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Original Articles

Inferences for stress–strength reliability of Burr Type X distributions based on ranked set sampling

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Pages 3324-3340 | Received 13 Mar 2019, Accepted 01 Jan 2020, Published online: 14 Jan 2020

References

  • Abbas, K., and Y. Tang. 2014. Objective Bayesian analysis of the Frechet stress-strength model. Statistics & Probability Letters 84:169–75. doi:10.1016/j.spl.2013.09.014.
  • Abu-Dayyeh, W., A. Assrhani, and K. Ibrahim. 2013. Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling. Statistical Papers 54 (1):207–25. doi:10.1007/s00362-011-0420-3.
  • Ahmad, K. E., M. E. Fakhry, and Z. F. Jaheen. 1997. Empirical Bayes estimation of PY<X and characterizations of Burr-type X model. Journal of Statistical Planning and Inference 64:297–308.
  • Akgül, F. G., Ş. Acıtaş, and B. Şenoğlu. 2018. Inferences on stress-strength reliability based on ranked set sampling data in case of Lindley distribution. Journal of Statistical Computation and Simulation 88 (15):3018–32. doi:10.1080/00949655.2018.1498095.
  • Akgül, F. G., and B. Şenoğlu. 2017. Estimation of PX<Y using ranked set sampling for the Weibull distribution. Quality Technology Quantitative Management 14 (3):296–309.
  • Al-Omari, A. I., and A. Haq. 2012. Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods. Journal of Applied Statistics 39 (4):745–63. doi:10.1080/02664763.2011.611488.
  • Al-Saleh, M. F., and S. Al-Hadhrami. 2003. Estimation of the mean of the exponential distribution using extreme ranked set sampling. Statistical Papers 44 (3):367–82. doi:10.1007/s00362-003-0161-z.
  • Al-Saleh, M. F., and K. Al-Shrafat. 2001. Estimation of average milk yield using ranked set sampling. Environmetrics 12 (4):395–9. doi:10.1002/env.478.
  • Aslam, M., S. Balamurali, M. Azam, and C.-H. Jun. 2014. Skip-Lot sampling plan of type SkSp-2 with two-stage group acceptance sampling plan as reference plan. Communications in Statistics - Simulation and Computation 43 (4):777–89. doi:10.1080/03610918.2012.715224.
  • Beg, M. A. 1980. Estimation of PY<X for exponential family. IEEE Transections on Reliability 29:158–9.
  • Birnbaum, Z. M. 1956. On a use of the Mann-Whitney statistics. In: Proceedings of the third Berkeley symposium on mathematical statistics and probability. Contributions to the theory of statistics and probability, vol. 1, 13–7. Berkeley, CA: University of California Press.
  • Burr, I. W. 1942. Cumulative frequency functions. The Annals of Mathematical Statistics 13 (2):215–32. doi:10.1214/aoms/1177731607.
  • Chen, Z., Z. D. Bai, and B. K. Sinha. 2004. Ranked set sampling: Theory and applications. New York, NY: Springer.
  • Dell, T. R., and J. L. Clutter. 1972. Ranked set sampling theory with order statistics background. Biometrics 28 (2):545–55. doi:10.2307/2556166.
  • Dong, X., L. Zhang, and F. Li. 2013. Estimation of reliability for exponential distributions using ranked set sampling with unequal samples. Quality Technology & Quantitative Management 10 (3):319–28. doi:10.1080/16843703.2013.11673417.
  • Downton, F. 1973. On the estimation of Pr⁡Y<X in the normal case. Technometrics 15:551–8.
  • El-Neweihi, E., and B. K. Sinha. 2000. Reliability estimation based on ranked set sampling. Communications in Statistics - Theory and Methods 29 (7):1583–95. doi:10.1080/03610920008832566.
  • Ghitany, M. E. 2005. On reliability estimation based on ranked set sampling. Communications in Statistics - Theory and Methods 34 (5):1213–6. doi:10.1081/STA-200056805.
  • Gunasekera, S. 2015. Generalized inferences of R=Pr⁡X>Y for Pareto distribution. Statistical Papers 56 (2):333–51. doi:10.1007/s00362-014-0584-8.
  • Gupta, R. C., S. Ramakrishnan, and X. Zhou. 1999. Point and interval estimation of PX<Y: The normal case with common coefficient of variation. Annals of the Institute of Statistical Mathematics 51:571–84.
  • Guttman, I., R. A. Johnson, G. K. Bhattacharyya, and B. Reiser. 1988. Confidence limits for stress-strength models with explanatory variables. Technometrics 30 (2):161–8. doi:10.1080/00401706.1988.10488363.
  • Hanley, J. A. 1989. Receiver operating characteristic (ROC) methodology: The state of the art. Critical Reviews in Diagnostic Imaging 29 (3):307–35.
  • Jaheen, Z. 1996. Empirical Bayes estimation of the reliability and failure rate functions of the Burr Type X failure model. Journal of Applied Statistical Science 3:281–8.
  • Kim, C., and Y. Chung. 2006. Bayesian estimation of PY<X from Burr-type X model containing spurious observations. Statistical Papers 47:643–51.
  • Kundu, D., and R. D. Gupta. 2006. Estimation of PY<X for Weibull distributions. IEEE Transactions on Reliability 55:270–80. doi:10.1109/TR.2006.874918.
  • Lio, Y., T.-R. Tsai, M. Aslam, and N. Jiang. 2014. Control charts for monitoring Burr type-X percentiles. Communications in Statistics - Simulation and Computation 43 (4):761–76. doi:10.1080/03610918.2012.714033.
  • Mahdizadeh, M., and E. Zamanzade. 2016. Kernel-based estimation of PX>Y in ranked set sampling. SORT 40:243–66.
  • Mahdizadeh, M., and E. Zamanzade. 2017. Reliability estimation in multistage ranked set sampling. REVSTAT 15:565–81.
  • Mahdizadeh, M., and E. Zamanzade. 2018a. Smooth estimation of a reliability function in ranked setsampling. Statistics 52 (4):750–68. doi:10.1080/02331888.2018.1477157.
  • Mahdizadeh, M., and E. Zamanzade. 2018b. Interval estimation of P(X < Y) in ranked set sampling. Computational Statistics 33:1325–48.
  • Mahdizadeh, M., and E. Zamanzade. 2018c. A new reliability measure in ranked set sampling. Statistical Papers 59 (3):861–91. doi:10.1007/s00362-016-0794-3.
  • Mahdizadeh, M., and E. Zamanzade. 2018d. Efficient reliability estimation in two-parameter exponential distribution. Filomat 32 (4):1455–63. doi:10.2298/FIL1804455M.
  • McIntyre, G. A. 1952. A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research 3 (4):385–90. doi:10.1071/AR9520385.
  • Mehrotra, K., and P. Nanda. 1974. Unbiased estimation of parameters by order statistics in the case of censored samples. Biometrika 61 (3):601–6. doi:10.1093/biomet/61.3.601.
  • Modarres, R., and G. Zheng. 2004. Maximum likelihood estimation of dependence parameter using ranked set sampling. Statistics & Probability Letters 68 (3):315–23. doi:10.1016/j.spl.2004.04.003.
  • Modarres, R., T. P. Hui, and G. Zheng. 2006. Resampling methods for ranked set samples. Computational Statistics & Data Analysis 51 (2):1039–50. doi:10.1016/j.csda.2005.10.010.
  • Murray, R. A., M. S. Ridout, and J. V. Cross. 2000. The use of ranked set sampling in spray deposit assessment. Aspects of Applied Biology 57:141–6.
  • Muttlak, H. A., W. A. Abu-Dayyeh, M. F. Saleh, and E. Al-Sawi. 2010. Estimating P(Y < X) using ranked set sampling in case of the exponential distribution. Communications in Statistics - Theory and Methods 39:1855–68.
  • Raqab, M. Z. 1998. Order statistics from the Burr Type X model. Computers & Mathematics with Applications 36 (4):111–20. doi:10.1016/S0898-1221(98)00143-6.
  • Riaz, M., R. Mehmood, N. Abbas, and S. A. Abbasi. 2016. On effective dual use of auxiliary information in variability control charts. Quality and Reliability Engineering International 32 (4):1417–43. doi:10.1002/qre.1848.
  • Samawi, H. M., and O. A. M. Al-Sagheer. 2001. On the estimation of the distribution function using extreme and median ranked set sampling. Biometrical Journal 43 (3):357–73. doi:10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-Q.
  • Sartawi, A. H., and M. S. Abu-Salih. 1991. Bayesian prediction bounds for the Burr Type X model. Communications in Statistics - Theory and Methods 20:2307–30.
  • Sengupta, S., and S. Mukhuti. 2008a. Unbiased estimation of P(X > Y) for exponential populations using order statistics with application in ranked set sampling. Communications in Statistics - Theory and Methods 37 (6):898–916. doi:10.1080/03610920701693892.
  • Sengupta, S., and S. Mukhuti. 2008b. Unbiased estimation of P(X > Y) using ranked set sampling data. Statistics 42 (3):223–30. doi:10.1080/02331880701823271.
  • Simonoff, J. S., Y. Hochberg, and B. Reiser. 1986. Alternative estimation procedure for PX≤Y in categorized data. Biometrics 42 (4):895–907. doi:10.2307/2530703.
  • Surles, J. G., and D. M. D’Ambrosio. 2004. A Burr Type X chain-of-links model for carbon fibers. Journal of Composite Materials 38 (15):1337–43. doi:10.1177/0021998304042735.
  • Surles, J. G., and W. J. Padgett. 2001. Inference for reliability and stress-strength for a scaled Burr type X distribution. Lifetime Data Analysis 7 (2):187–200.
  • Takahasi, K., and K. Wakimoto. 1968. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics 20 (1):1–31. doi:10.1007/BF02911622.
  • Tavirdizade, B., and H. K. Garehchobogh. 2016. Inference on Pr⁡X>Y based on record values from the Burr Type X distribution. Hacettepe Journal of Mathematics and Statistics 45:267–78. doi:10.15672/HJMS.2015468581.
  • Zamanzade, E., and M. Mahdizadeh. 2018. Estimating the population proportion in pair ranked set sampling with application to air quality monitoring. Journal of Applied Statistics 45 (3):426–37. doi:10.1080/02664763.2017.1279596.
  • Zheng, G., and M. F. Al-Saleh. 2002. Modified maximum likelihood estimators based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54 (3):641–58. doi:10.1023/A:1022475413950.
  • Zheng, G., and M. F. Al-Saleh. 2003. Improving the best linear unbiased estimator for the scale parameter of symmetric distributions by using the absolute value of ranked set samples. Journal of Applied Statistics 30 (3):253–65. doi:10.1080/0266476022000030039.

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