$1.$ Gap Analysis and Problem StatementThe case study shows that there is a big difference between the current state and the ideal state in the process of making coupling discs. At first, $37\mathrm{.}95\%$ of these parts were rejected, mostly because of problems with the dowel pinhole width. This caused a lot of customer complaints and lower product quality. The goal was to cut this failure rate by a huge amount to make customers happier and ensure the product would work. The gap analysis shows that there is a $31\mathrm{.}38\%$ difference between the current rejection rate and the goal of lowering flaws by a large amount. So$,$ the problem statement can be summed up in a few words: "The company has a high rejection rate of $37\mathrm{.}95\%$ when making coupling discs, mostly because the dowel pin hole diameter is too small. This causes a lot of customer complaints and lower product quality." $2.$ Qualifying Criteria for Recognizing a True ProblemSeveral qualifying factors made it clear that the production process had a real problem. First, the large number and regularity of customer complaints directly pointed to problems with the dowel pinhole diameter, showing that many people were unhappy. Second, the rejection rate of $37\mathrm{.}95\%$ was well above what was considered reasonable, showing a major quality control problem. Lastly, the defect had a major effect on the usefulness and dependability of the product because it directly affected how well the coupling discs worked. This was more proof that there was a big problem that needed to be fixed right away$\mathrm{.}3.$ Knowledge or Presumption of Root CausesThe team probably had rough ideas about what went wrong, like using the wrong tools or not inspecting properly. These assumptions were very important in guiding the study because they helped the team focus on certain areas. This targeted method made root cause analysis faster and more accurate because the team could quickly find and fix the main problems that caused the defect. By assuming that problems have root causes, the process of fixing them became easier and more focused on the most likely causes of the problem. $4.$ Breaking Down the ProblemThe team broke the problem down into clear, doable parts so they could work on it more effectively. The main problem that was found was that the dowel pinhole width wasn't big enough. More research showed that bad tool use and testing methods were contributing factors. By breaking the problem down into these specific issues, the team was able to deal with each factor thoroughly, making sure that the overall problem was solved completely$\mathrm{.}5.$ Discovery of Sub$-$Level ProblemsThe study found small issues with the way tools were used and how they were inspected. It was found that improper tool use and poor inspection methods were major causes of the main defect. Because of this finding, the team had to change their focus and work on the tooling and inspection processes to fix the problem with the dowel pinhole diameter problem. Realizing these smaller issues led to a more comprehensive approach to problem$-$solving, ensuring that all causes causing the problem were dealt with to stop it from happening again. $6.$ Decision on Specific Problems or Sub$-$Problems to Focus OnThe team put all of the discovered sub$-$problems at the top of their list because they directly affected the main defect. Tooling and inspection practices were originally brought up$,$ but because the problem was so big, it was important to look at everything that was causing it$.$ By making these areas their top priorities, the team ensured that the problems would be solved completely and correctly. This strategic method let the team deal with each problem in a planned way, which greatly lowered the number of rejections. $7.$ Structured Problem$-$Solving Method UsedThe team used the $8$D approach as a structured way to solve their problems, which helped them figure out how to solve them. The framework of this method worked well for the case study because it covers everything from putting together a team to taking preventative measures. The $8$D method's focus on finding the root cause and taking corrective steps was very important for fixing the main problems and keeping them from happening again. The team was right to choose this way because it workedthe rejection rate dropped significantly to $6\mathrm{.}57\%,$ which was proof of its effectiveness.

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