Shock Models Arising from Processes with Stationary, Independent, Nonnegative Increments.

Abstract

Let H(t) be the life distribution of a device subject to shocks governed by an integer-valued stochastic process with stationary, independent, nonnegative increments. H(t) is a function of the probabilities PR of surviving the first k shocks, k = 1, 2, ... . We show that H(t) inherits various aging properties (IFR, IFRA, NBU) of the discrete survival function Pk. Analogous results hold in the continuous case where H(t) is the life distribution of a device subject ot wear according to a wear process with stationary, independent nonnegative increments. In the cumulative damage model for the wear process or for the shock process, H is IFRA if the process enjoys a TP2 property. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1980
Accession Number
ADA093127

Entities

People

  • Frank Proschan
  • Harry Joe

Organizations

  • Florida State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Analogs
  • Continuity
  • Distribution Functions
  • New York
  • Probability
  • Reliability
  • Scientific Research
  • Security
  • Stationary
  • Statistics
  • Stochastic Processes
  • Survival
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.