Failure Time Distributions: Estimates and Asymptotic Results.

Abstract

The paper deals with life distributions for coherent systems of components. Two major questions are discussed: (1) estimation of system life from data, or knowledge, on component lives, and (2) asymptotic models. Both questions are related to extremes of a sequence of random variables through the path set and cut set decomposition of coherent systems, which reduce a coherent system to either a parallel or series system. Since for these decompositions, the classical theory of extremes of independent and identically distributed random variables does not provide an acceptable approximation, the emphasis is on dependent random variables, or when the random variables are not identically distributed. The inequalities presented when discussing question (i) above are applicable not only to extreme value problems but to an arbitrary multivariate distribution using lower dimensional marginals. The asymptotic models are discussed in the light of hazard rate properties of the limiting distributions of the models. A parametric family of distributions is proposed for approximating life distributions whose hazard rate is bath-tub shaped, this representing a burn-in period, an accidental failure period and a wear-out period. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1980
Accession Number
ADA086828

Entities

People

  • Janos Galambos

Organizations

  • Temple University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Decomposition
  • Distribution Functions
  • Hazards
  • Inequalities
  • Mathematics
  • New York
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Reliability
  • Sequences
  • Statistical Analysis
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.