Using Regression based Control Limits and Probability Mixture Models for Monitoring Customer Behavior

Document Type : Research Paper

Authors

Department of Industrial Engineering, KN Toosi University of Technology, Tehran, Iran. 1999143344

Abstract

In order to achieve the maximum flexibility in adaptation to ever changing customer’s expectations in customer relationship management, appropriate measures of customer behavior should be continually monitored. To this end, control charts adjusted for buyer’s/visitor’s prior intention to repurchase or visit again are suitable means taking into account the heterogeneity across customers. In the case of a subscription-based service provider, this paper discusses three types of adjusted control charts considering grouped data on attribute usage measures are available at each subscription period. With appreciating the characterizing effect of customer’s overall satisfaction on his future behavior, regression based models and probability mixture models are used to account for heterogeneity in customers’ mean usage rate. Besides adjusted Shewhart and CUSUM control charts for Bernoulli and Poisson distributed usage indicators, the likelihood ratio test based on mixture probability models are investigated in term of detect ability of the shifts in usage behavior through a comparative simulation study.

Keywords

Main Subjects


[1] Cook D.A., Steiner S.H., Cook R.J., Farewell V.T., Morton A.P. (2003), Monitoring the evolutionary
process of quality: risk-adjusted charting to track outcomes in intensive care; Critical Care in
Medicine 31; 1676–1682.
[2] Fader P.S., Hardie B.G.S., Lee K.L. (2005), Counting your customers’ the easy way: an alternative to
the Pareto/NBD model; Marketing Science 24; 275–284.
[3] Fader P.S., Hardie B.G.S. (2005), The value of simple models in new product forecasting and
customer-base analysis; Applied Stochastic Models in Business and Industry 21; 461-473.
[4] Fornell C., Johnson M.D., Anderson E.W., Cha J., Bryant B.E. (1996), The American customer
satisfaction index: nature, purpose, and findings; Journal of Marketing 60(4); 7-18.
[5] Grigg O., Farewell V.T. (2004), An overview of risk-adjusted charts; Journal of the Royal Statistical
Society, Series A 167; 523–539.
[6] Gryna F.M. (1999), Market research and marketing. In: Juran J., Godfrey A.B., Juran’s quality
handbook; 5th Edition, McGraw-Hill; New York.
[7] Hauck D.J., Runger G.C., Montgomery D.C. (1999), Multivariate statistical process monitoring and
diagnosis with grouped regression-adjusted variables; Communications in Statistics: Simulation and
Computation 28; 309–328.
[8] Hawkins D.M. (1993), Regression adjustment for variables in multivariate quality control; Journal of
Quality Technology 25; 170–182.
[9] Jearkpaporn D., Borror C.M., Runger G.C., Montgomery D.C. (2007), Process monitoring for mean
shifts for multiple stage processes; International Journal of Production Research 45(23); 5547–5570.
[10] Johnson N.L., Kemp A.W., Kotz S. (2005), Univariate discrete distributions; 3rd edition, John Wiley
and Sons, Inc., Hoboken; New Jersey.
[11] Jones T.O., Sasser W.E.Jr. (1995), Why satisfied customers defect; Harvard Business Review
(November–December); 88–99.
[12] Moe W., Fader P.S. (2004), Capturing evolving visit behavior in clickstream data; Journal of
Interactive Marketing 18; 5-19.
[13] Montgomery D.C. (2005), Introduction to statistical quality control; 5th edition, John Wiley and Sons,
Inc.; New York.
[14] Mood A.M., Graybill F.A., Boes D.C. (1974), Introduction to the theory of statistics; 3rd edition,
McGraw-Hill; New York.
[15] Moustakides G.V. (1986), Optimal stopping times for detecting changes in distributions; The Annals of
Statistics 14; 1379–1387.
[16] Myers R.H., Montgomery D.C., Vining G.C. (2002), Generalized linear models, with applications in
engineering and the sciences; John Wiley and Sons, Inc.; New York.
[17] Nadaradjah S., Kotz S. (2009), Models for purchase frequency; European Journal of Operational
Research 192; 1014-1026.
[18] Schmittlein D.C, Morrison D.G., Colombo R. (1987), Counting your customers: who they are and
what will they do next?; Management Science 33; 1–24.
[19] Sego L.H. (2006), Applications of control charts in medicine and epidemiology; Ph.D. Thesis, Virginia
Polytechnic Institute and State University; Blacksburg, VA.
[20] Skinner K.S., Montgomery D.C., Runger G.C. (2003), Process monitoring for multiple count data
using generalized linear model-based control charts; International Journal of Production Research 41;
1167–1180.
[21] Steiner S.H., Cook R.J., Farewell V.T. (1999), Monitoring paired binary surgical outcomes using
cumulative sum charts; Statistics in Medicine 18; 69–86.
[22] Steiner S.H., Cook R.J., Farewell V.T., Treasure T. (2000), Monitoring surgical performance using
risk-adjusted cumulative sum charts; Biostatistics 1; 441–452.
[23] Wade M.R., Woodall W.H. (1993), A review and analysis of cause-selecting control charts; Journal of
Quality Technology, 25; 161–169.
[24] Woodall W.H. (2006), The use of control charts in health-care and public-health surveillance (with
discussion); Journal of Quality Technology 38; 89–104.