Different levels of problems; different tactics for problem-solving

If you look at all the problems in an organisation, there are a lot of day-to-day problems, a fewer number of process-level problems, and the fewest number of strategic-level problems.

This leads to two points:

1. Leaders need to be able to delegate problem-solving, otherwise all the time will be spent on the large number of day-to-day problems and not enough time will be spent on the process and strategic level problems.  In general, operators / team members should handle (i.e., authority and responsibility) day-to-day problems, mid-level managers facilitate process-level problems, and the top-level leaders facilitate strategic-level problems.
2. The level of problem influences the type of problem solving approach used.  The rule of thumb is to use the simplest problem solving approach that will work.  So while some problems may call for A3s and value stream mapping, others might be fine with a simply 5 Whys assessment.

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For more on A3s, see Managing to Learn and Understanding A3 Thinking.

For more on VSM, see Learning to See.

For more on Fishbone or Ishikawa or Cause-Effect diagrams, see the Wikipedia article.  The best advice I've received from cause-effect diagrams came from Alan Beacham.  His proposed steps as I remember it:

1. Brainstorm potential causes.  Don't worry about what categories you're supposed to use yet.
2. Group the causes by affinity.  These are now your categories.  You may want to reference suggested categories to seed more ideas.
3. Filter out causes that are unlikely.
4. Apply 5 Whys to remaining causes to flesh out the rest of the tree.

I also like the logical thinking processes from the Theory of Constraints community. For more info on this, see The Logical Thinking Process and A Guide to Implementing the Theory of Constraints (online).

For more on 5 Whys, see the Wikipedia article. There are plenty of online references on 5 Whys.  For example, The Last Step to 5 Whys Process - The "So What?" Test.