I've come across a nice article by Bob Sproull that describes how he has combined Theory of Constraints with Six Sigma and Lean to create what he calls the Ultimate Improvement Cycle, Maximizing Profits Through the Integration of Lean, Six Sigma and Theory of Constraints, from Six Sigma IQ (IQPC). Obviously, this is related to his book, The Ultimate Improvement Cycle. Sproull is not the only one to talk about this concept, and there are a few pointers in the end notes of the article.
Although I am a huge supporter of both Lean and Six Sigma, the profits realized from these two initiatives, or even the hybrid Lean Six Sigma, pale in comparison to what can happen from an integrated Lean, Six Sigma Theory of Constraints (TOC) (or as I call it, the Ultimate Improvement Cycle [UIC]). In fact, one double blind study of 21 electronics plants has confirmed that an integrated Lean Six Sigma Theory of Constraints improved profits roughly 22 times that of Lean and 13 times more than Six Sigma if these were both singular process improvement initiatives.
The Theory of Constraints community is often given a hard time for the seemingly-blind belief that TOC is the way to run a business. Maybe one of the elements of that has been the rejection or diminution of many other useful tools in the management toolbox. Looking across the wider landscape, as Sproull is doing here, should help fit TOC into the big picture. Where do each of these tools fit best? How can they bring the most advantage to an organization? This work clearly focuses on TOC and Lean and Six Sigma. But there is nothing preventing one from looking at other methodologies in the same light: what can you use in an Ultimate Improvement Cycle of your own?
How do they fit? Read the article or the book for the details and some explanatory graphics. But the basic idea is that if you don't focus improvement efforts at the constraint of the business - the thing that is limiting your profits - then that improvement is going to show little to no return. This is the biggest complaint about applying the improvement efforts to everything in the business. You might get lucky and improve on the constraint, but you'll also spend a lot of time (and money) improving areas that don't necessarily need it. This is Step 1 in the TOC parlance: Identify the Constraint.
In Step 2 of TOC, you look for ways to get "improve" the constraint: get as much of the right thing out of the constraint and as little as possible of the wrong thing. Ensure that whatever is happening at the constraint is of high quality (low waste, low rework).
In Step 3 of TOC - by far the hardest because it affects everything else - ensure that everything else in the business supports the constraint. Make sure the constraint is never starved for work. All work that is delivered to the constraint should be of high quality - get rid of defective work BEFORE it hits the constraint. Any processes after the constraint should be careful that they don't create a rework situation where the constraint would have to redo what it has already done.
In my reading of Sproull and other discussions on this topic, it is in Steps 2 and 3 where the improvement methodologies really come into play. TOC doesn't provide any specific guidance on HOW to exploit and subordinate, it just directs you to do it. (Clarification: the TOC applications guide you on the HOW at the high level, but there are many lower levels which are left to the specifics of the implementation.) These aren't the only connection points that Sproull makes to the TOC Process of Ongoing Improvement, as the Five Focusing Steps are known. But they are some of the most obvious in my mind.