A problem is something that has a potentially adverse effect. Another way of looking at this is that a problem is the gap between what should be and reality.
Unfortunately, not all problems are obvious. Think about water damage in a crawlspace. You can have a problem and not even know it. This is one of the big challenges with Lean implementations. People may not see the problem with excess inventory, or recognize that large batches are the equivalent of a backed up drain under your floorboards.
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Often problems have an aspect of uncertainty. They might have an unknown root cause or unknown solutions. But in a Lean Six Sigma environment, a problem may come up that has both a known cause and a known solution. For example, you may experience a parts shortage on a high-use component. After some brief analysis, you may learn that the problem could be quickly resolved with kanban cards. The challenge may just be in finding the time to fix it.
Problems are the result of poor processes. They are also flags that highlight the opportunity to fix those poor processes. One of the cardinal sins of continuous improvement is to live with recurring problems without doing something about it. Obviously, there are times when the problem is insignificant, but it is surprising how often people will live with something seriously wrong. They get numb to the difficulty, and eventually don’t even view it as a problem anymore. Despite the numbness, morale still falls.