  The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM)
control charts have been used in profile monitoring to track drift shifts that
occur in a monitored process. We construct Bayesian EWMA and Bayesian CUSUM
charts informed by posterior and posterior predictive distributions using
different loss functions, prior distributions, and likelihood distributions. A
simulation study is performed, and the performance of the charts are evaluated
via average run length (ARL), standard deviation of the run length (SDRL),
average time to signal (ATS), and standard deviation of time to signal (SDTS).
A sensitivity analysis is conducted using choices for the smoothing parameter,
out-of-control shift size, and hyper-parameters of the distribution. Based on
obtained results, we provide recommendations for use of the Bayesian EWMA and
Bayesian CUSUM control charts.
