Reliable Computing

, Volume 10, Issue 2, pp 83–106 | Cite as

Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals

  • Hung T. Nguyen
  • Vladik Kreinovich
  • Luc Longpré

Abstract

In many engineering problems, we want a physical characteristic y to lie within given range Y; e.g., for all possible values of the load x from 0 to x0, the resulting stress y of a mechanical structure should not exceed a given value y0. If no such design is possible, then, from the purely mathematical viewpoint, all possible designs are equally bad. Intuitively, however, a design for which yy0 for all values x ∈ [0,0.99 ⋅ x0] is “more probable” to work well than a design for which yy0 only for the values x ∈ [0,0.5 ⋅ x0]. In this paper, we describe an interval computations-related formalization for this subjective notion of probability. We show that this description is in good accordance with the empirical distribution of numerical data and with the problems related to estimating the lifetime of the Universe.

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Hung T. Nguyen
    • 1
  • Vladik Kreinovich
    • 2
  • Luc Longpré
    • 2
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA, e-mail
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA, e-mail

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