I think you might be mixing up the intentions of the two analysis tools you you mentioned - Root Cause Analysis and Design of Experiments. Consider thinking of it this way:
Root Cause Analysis is something you do in order to help identify, well, the "Root Cause" of some issue or problem. There are multiple ways to go about doing a root cause analysis in the same way there are multiple way to clean your house. Over time, industry has developed a number of analysis "tools" that can be used to help in figuring out a root cause. Short of explaining each tool, for now I suggest just reading up a bit on some of the following techniques:
- 5-Whys: Basically keep asking "why" it happened until you get to an answer that you can control
- Fishbone Diagram: visual tool to help map out the different sources that can contribute to the failure - machine related, material related, people related, environment related, etc.
- Pareto Charts, Scatter Charts, or other graphs: help to identify trends or interactions that might signal when or how a problem started.
- Failure Modes and Effects Analysis (FMEA): A very methodical tool for evaluating and how various root causes/issues drive different failure modes and their effects which also considering their severity and a number of other factors. This is what's considered a "bottom-up" approach to root cause analysis.
- Fault Tree Analysis (FTA): The "top-down" brother of an FMEA where a fault is traced down through all the possible chains of events that could lead to it.
- Anticipatory Failure Determination (AFD): A creative approach where you try to figure out HOW to actually MAKE the issue happen. In your case, if you wanted to MAKE seal to leak, how would you do it?
These are all tools that are regularly used in risk based industries (think auto manufacturers, medical devices manufacturers, aerospace, etc.) but certainly in lots of other places as well.
Now, the second topic you mentioned - Design of Experiments - while also an option to help with root cause determination, it more suited to helping test a theory, or develop a design or specification. It's commonly used in determining how variation in different inputs can impact the output. Consider something as simple as boiling an egg. Your inputs could be a number of things:
- Amount of Water
- Temperature of Water
- Time spent boiling
- Amount of salt added to water
- Age of the egg
- Size of the pot
A DOE is performed to analyze the compound interactions between this. In a very high level summary the team would perform the following steps:
- First decide what they wanted to consider a "correctly" boiled or "good" version of a hard boiled egg WAS. What are our specifications for what we WANT.
Then there are some ways to eliminate inputs or "factors" which don't really influence the outcome. The more factors we have to evaluate the more complicated the DOE. In this case, we can probably reasonably eliminate:
The size of the pot (unlikely to impact the finished egg - assuming of course its big enough to fit the egg and hold water)
- Age of the egg maybe? Do we feel that this strongly influences the final product?
- Amount of water - as long as it's boiling (and we don't break the egg) then this probably doesn't matter.
This leaves us with 3 "factors" that we now want to evaluate (and which also seem reasonable):
- Temperature of the Water
- Amount of salt added
- Time spent boiling.
Once a DOE is set up, we would define a number of different experiments where we boiled an egg while varying those parameters in known amounts. Eventually we'd end up with some data that we could statistically analyze to help us understand what input factors we want to control. We'd end up finding that the temperature of the water is somewhat influenced by the amount of salt added. We'd also learn that the amount of time we needed to boil was correlated with the temperature. Eventually, through our analysis, we'd likely come to the conclusion that while temperature is important, the amount we raise it by adding an acceptable amount of salt, doesn't impact the way our egg end up nearly as much as does the time we actually spend boiling it! Not long enough and we end up with raw egg. Too long and we turn it to dried rubber. Our DOE has helped us identify that, when we now go to boil eggs, controlling the time we boil is the best way to guarantee us an egg made exactly the way we want it!
Now, while this may seem a super trivial example, hopefully you can envision how the concept of a DOE as a "tool" could be extremely useful. And just as there were multiple different tools for performing RCA, the same exits for design analysis!
Hope this helps to better understand how these tools relate.