Based on the nature of your question, I would assume you are referencing the “Capability Maturity Model Integration” system and “Capability Maturity Model”, or CMMI and CMM, respectively.  My understanding is that CMM is a generalized model for judging or otherwise assessing the maturity of software processes.  In addition, it is a means for identifying and characterizing the key practices that are required to increase the maturity of these processes. 

Although software improvement was the original aim of CMM and CMMI, it has since been generalized and expanded to include other functions (such as systems engineering and product development).  Personally speaking, the guiding light of CMM and CMMI is a “good thing,” but there is little overlap with Six Sigma.  In my humble opinion, CMM and CMMI do not have the ability to trace their respective contributions to the bottom line.  These initiatives are more related to the word “reporting” than the term “enabling.”

From this perspective, it can be said that Six Sigma is aimed at defining and executing application projects so as to derive certain immediate and visible economic benefits.  On the other hand, the intents of CMM and CMMI are focused on describing how “mature” an organization’s processes are (in terms of process improvement initiatives, programs, strategies, tools, methods, and so on).

In a nutshell, it should be possible to concurrently implement Six Sigma, CMMI, and CMM.  In this context, CMM could be used to progressively report on the “quality maturity” of an organization or set of processes.  But why bother?  If Six Sigma is “make’in the ol’e bacon jump on the breakfast table,” there is little need to report the “hog’s maturity level.”  Remember, when it comes to breakfast, the chicken only momentarily participates, but the hog is eternally committed.

To me, the bottom line is simple – industrial leaders such as Bob Galvin, Larry Bossidy, and Jack Welch do not “advertise” CMM or CMMI as “essential business tools.”  However, the use of Six Sigma is highly regarded as such.  A simple review of the literature will confirm this assertion.  It would largely appear that the aims and goals of CMM and CMMI are quite laudable, but not essential.  However, it must be recognized that I have had little application experience with CMM or CMMI; consequently, my opinion on this subject must be viewed as the “Eiffel Tower Perspective.” 

For me to provide you advice about Six Sigma is one thing, but to expound on the interactive nature between Six Sigma and CMM or CMMI is quite another.  Although my work has often taken me very deep into the world of software design, development, coding, documentation, testing, and so on, I would not consider this field among my “core competencies.”  In other words, take my opinion (on this subject) with a grain of salt. 

However, based on the confidence of what I do know, it would be very comfortable for me to assert that CMM and CMMI should be constructed to support Six Sigma (as an overarching goal), not the other way around – as some would like to see it.  I would strongly suggest that you broach this subject with the people from Carnegie Mellon Software Institute.  But remember, they too are quite likely to view their own world as “the center of the improvement universe.”

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