After studying Lean Method, I found that CMMI is somewhat conflicting with it.
There is a lot of processes that CMMI requires and do not contribute to any value to customers, especially documentation. That is also the area that a lot of software engineers complaint about. To work on documentation, it really increase the cycle time or the project completion time. But from CMMI point of view, it is very necessary because if there is no documentation, it would become nightmare for maintenance. ay be this is not a direct value to customers. Instead, it is indirect value. Or can I say it is type 1 Muda?
No doubt, there is plenty of documentation that produce no viable value. In those cases, I generally question whether there is a valid reason for the documentation, or even whether it is truly required by a standard, regulatory agency or methodology, wherever the excuse for the requirement lays.
Nonetheless, there are cases where documentation serves a useful purpose, and even some cases where it provides value from a customer point of view. There is value in documenting procedures, for example, where it provides the means for organizations to shift resources to meet changing customer demand, reduce variability in product or service, and/or to prevent occurrences of error. Each of these would positively impact the customer in multiple ways. For software processes, it sounds like you are also talking about documentation that is used by the customers. In that case, you might argue that value is provided to the customer if an untrained customer representative can use the software without error for its intended task.
There is certainly more than one way of looking at these things, and it usually leads to interesting discussions, so have fun with it.
Learn more about the Lean Six Sigma principles and tools for process excellence in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Lean Six Sigma DMAIC short course ($249), or his online Green Belt certification course ($499).