Customer satisfaction data collected by a large cellular phone service provider are to be used to evaluate and improve the quality of their service. For this purpose, we propose a Bayesian treatment of a joint-response chain graph relating partial assessments of specific aspects of quality to an overall assessment of the service quality. The resulting Bayesian model can be used to render basic geographical and temporal differentiation, allowing the company to undertake direct corrective actions. Both normal and binary models are considered for our customer satisfaction data and are compared with other currently used methods in the study of customer satisfaction. Copyright © 2011 John Wiley & Sons, Ltd.