A Robust Latent Cusum Chart for Monitoring Business Customer Attrition

• Activity Number: 239
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Jingjing Yan*+ and Steven MacEachern and Chunjie Wu
• Companies: The Ohio State University and The Ohio State University and Shanghai University of Finance and Economics
• Keywords: Statistical Process Control ; Average run length ; Customer attrition ; Latent model ; Latent CUSUM

Abstract

The customer attrition rate is one of the key analytic metrics for customer-based businesses. Shifts occurring in the customer attrition rate of a business are usually small and persistent, and so CUSUM charting methodology would seem ideal for their detection. However, customer summaries are available only on an uneven time scale (e.g., four and five week ``business months''), and this prevents the use of traditional CUSUM methods. This talk develops a latent CUSUM chart which is based on an oversimplified exponential model for customer departures which are then summarized as ``monthly'' departures. Estimation of parameters via both maximum likelihood and least squares is considered. While both estimation methods perform well, rapidly detecting both small and large shifts, least squares methods are advantageous when attempting to detect a very small shift. The robustness of the chart to departures from the (too simple) latent model is studied, and the chart is found to perform well. The charts are applied to customer departure data from a large insurance company.