Track 3 Session 8
2:20 to 3:20 p.m. Wednesday June 10, 2009

Estimating Probabilities of Rare Events Using Limited Data

This presentation discusses modeling small data samples with the objective of providing a basis for decision making when little data is available. Often reliability engineers will attempt to fit small samples to distributions based on a number of criteria, only to discover that no distribution provides a good fit, and multiple distributions provide the same (and usually low) level of confidence in the modeling approach. Although careful analysis is usually required in such cases, the analyst may discover that measures of central tendency, such as the mean and median, do not depend strongly on the approach chosen. Decision makers often balance a number of competing factors and will typically find rough agreement sufficient. On the other hand, estimates of the likelihood of events in the tails of the distribution (i.e. rare events) are sometimes important. Relying on any distribution-based approach, especially when the physics underlying the analysis may be uncertain, can lead to conclusions that can be quite different depending on the distribution chosen. This presentation discusses two methods for describing the probabilities of events that are distant from the mean, neither of which assume a closed-form distribution.