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Dimensional integrity has a significant impact on the quality of the final products in multistation assembly processes. A large body of research work in fault diagnosis has been proposed to identify the root causes of the large dimensional variations on products. These methods are based on a linear relationship between the dimensional measurements of the products and the possible process errors, and assume that the number of measurements is greater than that of process errors. However, in practice, the number of measurements is often less than that of process errors due to economical considerations. This brings a substantial challenge to the fault diagnosis in multistation assembly processes since the problem becomes solving an underdetermined system. In order to tackle this challenge, a fault diagnosis methodology is proposed by integrating the state space model with the enhanced relevance vector machine (RVM) to identify the process faults through the sparse estimate of the variance change of the process errors. The results of case studies demonstrate that the proposed methodology can identify process faults successfully.