Reading about six sigma, Lean, TQM and the other initiatives is confusing to a certain degree. While it is supposed to be reading about different things, the reader ends up reading about nearly the same thing in different ways. They are all aim at improvement, customer satisfaction and quality.
However, I have not read about lean using statistics yet. But does that matter? There is no rule in any of the 'initiatives' that does not allow using tools especially if these tools help in achieving its main goals.
Reading in the literature might be a bit different from reality. I don't think that companies will go for a methodology and just read in the book and apply. The idea will be, just use what brings profit. And at the end of the day every company will have its own mix of many tools and ideas that literature has not finished thinking bout a new name for them. I think it is difficult to find names because quality initiatives are making lots of babies in the market.