Bayesian sequential update for monitoring and control of high-dimensional processes

High-Speed Monitoring of Multidimensional Processes Using Bayesian Updates

“…We also assume that the errors are identically distributed over the sampling time, which makes sense to describe the complete randomness of the in-control process. Some literature on monitoring autocorrelated measurements attempts to estimate the autocorrelation parameters first [33]- [39] or at least assumes the autocorrelation parameters to be known, that is, the matrices 𝐓𝐓 and 𝐑𝐑 are estimated or given. Throughout the paper, we assume Markovian state dynamics with the identity matrices for 𝐓𝐓 and 𝐑𝐑 to generalize the model under the assumption that the process parameter is unknown and nonmeasurable.…”

“…Let the location and scale parameters be 𝛉𝛉 and 𝐊𝐊 , respectively. As shown in [33] and [34], these two parameters are determined recursively at every sampling epoch. More importantly with the Gaussian error distribution, not only the location parameter but also the scale parameter is updated clearly as a closed form (see [34] for detailed derivation of 𝛉𝛉 𝑡𝑡 and 𝐊𝐊 𝑡𝑡 ).…”

“…[32] applied dynamic Bayesian estimation to detect machine failures in a discrete multivariate situation. Recently, [33] applied Bayesian sequential update when the assignable causes are sparse. This paper proposes a Bayesian method to monitor the process mean in multivariate online processes and shows the advantage of using updated prior distribution in high-dimensional process monitoring.…”

“…Few studies have been conducted in this circumstance. Although [33] applied the Bayesian sequential update in high-dimensional processes, it assumed sparsity in the out-of-control process. The proposed model is developed without sparsity assumption, thereby generalizing [33].…”

“…Although [33] applied the Bayesian sequential update in high-dimensional processes, it assumed sparsity in the out-of-control process. The proposed model is developed without sparsity assumption, thereby generalizing [33]. Second, the proposed method is computationally inexpensive.…”