How do KPIs help to narrow down customer expectation gaps?

The KPIs don’t help to do it, but the discussion that happens when you start looking for the respective KPIs help. Imagine this dialog as an illustration of my point: – What are the expectations of our customers, and what do we actually give them? – They want a product of higher quality!
– How do they perceive the quality? What aspects of the quality are important for them?
– They want faster turnaround time… (a lagging performance metric!)
– How can we decrease turnaround time?  – We can optimize operations by reducing complexity (a leading performance metric!)
– What is a complexity in our case?
– It is the … {number of interconnected parts, number of operations needed, the difficulty to change something…}
 
Thus, the performance metrics help to achieve an agreement about where the real problem is and how to solve it.