## 1 Introduction  
In recent years, with the diversification of market demand and the personalization of customer demand, there has been an increasing number of manufacturing enterprises in the multi-variety and small-batch production mode. On the one hand, multi-variety and low-volume production enterprises generally adopt the order production mode. On the other hand, due to the characteristics of multi-variety, low-volume production enterprises, these enterprises usually face many risks, such as multi-supplier risks, inventory risks, and production planning risks [1, 2, 3]. These two causes increase the possibility of late deliveries of orders. The current research on multi-variety, low-volume businesses focuses on production process optimization [4, 5], which is essential to increasing business productivity. However, for a manufacturing company, being able to meet delivery deadlines for consumers is still a crucial aspect of the company's competitiveness [6]. Studying a firm's risk of late delivery is therefore extremely important [7, 8]. Most existing studies on delayed delivery risk have focused on the countermeasures to the risk after it occurs, for example, ensuring delivery through production optimization [9; 10] and improving delivery strategies [11; 12]. However, current research ignores how risks arise. For multi-variety, low-volume production companies, any environment in the production process can contribute to the eventual risk of delayed delivery. However, risks are conductive: the occurrence of one risk often causes the occurrence of other risks, which leads to the transmission of risks attached to information flow, material flow, and capital flow [13]. For example, human error caused by a distribution agent can lead to overall delays in the supply chain [14], and supply chain disruptions can further lead to risks of late deliveries [15]. Research on the transmission of risk in finances, information, and prices is more abundant [16; 17; 18; 19; 20], but research on the transmission of delayed delivery risk in manufacturing firms is not well-developed [21]. Some researchers have studied the risk transmission process in the whole supply chain system from suppliers, manufacturers, wholesalers, and retailers to customers [22], and the risk transmission process in trade from the perspective of the industrial chain [23]. However, it is difficult to directly apply these studies to the risk management of manufacturing enterprises. In our field research on multi-variety and small-batch manufacturing enterprises, we have found that managers want to understand the transmission path of late delivery risk, that is, when a risk emerges, which risk factors also emerge and eventually lead to late delivery risk, but there is not much referable work on late delivery risk in enterprises. Association rules can reflect the association relationship between risk indicators and risk factors by mining frequent item sets. By mining the association relationship of financial risk indicators, [PERSON] determined credible risk management association rules [24]. [PERSON] constructed a risk interaction network based on strong association rule mining [25]. Moreover, through the mining of management rules, the self-learning and self-tuning of the risk time knowledge ontology database can be realized [26]. It can be seen that the analysis of risk factors by using association rules is the basis of research on risk identification, risk evaluation, risk transmission, risk management, etc. Association rules can be flexibly used in the analysis of multiple data types, such as numerical data and text data, and their use has become a common research method in the field of risk. Bayesian networks are an extension of the Bayesian method and one of the commonly used research methods in the field of uncertain knowledge representation and reasoning. They can provide a quantitative measure of risk.