ON CUMULATIVE DAMAGE AND RELIABILITY OF COMPONENTS

Abstract

Let T, X(t), and C denote the time to failure, the accumulated damage by time t, and the 'critical' damage. Let F be the distribution function of T. Let 'E' stand for the event of the component undergoing damage and (t sub n) denote the sequence of intervals of time between successive occurrences of 'E'. Let T sub n = summation over n of t sub i and Y sub i denote the amount of damage experienced at time T sub n. Assume (t sub n, Y sub n) is a sequence of independent, identically distributed variables with distribution function H(t,y) , so that (t sub n) and (Y sub n) are renewal processes. The inequality F(t) < or = H(t,infinity) is obtained with equality if and only if C = 0. For 'E', a Poisson process, sufficient conditions are given for F, to be IHR and DMR. The classes of distribution functions are considered with the topology of complete convergence. Empirical estimates for F from observing occurrences of 'E' are given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1968
Accession Number
AD0680008

Entities

People

  • B. P. Lientz
  • V. K. Murthy

Organizations

  • System Development Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Continents
  • Corporations
  • Distribution Functions
  • Equations
  • Inequalities
  • Intervals
  • Law
  • New York
  • North Carolina
  • Probability
  • Random Variables
  • Reliability
  • Sequences
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.