Advertisement

A Note on Shock Model Justification for IFR Distributions

  • Purushottam Laud
  • Roy Saunders
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)

Summary

We consider the model in which the failure rate for a device changes when the device is subjected to shocks which occur stochastically over time. We show that increasing failure rate distributions can be obtained by making simple models for the effects of shocks. The results provide a physical motivation for using the Weibull distributions for failure time data. Random failure rates used in Bayesian inference are also obtained in a similar manner by modeling the effects of shocks to be stochastic.

Key Words

Failure rate Poisson process shock model stochastic failure rate Weibull distribution weak convergence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barlow, R.E., Proschan, F. (1965). Mathematical Theory of Reliability. Wiley, New York.zbMATHGoogle Scholar
  2. Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.zbMATHGoogle Scholar
  3. Dykstra, R. L., Laud, P.W. (1980). A Bayesian nonparametric approach toward reliability. Annals of Statistics (to appear).Google Scholar
  4. Esary, J.D., Marshall, A.W., Proschan, F. (1973). Shock models and wear processes. Annals of Probability, 4, 627–649.MathSciNetCrossRefGoogle Scholar
  5. Gaver, D.P., Jr. (1963). Random hazard in reliability problems. Technometrics, 5, 211–226.MathSciNetCrossRefGoogle Scholar
  6. Rao, J.S., Sethuraman, J. (1975). Weak convergence of empirical distribution functions of random variables subject to perturbation and scale factors. Annals of Statistics, 3, 299–313.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Reynolds, D.S., Savage, I.R. (1971). Random wear models in reliability theory. Advances in Applied Probability, 3, 229–248.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Purushottam Laud
    • 1
  • Roy Saunders
    • 1
  1. 1.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

Personalised recommendations