AN INVESTIGATION OF THE BURN-IN AND RELATED PROBLEMS

Abstract

Two problems involving the derivation of bounds on distributions with a decreasing failure rate (DFR distributions) are presented. Given that an item has a decreasing failure rate, sharp upper and lower bounds on the burn-in time to achieve a specified mean residual life are derived. The bounds rely only on the DFR assumption and knowledge of the first moment and a percentile of the failure distribution. An early estimate of the five year survival proportion (commonly called the five year cure rate) is of great interest in assessing the value of a treatment for a mortal disease such as cancer. Assuming that the distribution of time to death is DFR and assuming a knowledge of the mean and a percentile, sharp upper and lower bounds on the survival proportion are obtained. In addition some bounds on the hazard rate and density of a DFR distribution are given.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1964
Accession Number
AD0613276

Entities

People

  • Michael J. Lawrence

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Biomedical
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Electronic Equipment
  • Engineering
  • Jet Propulsion
  • Life Tests
  • Mathematical Models
  • Mathematics
  • Military Research
  • New York
  • Operations Research
  • Probability
  • Reliability
  • Semiconductors
  • Space Sciences
  • Statistics
  • Survival
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Nuclear Civil Defense.
  • Regression Analysis.