Here is an example of improvement made possible by expanding the view of the system (and viewing the results from the perspective of the customer instead of just looking at internal process measures).
I was working to improve the processing time for court orders of child support (in the retirement system for the USA federal government). The time to process the court orders was taking far too long (longer than legally allowed). The first process improvements took place in the office (there were many easy ways to improve the process). In a few months things we finally starting to be under control and it was obvious the results were still far from acceptable. Looking at the whole process the time delay due to our office had been nearly entirely eliminated.
However the total time was still far too long. That time was not under our control, so how could it be our problem? Just because you do not control a portion of the process does not mean you cannot influence those results. By using a system that was already in place (but was used very rarely) to have the mail go directly to us rather than to a central mail processing location I was able to improve the process by more as any internal improvements.
The delay from getting mail forwarded to our location from the central mailing location was many weeks long. I was able to have the orders for child support sent directly to us. Thus I was able to greatly improve the results with an improvement that was seen as not part of our system (the mail system delay before we received the orders). There are often ways to make improvements that are (or seem) outside of your area of responsibility and control.
By expanding the system view and looking at the results of the entire system it is often possible to find improvements that are not possible by only looking at “your” system. These changes can sometimes be more challenging to accomplish as they may require convincing others to make changes.