Hierarchical Bayesian Analysis for Stress-Strength Model in Normal Case

  • Lee, In-Suk (Department of Statistics, Kyungpook National University) ;
  • Cho, Jang-Sik (Department of Statistics Information Science, Kyungsung University) ;
  • Kang, Sang-Gil (Department of Statistics, Kyungpook National University)
  • Published : 2000.04.30

Abstract

In this paper, we consider hierarchical Bayesian analysis for P(Y < X) using Gibbs sampler, where X and Y are independent normal distributions with unknown means and variances, respectively. Also numerical study using real data is provided.

Keywords

References

  1. IEEE Transactions on Reliability v.40 Confidence Bounds for Pr(X > Y) in 1-Way ANOVA Random Model Aminzadeh, M. S.
  2. Journal of the Korean Society of Quality Management v.23 Bootstrap Confidence Bounds for P(X > Y) Cho J. S.
  3. Technometrics v.12 The Estimation of Reliability From Stress-Strength Relationships Church, J. D.;Harris, B.
  4. IEEE Transactions on Reliability v.41 Bayes Computation for Life Testing and Reliability Estimation Dey, D. K.;Tai-ming, Lee
  5. Technometrics v.15 The Estimation of Pr(X < Y) in the Normal Case Downton, F.
  6. Quality and Industrial Statistics(5th ed.) Duncan, A. G.
  7. Journal of the American Statistical Association v.66 Estimation of the Probability That Y < X Enis, P.;Geisser, S.
  8. Journal of the American Statistical Association v.85 Sampling Based Approaches to Calculating Marginal Densities Gelfand, A. E.;Smith, A. F. M.
  9. Statistical Science v.7 Inference From Iterative Simulation Using Multiple Sequences Gelman, A.;Rubin, D.
  10. IEEE Transactions on Pattern Analysis and Machine Intelligence v.6 Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images Geman, S.;Geman, D.
  11. Technometrics v.30 Confidence Limits for Stress-Strength Models With Explanatory Variables Guttman, I.;Johnson, R. A.;Bhattacharyya, G. K.;Reiser, B.
  12. Technometrics v.28 Statistical Inference for Pr(Y < X) : The Normal Case Reiser, B.;Guttman, I.
  13. Journal of the American Statistical Association v.34 Testing Reliability in a Stress-Strength Model When X and Y are Normally Distributed Weerahandi, S.;Johnson, R.