"80% of companies say they deliver superior customer service. 8% of customers say that those same companies deliver superior customer service." - Lee Resources
You have to find a good way to measure customer satisfaction after people have had an experience with your support team. If you don't, you'll never know with much certainty how you're doing. Besides the survey, there are other KPIs you will want to identify and track with your team whenever possible. The sad truth is, most of your customers, satisfied or not, won't bother with lengthy surveys or detailed feedback, so having these additional behavioral measurements will help you decipher service performance.
Servicing blind is why a lot of companies believe they're doing better than they are.