An integrated change point detection and online monitoring approach for the ratio of two variables using clustering-based control charts

Online monitoring of the ratio of two random characteristics rather than monitoring their individual behaviors has many applications. For this aim, there are various control charts, known as RZ charts in the literature, e.g. Shewhart, memory-type and adaptive monitoring schemes, have been designed to detect the ratio's abnormal patterns as soon as possible. Most of the existing RZ charts rely on two assumptions about the process: (i) both individual characteristics are normally distributed, and (ii) the direction (upward or downward) of the RZ's deviation from its in-control (IC) state to an out-of-control (OC) condition is known. However, these assumptions can be violated in many practical situations. In recent years, applying the machine learning (ML) models in the Statistical Process Monitoring (SPM) area has provided several contributions compared to traditional statistical methods. However, ML-based control charts have not yet been discussed in the RZ monitoring literature. To this end, this study introduces a novel clustering-based control chart for monitoring RZ in Phase II. This method avoids making any assumptions about the direction of RZ's deviation and does not need to assume a specific distribution for the two random characteristics. Furthermore, it can estimate the Change Point (CP) in the process.