An importance measure for multistate systems with external factors

Many technical systems are operated under the impact of external factors that may cause the systems to fail. For such systems, an interesting question is how those external factors and their impacts on the system can be identified at an earlier stage. Importance measures in reliability engineering are used to prioritise weak components (or states) of a system. Component failures and the impact of external factors in the real world may be statistically dependent as external factors may affect system performance. This paper proposes a new importance measure for analysing the impact of external factors on system performance. The measure can evaluate the degree of the impact of external factors on the system and can therefore help engineers to identify the factors with the strong impact on the system performance. A real-world case study is used to illustrate its applicability.