To extend and improve this study, a suitable area can be to use more sensitive methods in order to shorten the delay between change point and detection time. Using monitoring methods, which accumulate information over time like cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts, has proved to be especially helpful in detecting small persistent changes in process distribution parameters. As emphasized in an interesting comment by paper reviewers, using control charts that besides considering usage heterogeneity are able to employ the information accrued over time can be promising in terms of increasing the sensitivity of monitoring procedure with respect
to small shifts of customers’ usage rate. Concerning this issue, there have been several remarkable papers in healthcare surveillance, which have employed a similar approach for monitoring clinical treatment and hospital care quality indicators considering heterogeneity across patients (Biswas & Kalbfleisch, 2008; Sego, Reynolds, & Woodall, 2009; Steiner & Jones, 2010). For example, Sego et al. (2009) investigate the use of logistic regression to design a CUSUM chart for monitoring the post-operative mortality after a surgical operation. They also propose a more effective tool, which uses a time-to-event regression method instead of a binary-response regression method. Steiner and Jones (2010) propose an EWMA procedure for monitoring patients’ survival times after cardiac surgery using a particular risk score for each patient. Biswas and Kalbfleisch (2008) also use risk-adjusted CUSUM control chart to assess the quality of kidney transplant operations. They have used Cox proportional hazard regression model to take heterogeneity across subjects into account. Altogether, the recent advances in model-based monitoring procedures lead us to think about the integration of a memory-based chart with a successful diagnosing mechanism as an area that deserves further investigation. The result may provide both quick detection as well as the possibility of taking appropriate corrective actions.
Lastly, in this paper we just considered situations where a firm records customer usage from various services by a binary vector. Therefore, an interesting area to expand the applicability of the model could be to use heterogeneity models, which can address the quantity of usage as well. Truncated regression models like Tobit model have been especially recommended by paper reviewers for this purpose