BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks

Nadeb H, Torabi H. Preservation of Stochastic Orderings of Interdependent Series and Parallel Systems by Componentwise Switching to Exponentiated Models. JIRSS. 2021; 20 (2) :117-128

URL: http://jirss.irstat.ir/article-1-744-en.html

URL: http://jirss.irstat.ir/article-1-744-en.html

This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the parallel systems the reversed hazard, usual, convex transform, star, superadditive and dispersive orderings are studied. Also, we present a necessary and sufficient condition for being finiteness of the moments of the switched series and switched parallel systems.

Type of Study: Original Paper |
Subject:
60Exx: Distribution theory

Received: 2021/02/22 | Accepted: 2021/09/29 | Published: 2022/04/12

Received: 2021/02/22 | Accepted: 2021/09/29 | Published: 2022/04/12

1. Abbasi, N., Alamatsaz, M. H., and Cramer, E. (2016), Preservation properties of stochastic orderings by transformation to Harris family with different tilt parameters. Latin American Journal of Probability and Mathematical Statistics, 13(1), 465-479. [DOI:10.30757/ALEA.v13-19]

2. Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. (2008), A first course in order statistics. Philadelphia: Siam. [DOI:10.1137/1.9780898719062]

3. Balakrishnan, N., Barmalzan, G., and Haidari, A. (2020), Exponentiated models preserve stochastic orderings of parallel and series systems. Communications in Statistics-Theory and Methods, 49(7), 1592-1602. [DOI:10.1080/03610926.2018.1532007]

4. Balakrishnan, N., Nanda, P., and Kayal, S. (2018), Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components. Applied Stochastic Models in Business and Industry, 34(6), 816-834. [DOI:10.1002/asmb.2353]

5. Barlow, R. E., and Proschan, F. (1996), Mathematical Theory of Reliability. Philadelphia: Siam. [DOI:10.1137/1.9781611971194]

6. Belzunce, F., Ruiz, J. M., and Ruiz, M. C. (2002), On preservation of some shifted and proportional orders by systems. Statistics and Probability Letters, 60(2), 141-154. [DOI:10.1016/S0167-7152(02)00302-4]

7. Brown, M., and Shanthikumar., J. G. (1998), Comparing the variability of random variables and point processes. textit{Probability in the Engineering and Informational Sciences {bf 12(4), 425-444. [DOI:10.1017/S0269964800005301]

8. Das, S., and Kayal, S. (2020), Ordering extremes of exponentiated location-scale models with dependent and heterogeneous random samples. Metrika, 83, 869-893. [DOI:10.1007/s00184-019-00753-2]

9. David, H., and Nagaraja, H. (2003), Order statistics, 3rd ed. New York: Wiley. [DOI:10.1002/0471722162]

10. Dykstra, R., Kochar, S. C., and Rojo, J. (1997), Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference, 65(2), 203-211. [DOI:10.1016/S0378-3758(97)00058-X]

11. Gumbel, E. J. (1960), Distributions des valeurs extremes en plusiers dimensions. Publications de lInstitut de statistique de lUniversit'e de Paris, 9, 171-173.

12. Jiang, R., Ji, P., and Xiao, X. (2003), Aging property of unimodal failure rate models. Reliability Engineering & System Safety, 79(1), 113-116. [DOI:10.1016/S0951-8320(02)00175-8]

13. Joe, H. (2014), Dependence Modeling with Copulas. Boca Raton: Chapman & Hall/CRC. [DOI:10.1201/b17116]

14. Keilson, J., and Sumita, U. (1982), Uniform stochastic ordering and related inequalities. Canadian Journal of Statistics, 10(3), 181-198. [DOI:10.2307/3556181]

15. Khaledi, B. E., and Kochar, S. C. (2000), Some new results on stochastic comparisons of parallel [DOI:10.1017/S0021900200018301]

16. systems. Journal of Applied Probability, 37(4), 1123-1128.

17. Kochar, S. C., and Xu., M. (2007), Stochastic comparisons of parallel systems when components have proportional hazard rates. Probability in the Engineering and Informational Sciences, 21(4), 597-609. [DOI:10.1017/S0269964807000344]

18. Kochar, S. C., and Xu., M. (2009), Comparisons of parallel systems according to the convex transform order. Journal of Applied Probability, 46(2), 342-352. [DOI:10.1017/S0021900200005490]

19. Lariviere, M. A. (2006), A note on probability distributions with increasing generalized failure rates. Operations Research, 54(3), 602-604. [DOI:10.1287/opre.1060.0282]

20. Li, X. (2005), A note on expected rent in auction theory. Operations Research Letters, 33(5), 531-534. [DOI:10.1016/j.orl.2004.09.010]

21. Lillo, R. E., Nanda, A. K., and Shaked, M. (2001), Some shifted stochastic orders. In Recent Advances in Reliability Theory, Eds. N. Limnios and M. Nikulin. Boston: Birkhauser. [DOI:10.1007/978-1-4612-1384-0_6]

22. Muller, A., and Stoyan, D. (2002). Comparison methods for stochastic models and risks. John Wiley & Sons, New York.

23. Nadeb, H., and Torabi, H. (2018), Stochastic comparisons of series systems with independent heterogeneous Lomax-exponential components. Journal of Statistical Theory and Practice, 12(4), 794-812. [DOI:10.1080/15598608.2018.1474819]

24. Nadeb, H., and Torabi, H. (2020), Preservation properties of stochastic orders by transformation to the transmuted-G model. Communications in Statistics-Theory and Methods, 49(17), 4333-4346. [DOI:10.1080/03610926.2019.1601220]

25. Nadeb, H., Torabi, H., and Dolati, A. (2021), Some general results on usual stochastic ordering of the extreme order statistics from dependent random variables under Archimedean copula dependence. Journal of the Korean Statistical Society, 50(4), 1147-1163. [DOI:10.1007/s42952-021-00109-5]

26. Nakai, T. (1995), A partially observable decision problem under a shifted likelihood ratio ordering. textit{Mathematical and Computer Modelling, 22(10-12), 237-246. [DOI:10.1016/0895-7177(95)00201-C]

27. Nanda, A. K., Bhattacharjee, S., and Alam, S.S. (2007), Properties of aging intensity function. Statistics $&$ Probability Letters, 77(4), 365-373. [DOI:10.1016/j.spl.2006.08.002]

28. Nelsen, R. B. (2006), An Introduction to Copulas. New York: Springer.

29. Patra, L. K., Kayal, S., and Nanda, P. (2018), Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components. Applications of Mathematics, 63(1), 55-77. [DOI:10.21136/AM.2018.0105-17]

30. Pickands, J. (1981), Multivariate extreme value distributions. Proceedings 43rd Session International Statistical Institute, 859-878.

31. Ramos Romero, H. M., and Diaz, S. (2001), The proportional likelihood ratio order and applications. Questiio, 25(2), 211-223.

32. Sengupta, D., and Deshpande, J. V. (1994), Some results on the relative ageing of two life distributions. Journal of Applied Probability, 31(4), 991-103. [DOI:10.1017/S0021900200099514]

33. Shaked, M., and Shanthikumar, J. G. (2007), Stochastic Orders. New York: Springer. [DOI:10.1007/978-0-387-34675-5]

34. Shanthikumar, J. C., and Yao, D. D. (1986), The preservation of likelihood ratio ordering under convolution. Stochastic Processes and their Applications, 23(2), 259-267. [DOI:10.1016/0304-4149(86)90039-6]

35. Zhao, P., and Balakrishnan., N. (2011), Some characterization results for parallel systems with two heterogeneous exponential components. Statistics, 45(6), 593-604. [DOI:10.1080/02331888.2010.485276]

36. Zhao, P., and Balakrishnan., N. (2012), Stochastic comparisons of largest order statistics from multiple-outlier exponential models. Probability in the Engineering and Informational Sciences, 426(2), 159-182. [DOI:10.1017/S0269964811000313]

37. Zhao, P., and Balakrishnan., N. (2013), Hazard rate comparison of parallel systems with heterogeneous gamma components. Journal of Multivariate Analysis, 113, 153-160. [DOI:10.1016/j.jmva.2011.05.001]

38. Zhao, P., and Balakrishnan., N. (2015), Comparisons of largest order statistics from multiple-outlier gamma models. Methodology and Computing in Applied Probability, 17(3), 617-645. [DOI:10.1007/s11009-013-9377-0]

Send email to the article author

Rights and permissions | |

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |