Rollin', Rollin', Rollin'...
©2020, George J. Irwin. All rights reserved.

A lesser known but important concept in process measurement could be witnessed one frosty winter night in a parking lot in the Great White North... and is also one answer to "What happens when you let a bunch of Black Belts go out to dinner together?"

Picture a series of five head-on parking spaces, with appropriately striped yellow boundaries, and each occupied by a car. The left-most car was parked poorly, with the right side just about right over the right-hand yellow line. This caused the second car to park far enough to the right to enable the driver to get out… which means that car is encroaching on the space to its right. The driver of the third car had to make the same adjustment and therefore took up the rest of the third space plus about a quarter of the fourth space. The fourth driver didn't seem to care very much at all about yellow lines and simply straddled the yellow line between the fourth and fifth spaces. And the fifth driver did his or her best to squeeze in but still wound up using half the fifth space and some of the real estate beyond that, which was a fire lane.

I tried to take a picture of this, but I had a pretty dumb smartphone and the light wasn't good so it didn't come out.

As I was doing this, I pointed to the lineup of cars not in their spaces, gestured to my fellow Black Belts and exclaimed, "Rolled Throughput Yield!"

No one laughed.

Some Lean Six Sigma Practitioners just have no sense of humor.

Anyway, the point here is that this process of Car Parking, if you will, was subject to each of the five drivers. This equates to steps in a process we would be more interested in measuring.

Let's say now that we have five steps in a process we're studying. Each one of these steps is performed correctly ninety percent of the time. What's the overall correctness of the entire five step process?

Don't say ninety percent!

The concept of Rolled Throughput Yield is not additive. It is not accurate to say that since each step is 90% good, the entire process is 90% good. It's actually a multiplier effect (warning: here comes some math):

90% x 90% x 90% x 90% x 90% = only about 53% correct. (OK, 53.1441%.)

Yikes!

That's because once there's a defect in the first step in the process, it can't be "fixed" in the succeeding steps—like the first car parked badly in the first space. What's left that can't be defective is only 90%, and that goes into the second step. If that step is only 90% good, then that's all that can be passed along to the third step, and so on.

Fixing any one of these five steps in the process helps, of course. Raising each step to only Four Sigma, which is 99.38% defect-free, brings the Rolled Throughput Yield up to almost 97 percent. The well-known Six Sigma is 99.9996% defect free. I'll let you do that math.