Project managers need to ensure that customer's are satisfied with a project's deliverables. Part of this process is ensuring that the customer's business processes are optimized. You can't provide the best possible project results if your customer's processes aren't efficient. Improving processes is about improving quality while reducing costs and waste.
Processes need measures. If you don't have measures then your processes aren't worth the paper they are printed on. Processes have to meet the needs of the organization, business unit that executes them, and the customer's requirements. Measures also help to identify and solve process problems, and help to ensure they are meeting the customer's requirements.
When it comes to process improvement, a good project manager understands:
How to develop team skills
How to break down work into processes
How to solve problems and to find the root cause of the problems
How to recommend solutions to problems that are acceptable to the majority
How to lead a team and when to let the team lead
Measure the effectiveness of a process by:
Looking at the cycle times between process steps
Identifying bottlenecks that cause unnecessary delays
Identify problems that cause defects to occur
In order to help develop good business processes, a project manager must have the knowledge, skills, and experience to ensure that the right people are doing the right things at the right time, using the right tools and delivering the results that are expected.