Belief Reliability Theory and Its Application in a Demand-Driven Uncertain Production System

The external environment of a production system studied in this paper consists of customer demands from outside the system, while the internal factors are determined by the system's inventory levels and planned production quantities. The function of the production system is to provide the required amount of products according to customer demands. If the system encounters a situation where demand exceeds supply, it indicates a failure from the normal system function. Hence there is a need to research and estimate the reliability of the production system. Within the framework of belief reliability theory, this paper first utilizes uncertain renewal process in an engineering context to propose a scientific method for analyzing the reliability of the demand-driven uncertain production system by integrating three scientific principles of reliability. Then the margin equation for the system is established, and the system's belief reliability is calculated using the margin-based reliable principle. Finally, analytical formulas for calculating the uncertainty distribution of the first hitting time of failure and the belief degree of failure occurrence are derived, which is expected to crucially enhance the efficiency of production system reliability estimation.