considering the widespread and complexity of today's system, competitive conditions, reduce the production costs of systems that can be trusted in critical condition, the reliability of the system, is attended as a key element. Maximizing the reliability is a method to reduce costs, considering the reliability of the system design stage. There are different types of manufacturing systems, the system in which the reliability has a significant impact on the costs of production, is called cellular manufacturing system. It is one of the latest kinds of manufacturing systems. Up to now, there haven't been any designs of cellular manufacturing systems by considering the reliability of systems up to now, when a mixed-Weibull distribution is used for distributing the system components. This thesis investigates the cell formation problem, which is one of the fundamental problemsfor designing the cellular manufacturing systems. This is a multi-objective problem, in which the objectives are: 1. Minimizing system costs including variable costs, handling costs and penalty costs, 2: Maximizing the reliability of the system when system components lifetime distribution follows the mixed-Weibull distribution. The exact -constraint algoritm is used to solve this model. An illustrative example which is explained in literature, is used to compare the results of mixed-Weibull model versus Weibull and exponential models.