A robust latent CUSUM chart for monitoring customer attrition

In competitive business, such as insurance and telecommunications, customers can easily replace one provider for another, which leads to customer attrition. Keeping customer attrition rate low is crucial for companies, since retaining a customer is more profitable than recruiting a new one. As a main statistical process control (SPC) method, the CUSUM scheme is able to detect small and persistent shifts in customer attrition. However, customer attrition summaries are typically available on an uneven time scale (e.g. 4-week and 5-week 'business month'), which may not satisfy the assumptions of traditional CUSUM designs. This paper mainly develops a latent CUSUM chart based on an exponential model for monitoring 'monthly' customer attrition, under varying time scales. Both maximum likelihood and least squares methods are studied, where the former mostly performs better and the latter is advantageous for quite small shifts. We apply a Markov chain algorithm to obtain the average run length (ARL), make calibrations for different combinations of parameters, and present reference tables of cutoffs. Three more complicated models are considered to test the robustness of deviations from the initial model. Furthermore, a real example of monitoring monthly customer attrition from a Chinese insurance company is used to illustrate the scheme.