Reliability and risk controlled by the simultaneous presence of random events on a time interval

[+] Author and Article Information
Michael Todinov

Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Oxford, OX33 1HX, UK

1Corresponding author.

ASME doi:10.1115/1.4037519 History: Received August 31, 2016; Revised August 01, 2017


The paper treats the important problem related to risk controlled by the simultaneous presence of critical events, randomly appearing on a time interval and shows that the expected time fraction of simultaneously present events is insensitive to the distribution of events durations. In addition the paper shows that the probability of simultaneous presence of critical events is practically insensitive to the distribution of the events durations. These counter-intuitive results provides the powerful opportunity to evaluate the risk of overlapping of random events through the mean duration times of the events only, without requiring the distributions of the events durations, their variance or the mixing proportions of the individual distributions, in the case of duration times represented by distribution mixtures. A closed-form expression for the expected fraction of unsatisfied demand for random events following a homogeneous Poisson process in a time interval is introduced for the first time. In addition, a closed-form expression related to the expected time fraction of unsatisfied demand, for a fixed number of consumers initiating random demands with a specified probability, is also introduced for the first time. The concepts stochastic separation of random events based on the probability of overlapping and the average overlapped fraction are also introduced. Methods for providing stochastic separation and optimal stochastic separation achieving balance between risk and cost of risk reduction are presented.

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