First passage time control charts assuming power law intensity for time to jointly monitor time and magnitude

Control charts are essential tools to monitor the quality of a process and commonly used in many industries besides industrial production. Due to the industrial revolution, many products have very low failure chances and labeled as the high-quality products, where the time-between-events (TBE) charts are commonly used to monitor such processes. This study purposes control charts to monitor time and magnitude assuming the power law process for the TBE whereas the magnitude is assumed cumulative as well as noncumulative over time. Besides two illustrative examples, a comparison to the existing rate and first passage time (FPT) charts is also presented in this study. It is shown numerically that the proposed charts are more efficient than the existing FPT and rate charts.