It is a common practice to survey callers to newly deployed systems. When calls get transferred to an agent, the agents may ask the callers if they are interested in taking a survey. For calls that stay in the IVR, they system may give the callers an option to take the survey. Most surveys include a few Likert-type items about the perceived quality of the application and an open-ended question that lets callers provide more information, and which are recorded and transcribed for content analysis.
When interpreting the results of these types of surveys, it's important to remember that the callers selected themselves, so the results are not necessarily representative of the entire population of callers. In particular, callers who have had an especially difficult time with the system may have hung up before receiving an invitation to complete the survey (Leppik & Leppik, 2005). On the other hand, callers who had a bad experience but did hear the invitation are much more likely to respond than those to had an average or good experience.
That said, the results of surveys can be of value when comparing mean responses over time and for tracking changes in the content of the open-ended responses (which can be of value in identifying opportunities for improvement).
Leppik, P., & Leppik, D. (2005). Gourmet customer service: A scientific approach to improving the caller experience. Eden Prairie, MN: VocaLabs