Stress-Strength Reliability of a Two-Parameter Bathtub-shaped Lifetime Distribution Based on Progressively Censored Samples

References

• Ahmad, K.E., Fakhry, M.E., Jaheenx, Z.F. (1997). Empirical Bayes estimation of P(Y < and characterization of Burr-Type X model. J. Statist. Plann. Infer. 64:297–308.
   Web of Science ®Google Scholar
• Badar, M.G., Priest, A.M. (1982). Statistical aspects of fiber and bundle strength in hybrid composites. In: Hayashi, T., Kawata, K., Umekawa, S., Eds., Progress in Science and Engineering Composites. ICCM-IV, Tokyo, 1129–1136.
   Google Scholar
• Balakrishnan, N. (2007). Progressive censoring methodology: an appraisal (with discussions). TEST 16:211–296.
   Web of Science ®Google Scholar
• Balakrishnan, N., Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and Applications. Boston: Birkhauser.
   Google Scholar
• Banerjee, A., Kundu, D. (2008). Inference based on Type-II hybrid censored data From a Weibull distribution. IEEE Trans. Reliab. 57:369–378.
   Web of Science ®Google Scholar
• Berger, J.O., Sun, D. (1993). Bayesian analysis for the poly-Weibull distribution. J. Amer. Statist. Assoc. 88:1412–1418.
   Web of Science ®Google Scholar
• Birnbaum, Z.W. (1956). On a use of Mann-Whitney statistics. Proc. Third Berkley Symp. Math. Statist. Probab. 1:13–17.
   Google Scholar
• Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statist. Probab. Lett. 49:155–161.
   Web of Science ®Google Scholar
• Chen, M.H., Shao, Q.M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. J. Computat. Graph. Statist. 8:69–92.
   Web of Science ®Google Scholar
• Cohen, A.C. (1991). Truncated and Censored Samples: Theory and Applications. New York: Marcel Dekker.
   Google Scholar
• Cramer, E. (2001). Inference for stress-strength systems based on Weinman multivariate exponential samples. Commun. Statist. Theory Meth. 30:331–346.
   Web of Science ®Google Scholar
• Cramer, E., Kamps, U. (1997). The UMVUE of P(X<Y) based on Type-II censored samples from Weinman multivariate exponential distributions. Metrika 46:93–121.
   Web of Science ®Google Scholar
• Efron, B. (1982). The jackknife, the bootstrap and other re-sampling plans. Philadelphia, PA: SIAM, CBMSNSF Regional Conference Series in Applied Mathematics. 34.
   Google Scholar
• Ferguson, T.S. (1967). Mathematical Statistics; A Decision Theoretic Approach. New York: Academic Press.
   Google Scholar
• Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals. Ann. Statist. 16:927–953.
   Web of Science ®Google Scholar
• Kotz, S., Lumelskii, Pensky, M. (2003). The Stress-Strength Model and its Generalization: Theory and Applications. Singapore: World Scientific.
   Google Scholar
• Krishnamoorthy, K., Mukherjee, S., Guo, H. (2007). Inference on reliability in two-parameter exponential stress-strength model. Metrika 65:261–273.
   Web of Science ®Google Scholar
• Kundu, D., Gupta, R.D. (2005). Estimation of R = P(Y < X]) for the generalized exponential distribution. Metrika 61:291–308.
   Web of Science ®Google Scholar
• Kundu, D., Gupta, R.D. (2006). Estimation of R = P(Y < X) for Weibull distribution. IEEE Trans. Reliab. 55:270–280.
   Web of Science ®Google Scholar
• Kundu, D., Raqab, M.Z. (2009). Estimation of R = P(Y < X) for three parameter Weibull distribution. Statist. Probab. Lett. 79:1839–1846.
   Web of Science ®Google Scholar
• Lawwless, N.S. (1982). Statistical Models & Methods for Lifetime Data. New York: John Wiley & Sons.
   Google Scholar
• Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos de Estadistica 3:281–288.
   Google Scholar
• Marshall, A.W., Olkin, O. (2007). Life Distributions. New York: Springer.
   Google Scholar
• Nelson, W. (1982). Applied Life Data Analysis. New York: John Wiley & Sons.
   Google Scholar
• Panahi, H., Asadi, A. (2011). Estimation of R= P [Y < X] for two-parameter Burr Type XII Distribution. World Acad. Sci. Eng. Technol. 73:509–514.
   Google Scholar
• Raqab, M.Z., Kundu, D. (2005). Comparison of different estimators of P(Y < X) for a scaled Burr Type X distribution. Commun. Statist. Simul. Computat. 34:465–483.
   Web of Science ®Google Scholar
• Raqab, M.Z., Madi, M.T., Kundu, D. (2008). Estimation of R = P(Y < X) for the 3-parameter generalized exponential distribution. Commun. Statist. Theor. Meth. 37:2854–2864.
   Web of Science ®Google Scholar
• Rezaeia, S., Tahmasbib, R., Mahmoodi, M. (2010). Estimation of P[Y<X] for generalized Pareto distribution. J. Statist. Plann. Infer. 140:480–494.
   Web of Science ®Google Scholar
• Tong, H. (1974). A note on the estimation of P(Y < X) in the exponential case. Technometrics 16:625.
   Web of Science ®Google Scholar
• Saracoglu, B., Kinaci, I., Kundu, D. (2012). On Estimation of R = P(Y < X) for Exponential Distribution Under Progressive Type-II Censoring. J. Statist. Computat. Simul. 82:729–744.
   Web of Science ®Google Scholar
• Wu, S.J. (2008). Estimation of the two-parameter bathtub-shaped lifetime distribution wpth progressive censoring. J. Appl. Statist. 35:1139–1150.
   Web of Science ®Google Scholar
• Wu, S.J., Lu, H.L., Chen, C.H., Wu, C.H. (2004). Statistical inference about the shape parameter of the new two-parameter bathtub-shaped lifetime distribution. Qual. Reliab. Eng. Int. 20:607–616.
   Web of Science ®Google Scholar