Some innovative multivariate Bayesian schemes for monitoring the mean vector with applications to monitoring production processes

Bayesian approaches have gained popularity for addressing operational research and management problems, including process monitoring and product quality assessment. In particular, Bayesian approaches are often used to address complex multivariable processes. This paper analyses and evaluates a multivariate Bayesian generalised likelihood ratio (MBGLR) scheme, a multivariate Bayesian cumulative sum (MBCUSUM) scheme and a combination of two MBCUSUM (2MBCUSUM) schemes to monitor the mean vector of a multivariate Gaussian process distribution. Monte Carlo simulations are employed to evaluate the detection performance of these three schemes. Furthermore, they are compared with the multivariate generalised likelihood ratio (MGLR) scheme, the multivariate empirical Bayes (MEB) scheme, and a CUSUM-type multivariate empirical Bayes (CUSUM-MEB) scheme based on the steady-state average time to signal (SSATS). Simulation results show that the MBGLR scheme exhibits strong overall monitoring performance when suitable prior parameters and window sizes are selected. While the MBCUSUM and 2MBCUSUM schemes outperform the MBGLR scheme in detecting certain small shifts, the MBGLR scheme consistently outperforms the MGLR, MEB, and CUSUM-MEB schemes across all shift magnitudes for the different instances considered in this study. Finally, a lumber manufacturing dataset and a carbon-fibre tubing manufacturing dataset are used to illustrate the practical applicability of the proposed schemes.