Distribution-Free EWMA Scheme for Joint Monitoring of Location and Scale Based on Post-Sales Online Review Process

Nowadays, the online comment process of product after-sales has become a key part of product development. Quality problems, such as the failure of products or services, are more likely to exist or hide in negative comments. Therefore, this paper focuses on detecting abnormal changes in both the time between review T and the emotional score S of negative comments. Due to the complexity of the online review process, the distribution assumption of S and T may be invalid. To solve this problem, this study propose a distribution-free monitoring scheme that combines the exponentially weighted moving average-based Lepage statistics of S and T using a max-type combining function. This scheme is designed for joint monitoring of location and scale parameters in Phase II of an unknown but continuous process. The scheme’s performance is evaluated via Monte Carlo simulation under in-control and out-of-control conditions, using statistical measures such as the mean, standard deviation, median, and selected percentiles of the run length distribution. Simulation results indicate that the scheme is effective in detecting shifts in both location and scale parameters. Furthermore, an application of the proposed scheme for monitoring online reviews is discussed to illustrate its implementation design.