There are many problem-solving methodologies. One that has been used around the world for many years, particularly in automotive-related industries, is 8D Problem-Solving, used by Ford and required internally and of its suppliers.
Ford developed 8D, also known as Team-Oriented Problem-Solving (TOPS) in 1987, which has 8 Steps: D1 – D8.
D1: Form a team with people knowledgeable about the problem
D2: Formally describe the problem
D3: Develop and verify interim containment action(s)
D4: Perform root cause analysis
D5: Determine permanent corrective action(s)
D6: Implement and verify permanent corrective(s)
D7: Take steps to prevent problem recurrence and identify other places to implement solutions.
D8: Close out the 8D process and celebrate the team.
In the latter part of the 1990’s Ford added an initial step D0: Prepare and Plan for 8D Process. This process was known as Global 8D.
A video from Quality Hub India provides basic explanation of the steps D1-D8. You can view the Quality Hub video here.
Another video from The Quality Channel covers the 8D steps with suggested key elements to consider for each step. While not labeled as D0, their first slide details some of the questions to be asked in that step. You can view the Quality Channel video here.
The key output of the 8D problem solving process is an 8D report. The Schaeffler Group (a German manufacturer for automotive, aerospace, and other industries) provides a public example of a Sample 8D Report. You can access that report here.