**Abstract**

One of the challenges in designing industrial systems is integrating accident risk analysis with the other technical analysis tools. In the face of this challenge, this paper introduces an analytic approach to defining the occupational risk entities in computeraided design software by visualizing the risk entities as geometric shapes. It uses energy/barrier analysis and the fuzzy set theory to model the protective role of barriers and infer the effects of harmful agents on humans and assets (targets). It defines dangers and targets presence zones by fuzzy sets, the so-called "fuzzy spaces" demonstrated as geometric profiles. The barriers affect these geometric profiles, and fuzzy union and intersection aggregate the effects of several dangers and protective measures. The model calculates the quantitative risk indexes for the various workplace points. The proposed model is adapted to evaluate the risk in the computeraided design platform during the workplace simulation. An example illustrates the model application in a one-dimensional space.

**Keywords:** fuzzy theory, risk analysis, computer-aided design

## **1. Introduction**

Järvinen et al. emphasized the potential of three-dimensional (3D) simulation models for implementing risk analysis without presenting any specific model [1]. Wang et al. developed an enhanced automated 3D visualization ergonomic analysis integrated with a proposed fuzzy logic-based joint-level ergonomic risk assessment methodology for work modification and workplace design [2]. Ojstersek et al. used the modeling and simulation method and ergonomic analyses in workplaces and presented potential opportunities for improving productivity and cost [3].

Despite many efforts, researchers have failed to develop practical risk management approaches in 3D platforms; implementing the new concurrent engineering approaches requires integrating safety-engineering techniques into the 3D design applications [4]. One of the significant challenges in this domain is the complexity of risk analysis due to the need to consider many system parameters that are very difficult to quantify. These parameters explain the characteristics of the harmful factors, their effect on vulnerable targets (humans, assets, and the environment), and the role of the safety barriers [5]. In the face of these challenges, this paper proposes

an integrated risk analysis approach to develop the appropriate 3D risk analysis modeling tools for use through the design process by introducing geometric methods for modeling risk in computer-synthesized three-dimensional and virtual reality platforms.

Shahrokhi and Bernard use the "fuzzy space" concept to model danger zones, target presence zones, and physical and perceptual barriers by geometrical profiles [6]. This model visualizes and identifies the risk concentration points in the simulated workplace. The present paper uses fuzzy spaces to illustrate the risk distribution in the workplace and applies fuzzy operations to calculate a quantitative risk index.
