1. A cause may be necessary but not sufficient for a problem to occur
This is a situation that crops up for most problems, where we quickly and certainly identify certain conditions, situations or factors that have been prevalent, without which the problem could never have happened. A popular example is when a change is implemented in a product and it fails after deployment, one of the obvious and necessary condition is that there has been an inadequacy in the testing / approval process, though that by itself could not have caused the problem. In short, any lapse in a failure containment system is always necessary but not sufficient reason for a failure. More examples are possible. In such situations, one of the immediate reaction is to fix the identified ""necessary" condition to help arrest or contain further occurrences, until we proceed and figure out the other causes.
2. A cause may be sufficient but not necessary for a problem to happen
This represents a situation where multiple, possibly independent causes exist. For example, being absent is sufficient to fail in an examination, but not necessary. However, being present for the exam is a necessary condition to pass the exam, but not sufficient.The problem with dealing with causes that are sufficient for the failure, is our ability to pre-identify all such potential causes exhaustively. Ideally we should prevent all such causes, and the degree of exhaustiveness with which we do so, will result in the degree of non-failure. Goes without saying the if such a situation occurs, it has to be addressed and the learning used in strengthening the related FMEA.
3. A cause may be neither sufficient nor necessary for a problem to occur.
Most of us will be familiar in the use of Brain storming and the Fish-Bone diagram. Once we list down a list of causes through brainstorming, we try to start narrowing down to potential ones and then the most probable ones. Those causes that are identified as "not necessary and sufficient" tend to get eliminated to help get closer to the actual cause. However, even if an individual cause may be insufficient to cause a problem, it has to be seen if it becomes a threat when combined with other cause(s).
4. A cause may be both sufficient and necessary for a problem to occur.
Whenever we consider a cause to be necessary and sufficient for a problem, we tend to make several involuntary assumptions. For example, if a person has to get an electric shock upon touching a metal surface of an appliance, it is necessary that there must be a current leakage. However a combination of current leakage and earthing failure makes it sufficient for providing an electric shock. (We are assuming many things, for example, no lightning should have struck the appliance when the person touched it!) If we look at it the other way, it is sufficient to have a reliable earthing on the appliance to avoid getting an electric shock. It is often difficult to relate one cause as sufficient and necessary for a problem. It is more common to associate it with a set of causes.