I've been involved with a good number of problem-solving projects and usually introduced after things have started. One thing that stands out is that teams almost always create a cause-and-effect diagram early on in the project. This is a wasteful part of the project that generates even more waste.
A dozen or so people in a room for several hours building up a cause-and-effect diagram is a waste of time on its own. Then, each element on the list has to be either confirmed or refuted as a candidate for root cause and that's another meeting or two. Teams will also run expensive tests in an effort to learn more about some of those items on the list.
The cause-and-effect diagram is a log of our collective guesswork. Most of the items on the list are not even close but we don't know that at the time.
Problem solving, or root-cause analysis, is an investigation into why something occurred when it should not have. The sensible approach to an investigation is to search for facts and evidence and to proceed from there. For example, if we make 1,000 widgets and 47 fail at testing, we should look at the production and quality records to see what variables could be correlated with the failures. If you find these variables, now you have something to brainstorm against. If you don't find any variables on your first attempt, use other techniques and try again.
At one company, we had this issue where the production records did not correlate with the failed items. Then we weighed all the production items in the QC lab. The reason for weighing is that weight is a covariate for many other factors. If any dimension on the parts are different, it will show up in weight. If a component on an assembly is missing, it will show up in weight. If your supplier swaps out a component, it might show up in weight. In our case, all the failures were heavier than the majority of products. They were all beyond two standard deviations above the mean and that is statistically improbable, so it had to be meaningful. That provided us with useful brainstorming and we learned something new and valuable that day.
Always consider problem solving or root-cause analysis to be an investigation. Work as a detective would when solving a crime. You want to be on the scene of the crime collecting evidence. The facts will steer your investigation in the right direction.
There's a lot about problem solving that you need to know to be successful.
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