Any answer would be useful but I am looking for metrics which are ideal for a Design Thinking process. Traditional metrics might generally focus on compliance but is there any metric that can be used to measure exploration and innovation?
I think when attempting to measure a process like design thinking you need to focus on the output of the process. If you want to measure innovation, for example, you could measure the number of unique ideas that satisfy the inputs. Exploration could be measured through how many unique 'how might we' statements or a logic/decision tree the team creates. It's important to clarify what you expect out of the process at the end of the day to your design team.
I always tell my design team I care very little about the artifacts and deliverables of the process as compared to the output of the process, which is generally a solution to a problem. The actual deliverables could be a high fidelity, fully functional prototype...or a sketch on a piece of paper. If the team is creating outputs from a process that can be communicated and moved forward then they are doing what I expect.