Post date: Apr 15, 2016 9:49:50 AM
<<Scott sent this email to Michael Deloach (medeloach@aep.com) and American Electric Power and Carl Dister (carl.dister@rfirst.com) at ReliabilityFirst.>>
Data for estimating failure probabilities is hard to get just because the components are well made and failures are so rare. To solve this problem, we introduced the idea of "c-boxes" in 2012 as an encapsulation of several notions that had arisen in the field of imprecise probabilities. The thing that c-boxes allow us to do is get real (Neyman) confidence intervals at any confidence level for the probability of the top or intermediate events of a fault tree. The method can even use data in which there are no observed failures, and it yields meaningful characterizations of uncertainty for that case that contract as the observational history grows. The results of this approach offer a statistical guarantee of engineering performance. These things are not possible using conventional statistical methods. There is no Wikipedia article on c-boxes yet, but there is a website about them with links to papers, slide presentations, and even software.
We've been applying this idea in several different areas since 2012. When I was visiting UTC in 2014, we started a paper introducing c-boxes in reliability analysis. We didn't finish the paper in the time I was there, and it's been in a holding pattern since then because I've been focusing on their applications in statistics, risk communication and DNA sequencing. However there is a draft manuscript that is pretty far along that describes an "imprecise" approach to evaluating fault trees of various complexity. When we stopped actively working on it, we were considering whether to break it into two manuscripts, one focusing on the problem when actual sample data is available, and another focusing on the problem where we only have expert elicitations to estimate the probabilities. We'll be coming back to this work soon I hope.