Belief Reliability Modeling for Demand-Driven Uncertain Production Systems with Delay Effects

This paper explores belief reliability modeling for demand-driven uncertain production systems with delay effects. In such systems, demand exhibits cyclical patterns, but real-world complexities introduce epistemic uncertainty, especially with limited data. Delay effects, where initial consumer responses differ significantly from later stages, further complicate demand dynamics. The study introduces a model incorporating delay effects to better predict inventory requirements and system capacity. By defining performance margin and belief reliability based on belief reliability theory, this paper provides a framework to assess system reliability, considering initial inventory, productivity, and demand fluctuations. The proposed model helps producers balance cost efficiency and reliability, ensuring adaptability to both initial demand surges and subsequent stabilization. Additionally, the paper derives analytical expressions for belief reliability and first hitting time of failure, offering practical tools for managing production risks and optimizing system performance under uncertainty. The results highlight the importance of delay effects in shaping demand patterns and system reliability, providing valuable insights for production planning and risk management.

Keywords: Belief reliability, Production, Uncertainty theory, Uncertain renewal process, Performance margin, Failure, Risk analysis.