I've done some reading in this area, but am not a quality control expert or statistician. Something I've noticed, especially in the writings of Deming, is that it's not just about the math, but also about how the workplace is managed, that matters. Deming wanted to make it so that the regular factory or office workers could proactively develop and test quality improvements themselves, as part of their regular work. This required finding techniques, such as graphing, that worked most of the time but didn't require math or access to a computer. That's the reason for the emphasis on graphical methods and manual calculations.
>Deming wanted to make it so that the regular factory or office workers could proactively develop and test quality improvements themselves, as part of their regular work.
Unsurprisingly, the Toyota Production System implements this. Individual line workers are responsible for kaizen, continuously finding better ways of doing things. I don't recall exactly what tools and techniques they use though, other than kanban cards iirc.
Naturally, management saw it differently. ;-)