The concept of censoring is the key to survival analysis and life data analysis. This issue can also enter via industrial statistics. When monitoring the length of time it
takes for a sample of units to fail, you can have
- Complete data: the exact time a unit fails is known
- Censored to the right: the time to fail for a unit is beyond the present run time
- Censored to the left: the known time is after the time a unit failed
Other issues that enters the data mix are
- Singly censored: all unfailed units have a common run time
- Multiply censored: the unfailed units have different run times
- Interval censored: the time to fail is known to be between a particular set of times.
- Time censored: the censoring time is fixed
- Failure censored: a test is stopped when a fixed number of units fail
- Competing failure modes: the sample units fail for different reasons
Common distributions capable of handling these situations are: lognormal, Weibull, and extreme value. The issues become interesting because there are graphical procedures to handle analysis as well as MLE and Method of Moments methods.
Systems reliability is an off-shoot of this topic which gets involved with Bayesian methods, renewal theory, and accelerated life testing. Wayne Nelson and Bill Meeker
have several good books on the topics.