A new type of Bayesian nonparametric control charts for individual measurements

Abstract

As a screening process, control chart has been widely used in many fields where a monitoring process is required for quality improvement. Most commonly used control charts with data measured on a continuous scale usually assume the underlying process follows a certain parametric distribution, such as normal. As such, the charts might lack in-control robustness and might not be sensitive to an out-of-control state if the underlying process is not as the assumed. To this point, a new type of Bayesian nonparametric control charts is derived upon a recently developed nonparametric prior named the transformed Bernstein polynomial prior (TBPP). This new chart automatically inherits the merits of TBPP and thus can efficiently adjust an initial guess on the underlying process to approach to the true one. Its robustness property makes it suitable to various types of monitoring processes.