USE OF THE WEIBULL DISTRIBUTION IN BAYESIAN DECISION THEORY

Abstract

The Weibull distribution is useful in analyzing the probabilistic lifetimes of many electrical components and complex systems. It is attractive for Bayesian decision-making because its right-hand cumulative function is of an exponential form which allows all life-test data to be easily incorporated into the decision-making process. Unfortunately no natural conjugate prior distribution exists if both the shape and scale parameters of the Weibull distribution are assumed to be unknown. If the shape parameter is assumed known, however, Bayesian analysis becomes little more difficult than for the exponential distribution, a special case of the Weibull. Prior, posterior, and preposterior analyses are given for the case of known shape parameter. In connection with preposterior analysis several sampling plans are discussed. The paper concludes with an analysis of a problem in optical sampling.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1966
Accession Number
AD0668677

Entities

People

  • Richard M. Soland

Tags

Communities of Interest

  • C4I
  • Human Systems
  • Space

DTIC Thesaurus Topics

  • Abstracts
  • Complex Systems
  • Decision Theory
  • Dynamic Programming
  • Functions (Mathematics)
  • Life Tests
  • Random Variables
  • Reliability
  • Sampling
  • Statistics
  • Terminals
  • Traveling Wave Tubes
  • Traveling Waves
  • Weibull Density Functions

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference