Mura: unevenness of flow. Thus, the first thing to do is establish a reasonable pull, an even flow.
Muri: overburdening the system. (System being the overall thing you are talking about; generally not a computer system.) Thus, once you establish a production “pipe”, don’t try to force more through that pipe than it can handle. As a fluid dynamics person will tell you, if you overburden the pipe, it means even less liquid will travel through the pipe in a given time period.
Muda: waste. This is further defined by Type I and Type II muda. And by the classic 7 wastes. “Muda” is an ugly work in Japanese. Kind of like an earthy but dirty Anglo-Saxon word, I think.
The classic definition of Type I muda is necessary waste, ie, something that does not add value in the customer’s eyes, but we feel, as a business, that it is necessary. (Compliance with government regs might be an example.) I call this “waste we have not yet figured out how to live without” (maybe not true of all things in this category).
The classic definition of Type II muda is unnecessary waste. I’ll call this obvious waste (as soon as you put yourself in position to see it).
There is of course an inter-relationship between the three (mura, muri, muda).
In general, I find these ideas very similar to things we say in Agile, Scrum, XP, etc.
Jim Womack suggested that Lean thinkers practice those in that order, ie, focus on mura first. Then muri. Then muda. Perhaps this is good advice for Agile. (BTW, if you don’t know Jim Womack, get one of his books: Lean Thinking. Recommended.)