Bayesian Life Testing using the Total Q on Test

Abstract

Suppose the basic shape of the cumulative failure (hazard) function has been identified for a certain component, and that an unknown parameter theta for a new production run of similar components is to be estimated. In particular, suppose that the failure function is of proportional type, R(x) = thetaQ(x), where Q is the known shape function, and that theta is sampled from a prior gamma density. By using a new statistic, called the total Q on test (TQT), it is possible to perform Bayesian updating during a variety of lifetime testing programs in a manner similar to total time on test plots. This statistic can also be used with complete lifetime data, extending over several product runs, to identify the failure form Q, and to estimate the gamma hyperparameters. Extensions include the use of several TQT statistics to estimate the relative strength of competing hazard functions.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1976
Accession Number
ADA022384

Entities

People

  • William S. Jewell

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • California
  • Computations
  • Data Analysis
  • Data Science
  • Data Sets
  • Delphi Method
  • Industrial Engineering
  • Information Science
  • Life Tests
  • Military Research
  • Operations Research
  • Plotting
  • Production
  • Random Variables
  • Statistical Analysis
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference