An Illustrative Problem in Computational Probability.

Abstract

An elementary, but useful problem is reliability design is used to illustrate some of the principles and concerns of computational probability. A number n of items with exponential life time are placed in parallel. The time until all items have failed is denoted by U sub n. It is desirable that U sub n exceed the duraction T, where T is a random variable, independent of the n life times. We wish to determine the smalles value of n for which P(U sub n > T) exceeds 1 - epsilon. It is shown that if T has a delayed distribution of phase type, this may be done by a recursive algorithm, which avoids numerical integrations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1980
Accession Number
ADA091035

Entities

People

  • Marcel F. Neuts

Organizations

  • University of Delaware

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Computations
  • Computer Programming
  • Delaware
  • Differential Equations
  • Equations
  • Integrals
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Numerical Integration
  • Probability
  • Probability Distributions
  • Random Variables
  • Reliability

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Analytical Mechanics
  • Statistical inference.