A toothpaste factory had a problem: they sometimes shipped empty boxes, without the tube inside. This was due to the way the production line was set up, and people with experience in designing production lines will tell you how difficult it is to have everything happen with timings so precise that every single unit coming out of it is perfect 100% of the time. Small variations in the environment (which can't be controlled in a cost-effective fashion) mean you must have quality assurance checks smartly distributed across the line so that customers all the way down the supermarket don't get pissed off and buy someone else's product instead.
Understanding how important that was, the CEO of the toothpaste factory got the top people in the company together and they decided to start a new project, in which they would hire an external engineering company to solve their empty boxes problem, as their engineering department was already too stretched to take on any extra effort.
The project followed the usual process: budget and project sponsor allocated, RFP, third-parties selected, and six months (and $8 million) later they had a fantastic solution - on time, on budget, high quality and everyone in the project had a great time. They solved the problem by using some high-tech precision scales that would sound a bell and flash lights whenever a toothpaste box weighing less than it should. The line would stop, and someone had to walk over and yank the defective box out of it, pressing another button when done.
A while later, the CEO decides to have a look at the ROI of the project: amazing results! No empty boxes ever shipped out of the factory after the scales were put in place. Very few customer complaints, and they were gaining market share. "That's some money well spent!" - he says, before looking closely at the other statistics in the report.
It turns out, the number of defects picked up by the scales was 0 after three weeks of production use. It should've been picking up at least a dozen a day, so maybe there was something wrong with the report. He filed a bug against it, and after some investigation, the engineers come back saying the report was actually correct. The scales really weren't picking up any defects, because all boxes that got to that point in the conveyor belt were good.
Puzzled, the CEO travels down to the factory, and walks up to the part of the line where the precision scales were installed. A few feet before it, there was a $20 desk fan, blowing the empty boxes out of the belt and into a bin.
"Oh, that - one of the guys put it there 'cause he was tired of walking over every time the bell rang", says one of the workers.
While toothpaste boxing may not be Asia's strong suit, the notion of gemba seems to work well.