In terms of your ‘service delivery’ and improving your ‘service delivery’, you want to do the same as recommended above with your client, to with your own service delivery. That is, you would or could map out the process (i.e. the 6-step design process) to understand the end to end User Journey – phase, goals, touch points, good points, pain points, improvement opportunities and process. An illustrative sketch is provided below:

And for each (sub) step or phase the User Journey (illustrative sketch below) you identify the same elements of the User Journey ie phase, goal, touch points, good points, pain points, improvement opportunities, and process(es) that support that part of the journey:

And for each process, document (whether detailed, or sketched – see below), the level 4 process, showing who is involved in the process (suppliers), what is required (inputs), what is produced (outputs) and who is the recipient (customer) of the process.

If you wanted to assess and even improve your service delivery, this is where you would look, and how you would do it understand the User Journey, and therefore experience your clients is experience in you providing your service to them, and the process(es) where and how you provide it and improve where needed.