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This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such problems, the challenge is solving an underdetermined system caused by a common phenomenon in practice; namely, the number of measurements is less than that of the process errors. To address this challenge, this paper attempts to solve the following two problems: (1) how to utilize the temporal correlation in the time series data of each process error and (2) how to apply prior knowledge regarding which process errors are more likely to be process faults. A novel sparse Bayesian learning method is proposed to achieve the above objectives. The method consists of three hierarchical layers. The first layer has parameterized prior distribution that exploits the temporal correlation of each process error. Furthermore, the second and third layers achieve the prior distribution representing the prior knowledge of process faults. Then, these prior distributions are updated with the likelihood function of the measurement samples from the process, resulting in the accurate posterior distribution of process faults from an underdetermined system. Since posterior distributions of process faults are intractable, this paper derives approximate posterior distributions via Variational Bayes inference. Numerical and simulation case studies using an actual autobody assembly process are performed to demonstrate the effectiveness of the proposed method.