Dynamic Count Time Series Modeling and Anomaly Detection for Online Automotive Quality Complaints

Feedback information concerning automotive quality often suffers from significant delays, making online consumer complaints an invaluable real-time source of information for monitoring and assessing product quality. Given that the frequency of online complaints is influenced by numerous factors, such as automobile quality, sales, Internet development, and public awareness of rights protection, it exhibits significant auto-correlation and dynamics. However, the existing modeling methods have been proven to be unreliable in practical applications, because they often assume that in-control (IC) processes remain static and employ models with fixed parameters. To this end, a dynamic modeling framework that integrates generalized linear regression with an integer-valued auto-regressive (INAR) state space model is proposed to capture the evolving nature of the process. Then, a procedure combining the Extended Kalman Smoothing (EKS) with the Expectation Maximization (EM) algorithm, referred to as EM-EKS, is used to estimate the model parameters. Furthermore, for online monitoring of any upward shifts in the number of complaints, a control chart (denoted as SDC-INAR(1)-G) with one-step-ahead forecasting value as the plotting statistic is constructed. Simulation studies show that the proposed SDC-INAR(1)-G method consistently exhibits much better performance than three benchmark approaches in different scenarios. Finally, the proposed SDC-INAR(1)-G method is applied to monitor online complaints of the Volkswagen Sagitar, focusing on two specific cases: the stationary process of "brake abnormal noise" and the non-stationary process of "transmission abnormal noise." The results further demonstrate that the SDC-INAR(1)-G method outperforms the static approaches in both cases. The state-space framework and adaptive EM-EKS parameter estimation of the proposed SDC-INAR(1)-G method ensure robust sensitivities to different shifts, offering reliable monitoring for both stationary and non-stationary data, at the same time, remaining computationally efficient for real-world applications.