Profile monitoring is one of the methods used in statistical process control (SPC) to understand the functional relationship between response and explanatory variables by tracking this relationship and estimating parameters. SPC is done in two phases: In Phase I, a statistical model is created and its parameters estimated using historical data. Phase II implements the statistical model and monitors the live ongoing process. Control charts are graphical tools used to monitor these functional relationships over time in both Phase I and Phase II. This study provides a step‐by‐step application for parametric, nonparametric, and semiparametric methods in profile monitoring and creates an in‐depth guideline with comparative analysis studies for novice practitioners. A comparative analysis under each distributional assumption is conducted for various control charts.

In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data.