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Risk analysis of production system, while the actual and appropriate data is not available, will cause wrong system parameters prediction and wrong decision making. In uncertainty condition, there are no appropriate measures for decision making. In epistemic uncertainty, we are confronted by the lack of data. Therefore, in calculating the system risk, we encounter vagueness that we have to use more methods that are efficient in decision making. In this research, using Dempster-Shafer method and risk assessment diagram, the researchers have achieved a better method of calculating tools failure risk. Traditional statistical methods for recognizing and evaluating systems are not always appropriate, especially when enough data is not available. The goal of this research was to present a more modern and applied method in real world organizations. The findings of this research were used in a case study, and an appropriate framework and constraint for tools risk were provided. The research has presented a hopeful concept for the calculation of production systems' risk, and its results show that in uncertainty condition or in case of the lack of knowledge, the selection of an appropriate method will facilitate the decision-making process.

The overall objective of the reliability allocation is to increase the profitability of the operation and optimise the total life cycle cost without losses from failure issues. The methodology, called risk-based reliability (RBR), is based on integrating a reliability approach and a risk assessment strategy to obtain an optimum cost and acceptable risk. This assessment integrates reliability with the smaller losses from failures issues, and so can be used as a tool for decision-making. The approach to maximising reliability should be replaced with the risk-based reliability assessment approach, in which reliability planning, based on risk analysis, minimises the probability of system failure and its consequences. This paper proposes a new methodology for risk-based reliability under epistemic uncertainty, using possibility theory and probability theory. This methodology is used for a case study in order to determine the reliability and risk of production systems when the available data are insufficient, and to help make decisions.