Importance measure method for sources of system output error based on decomposition of second-order moment

In this paper, we propose an error importance measure (EIM) method to quantify the relative contribution of error sources to the system output error. In order that the contribution of both variation and mean shift of error sources are taken into account, we use second-order moment to characterize the degree of system output deviation from ideal or target value. First, the second-order moment is decomposed into a series of terms through the Taylor series expansion, and the individual effects, the interaction effects, and the total effects for one or a group of error sources are defined accordingly. Second, we define the EIM indices as the value of total effect divided by second-order moment of output error. Third, three test models and an application case are introduced to demonstrate the effectiveness and engineering significance of the proposed EIM indices. The results show that the EIM indices can reflect both the impacts of variation and mean the shift in error sources.