A Meta‐Action‐Oriented Reliability Allocation for Machine Tools Using Bayesian Networks and Fuzzy Set Theory

ABSTRACT The rationality of reliability allocation is critical to improving the inherent reliability of machine tools. However, under fuzzy environments, traditional methods struggle to effectively characterize multi‐source uncertainties, leading to deviations between allocated and actual reliability levels. To address this issue, this paper proposes a meta‐action‐based reliability allocation method for machine tools by integrating Bayesian networks and fuzzy set theory. First, based on the Function–Motion–Action (FMA) decomposition framework, a meta‐action fault tree model is constructed for functional failure analysis, with meta‐actions serving as the basic units for reliability analysis and allocation. Second, fuzzy set theory is introduced to characterize the prior failure information of basic events, and expert information is aggregated to derive their prior failure probabilities, thereby accounting for the uncertainties arising from expert knowledge and incomplete information. Subsequently, the meta‐action fault tree is transformed into a Bayesian network, where whole machine failure is taken as diagnostic evidence. Bayesian backward inference is then employed to obtain the conditional diagnostic probabilities of meta‐action failures, which are further used to establish the reliability allocation model. Meanwhile, a safety factor is introduced to obtain reliability allocation intervals that account for design margins. Finally, a case study of a form‐grinding gear machine is conducted to validate the effectiveness of the proposed method. The results demonstrate that the proposed method effectively improves the accuracy of reliability allocation under fuzzy environments, providing theoretical support for the high‐reliability design of machine tools.