It may seem to you that all of us use identical acronyms, but the truth is we don’t. For example, S.M.A.R.T. has 87 possible meanings at Acronymfinder.com. I’m pretty sure you mean this one:
SMART = Specific, Measurable, Actionable, Relevant, and Timely (process metrics)
Just for the heck of it, try googling the exact term
"six sigma" +"case study"
then keep drilling down through the hits by adding some of the terms you ask for. Not everyone will necessarily use the terms “Pareto” or “Nominal Group Technique” (many “lone wolf” practitioners, particularly, eschew the NGT because they rarely have the requisite, knowledgeable team to work with.) The difficulty you are encountering in finding suitable material points up the fuzzy nature of many SS projects which often contain a hodgepodge of Quality tools, rarely using the same tools every time an initiative is undertaken. My guess is you will find at least one applicable study out of the thousands of hits you are sure to get.
The requirement for describing a six sigma initiative performed by the candidate for eligibility to take the American Society for Quality Certification Exam for Six Sigma Black Belt (CSSBB) does not require the details you request in your assignment because of potential trade secret problems. I suspect many folks who would otherwise be willing to give you such data are reluctant to do so because of the security issues posed.
Hint: the most crucial part (and often the most controversial) of the SMART process is “measurable.” For example, Jack Welch at GE often bragged of “Billions” saved as a result of six sigma initiatives, but the pure truth is those billions NEVER showed up on GE’s bottom line income reports. No one to my knowledge has ever given a satisfactory explanation for the discrepancy between Neutron Jack’s pronouncements and the CPA’s reporting in the annual report.