  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.
