EWMA control charts for the correlation coefficient

For the case of sensor health monitoring, keeping the correlation level of two sensors measuring related quantities under surveillance is a promising idea. The corresponding raw data streams behave often unsteady. But having a stable correlation level is a typical in-control pattern, whereas mean and variance may vary from time window to time window. However, there are nearly none control charts for monitoring correlation. Here, we consider EWMA control charts for the linear correlation coefficient ϱ. Despite it is known for a long time, the usage of the explicit (assuming normally distributed data) distribution of the estimator of ϱ while setting up a control chart seems to be non-existent. Here, we build an EWMA chart utilizing this estimator, namely the Pearson correlation, and calculate the most popular performance measure, the zero-state average run length (ARL), by means of various numerical methods. Less surprisingly, the two standard methods work poorly for certain chart designs. We solve these problems by utilizing piece-wise collocation. Moreover, we examine further configuration details and provide some guidelines. Two applications illustrate the usefulness of monitoring the ϱ level.