INFERENTIAL ANALYSIS OF THE RE-MODELED STRESS-STRENGTH SYSTEM RELIABILITY WITH APPLICATION TO THE REAL DATA
Keywords:
Stress-Strength model, maximum likelihood estimate, Bayes estimate, empirical distribution function, Gibbs sampler, Metropolis-Hastings algorithm, highest posterior density credible interval.Abstract
The present study deals with the classical and Bayesian analysis of re-modeled stress-strength system reliability by considering Weibull distribution as the distribution of both the stress and strength variables. The proposed re-modeled stress-strength system reliability is defined as the probability that the system is capable to withstand the maximum operated stress at its minimum strength i.e., P[U>V], where U=Min(X1, X2...Xm) and V=Max(Y1,Y2,......Yn). The observations X1, X2...Xm and Y1,Y2,......Yn are the measurements on the strength and stress variables at different time epochs. The goodness-of-fit of the two real data sets for the proposed model is also demonstrated.
Downloads
References
Abu-Salih, M.S. and Shamseldin, A. A. (1988). Bayesian estimation of
P(Y
Math. Phys. Sci., 6(1), p. 17-26.
Ahmad. K.E., Fakhry, M.E. and Jaheen, Z.F., (1997). Empirical Bayes
estimation of P(Y
Plan. Inf., 64, p. 297-308.
Awad, A.M., Azzam, M.M. and Hamdan, M.A. (1981). Some inference results
on Pr(Y
Meth. 10, p. 2515-2525.
Award, A.M. and Gharraf, M.K. (1986). Estimation of P(Y
case: a comparative study, Commum. Statist.-Simul.Comp., 15, p. 289-403.
Badar, M.G. and Priest, A.M. (1982). Statistical aspects of fiber and bundle
strength in hybrid composites, Progress in Science and Engineering
Composites, Hayashi, T., Kawata, K. and Umekawa, S. (eds.), ICCM-IV,
Tokyo, p. 1129-1136.
Baklizi, A. and Qader EL-Masri, A.E. (2004). Shrinkage estimation of P(X
in the exponential case with common location parameter, Metrika 59, p. 163-
Birnbaum, Z.W (1956). On a use of Mann-Whitney statistics, Proc. Third
Berkeley Symp. in Math. Statist. Probab. University of California Press,
Berkeley, Vol. 1, p. 13-17.
Birnbaum, Z.W. and McCarty, B.C. (1958). A distribution-free upper
confidence bounds for Pr(Y
Ann. Math. Statist. 29, p. 558-562.
Beg, M.A. and Singh, N. (1979). Estimation of P(Y
distribution, IEEE Trans. Reliab., 28, p. 411-414.
Chao, A. (1982). On comparing estimators of P[Y
IEEE Trans. Reliab., R-26, p.389-392.
Chen, M.H. and Shao, Q.M., (1999). Monte Carlo estimation of Bayesian
credible and HPD intervals, Journal of Computational and Graphical Statistics,
vol. 8, p. 69-92.
Church, J.D. and Harris, B. (1970). The estimation of reliability from stress-
strength Relationship, Technometrices, 12, p. 49-54.
Cramer, E. and Kamps, U. (1997a). The UMVUE of P(X
censored samples from Weinman multivariate exponential distributions,
Metrika, 46, p. 93-121.
Cramer, E. (2001). Inference for stress-strength models based on Weinman
Multivariate Exponential samples, Commum. Statist.-Theory and Meth. 30, p.
-346.
Draper N.R. and Guttman, I. (1978). Bayesian analysis of reliability in multi-
component stress-strength models, Commun. Statist. A-7, p. 441-451.
Gupta, R.D. and Gupta, R.C.(1990). Estimation of Pr(X>Y) in the multivariate
normal case, Statistics, 21, p. 91-97.
Jana, P.K. and Roy, D. (1994). Estimation of reliability under stress-strength
model in a bivariate exponential set-up, Calcutta Statist. Assoc. Bull., 44, p.
-181.
K. J. Craswell, D. L. Hanson, and D. B. Owen, (1964). Nonparametric Upper
confidence Bounds for P(Y < X) and Confidence Limits for Pr(Y < X) When
X and Y are Normal, Journal of the American Statistical Association, Vol. 59,
No. 307, p. 906- 924.
Kelley, G.D., Kelley, J.A. and Schucany, W. R. (1976). Efficient estimation of
P(Y
Kim, C., and Chung, Y., (2006). Bayesian estimation of P(Y
type X model containing spurious observations, Statistical Papers 47, p. 643-
