Existing risk in production systems has a direct relationship with unreliability of these systems. Under such circumstances, the approach to maximize the reliability should be replaced with a risk-based reliability assessment approach. Calculating the absolute reliability for systems and complex processes, when we are not provided with any data on failure, is extremely complex and difficult. Until now, studies of reliability assessment have been based on the probability theory, in which the failure time is anticipated after determining the type of size distributions. However, in this paper, the researchers have developed an approach to apply the possibility theory instead of the probability theory. Instead of using absolutely qualitative methods, this new approach applies the Dempster Shafer Theory. It is obvious when there are insufficient data; an index is needed to make a decision. Then, a novel method is proposed and used in a real case study in order to determine the reliability of production systems based on risk when the available data are not sufficient, helping us to make decisions. After calculating the failure probability and analyzing the assessment matrix and risk criteria, we may conclude that the failure risk of equipment is reduced while the system reliability is increased. (c) 2012 Elsevier Ltd. All rights reserved.