The next meeting of

the National Seminar on Probability and Statistics

will be held on  October 24, 2018 (Wednesday) at 2 p.m. in Room 403 of IMI-BAS. A talk will be delivered by

Anna Dembinska (Warsaw University of Technology, Poland)

on:

The number of failed components in a k-out-of-n system consisting of heterogeneous  elements – discrete case

Abtract: In this talk, I will examine properties of k-out-of-n systems when the component lifetimes are discretely distributed. The primary focus will be the random variable which represents the number of failed components upon system failure. For this variate I will present the probability mass function under the most general setting of possibly dependent and heterogeneous components. I will also provide formulas describing conditional probabilities for this variable given some information about the time of system failure. In addition to these results, I will show that, in the special case of series systems, this variable exhibits some aging properties, and we establish several characterizations of probability distributions based on such properties. For illustration, I will give some numerical examples.
My talk will be based on joint work with Katherine Davies from University of Manitoba, Canada.