Dynamic monitoring of polynomial profiles with attribute responses and between-profile correlation

Profile monitoring is a popular statistical process control problem in recent years. In many applications, quality characteristics of interest are attribute data due to the inherent feature of processes or limitation of data collection costs. The correlation among data is becoming more significant, since data collection intervals are becoming shorter in the big data era. However, research on monitoring profiles with attribute responses in the presence of Between-Profile Correlation (BPC) has received relatively scant attention. Motivated by a real example of automobile warranty claims, this article aims to monitor polynomial profiles with attribute responses and BPC. The generalized polynomial model and the learning curve model are adopted to characterize the profile relationship and the correlation between profiles, respectively. Then, an EWMA chart with dynamic control limits (dEWMA) is developed. Simulation studies show that ignoring the BPC does not affect the in-control performance of the chart with dynamic control limits, but does have devastating effects on the out-of-control performance. The proposed dEWMA chart can address the impact of correlation and provide superior monitoring performance compared with some competitors. Finally, a real example of warranty claims data is presented to illustrate the implementation of the proposed chart.