Are interval probabilities a viable way for quantifying uncertainties? [chapter]

K Breitung
2013 Safety, Reliability and Risk Analysis  
In the last decade several authors propagated the use of interval probabilities as alternative to Bayesian models in reliability problems. The basic idea of this approach is to start from some lower and upper bounds for functions of random variables describing the failure probabilities or rates of the components of a system and then to derive from these then bounds for the failure probability of the system. The advantage of such bounds is that there are no classical or Bayesian confidence
more » ... ilities, one is 100% certain that the calculated probabilities lie in the derived bounds. If one considers the basic problem in reliability of finding the failure probability, this can be seen as collecting information, one starts from total ignorance and gathering more and more information one arrives at more specific estimates of the probability. Using the mathematical definition of entropy and information, here it is shown that the method of interval probabilities requires an infinite amount of data as prerequisite. A prerequisite which in halfway realistic problems cannot be fulfilled. BASICS OF THE INTERVAL PROBABILITY METHOD In reliability problems the usual form is that a number of random variables (rv's) X X n X
doi:10.1201/b15938-475 fatcat:52tlaichpzbl7aeo42lg7ndlia