## 1 Introduction  
Machinery/machines are assembled, fitted with or intended to be fitted with a drive system consisting of linked parts or components, at least one of which moves, and which are joined together for a specification [1]. The manufacturer of machinery or his authorized representative is mandated by Directive 2006/42/EC Annex I to ensure that a risk assessment is carried out in order to determine the health and safety requirements that apply to the machinery, and the machinery must then be designed and constructed taking into account the results of the risk assessment [2]. Safety standards for industrial robots [3], collaborative robots [4], robot systems and integration [5], etc., clearly stipulate the technical requirements of hazard identification and risk assessment. Reference [1] specifies procedures of risk assessment and risk reduction to achieve safety in the design of machinery. After hazard identification, risk estimation is conducted for each identified hazard event/situation. The estimated risk level bears significant implications for the selection of hazard reduction measures and the ensuring of machine safety. The overestimation of the risk might lead to excessive machine safety design, thereby inflating costs. Conversely, insufficient risk estimation could compromise the safety of product design and inadvertently trigger dangers. Product standards usually specify Performance Level (PL) or Safety Integrity Level (SIL) requirements for their safety functions [3; 5; 6; 7]. If no product-related standards exist, the determination of the required performance level PLr for each safety function can be carried out by a risk estimation approach [8; 9], while reference [10] estimates the required SIL. Excessive dispersion in the risk estimation results may lead to inappropriate risk reduction measures being implemented [8]. Risk is relevant to the severity of harm and the probability of the occurrence of that severity of harm. In the process of risk estimation, each risk element is generally divided into several discrete grades or scores, and then the risk assessors select the grade or acquire the score by qualitative or quantitative approaches. The final risk level is obtained through risk estimation tools or methods, such as a risk matrix, risk graph, numerical scoring and hybrid tools using a combination of methods [11]. Reference [12] notes that machinery-related risk estimation is mainly based on qualitative and static tools, which lead to subjective decision-making. The influence of subjective factors on the results of risk estimation primarily comes from the following three aspects:  
1. **The definitions or descriptions of scaled risk elements typically employ qualitative or a combination of qualitative and quantitative textual descriptions, leading to disparate interpretations. ** For example, reference [11] suggests that the severity of the harm S can be classified as: S1-slight injury, and S2-serious injury. Understanding those descriptions is very subjective and there tends to be significant variation between different risk assessment members [13]. Given that risk assessments pertain to potential future scenarios, such statements are intrinsically uncertain, by virtue of their inherent nature, and it is not easy to define scales unambiguously by mostly using nominal and textual descriptions. Reference [14] shared an experience in which subjects had to allocate a quantitative value to the verbal labels of probability, and concluded that regardless of whether the verbal labels were detailed, the probability assigned would vary due to distinct interpretations. 2. **Risk assessment members' characteristics. ** The familiarity with the machine, background, and position of the persons who performed the risk assessment, and other factors such as optimism bias, confirmation bias, and overconfidence will affect the judgement of likelihood and consequence; the most significant divergence was detected in the estimation of the parameter Fr (frequency and duration of exposure) [8].