A frequent topic in the lean.org forums is some version of “what is the difference between lean and ____” where the blank is one of the industry buzzwords. Some of the common ones are various prefixes to “Sigma.” Others are old standards such as TQM, SPC, TOC, etc. These discussions are always interesting as the various camps line up. “Lean looks at waste, while xxx-Sigma looks at variation” is a common one. Apparently “Agile” is about high-tech machinery, and of course, none of that is found in “lean.”
My put on all of this is pretty simple. It’s all the same, people.
There is nothing about TPS that excludes any level of machining technology, so long as that technology is applied as a solution to a problem rather than for its own sake. The last time I checked, Toyota, and TPS, were obsessive about stamping out variation. Constraints? Yup. You bet I know what the constraint is, and you bet I manage it tightly. If I have done everything right, my enterprise constraint is production (rather than sales), but just barely. And internally, if I have done it right, my constraint is manual work rather than technology. Why? Because every Team Member can work on improving manual work cycles. Not the case with an engineering constraint.
In the end, this is all about the rational, deliberate application of skilled problem solving, using the scientific method, aka PDCA.
If you are looking at “which one to implement” stop fretting about it. Go out to your work area, stand and watch a while, see what is stopping your good people from doing a great job, and start fixing it.