Exponentiated models preserve stochastic orderings of parallel and series systems

References

• Balakrishnan, N., A. Haidari, and K. Masoumifard. 2015. Stochastic comparisons of series and parallel systems with generalized exponential components. IEEE Transactions on Reliability 64 (1):333–48.
   Web of Science ®Google Scholar
• Balakrishnan, N., P. Nanda, and S. Kayal. 2018. Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components. Applied Stochastic Models in Business and Industry online first. https://doi.org/10.1002/asmb.2353.
   Web of Science ®Google Scholar
• Barmalzan, G., A. T. Payandeh Najafabadi, and N. Balakrishnan. 2017. Orderings for series and parallel systems comprising heterogeneous exponentiated Weibull-geometric components. Communications in Statistics: Theory and Methods 46 (20):9869–88.
   Web of Science ®Google Scholar
• Dykstra, R. A., S. C. Kochar, and J. Rojo. 1997. Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference 65 (2):203–11.
   Web of Science ®Google Scholar
• Fang, L., and X. Zhang. 2015. Stochastic comparisons of parallel systems with exponentiated Weibull components. Statistics and Probability Letters 97:25–31.
   Web of Science ®Google Scholar
• Gupta, R. C., R. D. Gupta, and P. L. Gupta. 1998. Modeling failure time data by Lehmann alternatives. Communications in Statistics: Theory and Methods 27 (4):887–904.
   Web of Science ®Google Scholar
• Gupta, R. D., and D. Kundu. 1999. Generalized exponential distributions. Australian & New Zealand Journal of Statistics 41 (2):173–88.
   Web of Science ®Google Scholar
• Khaledi, B. E., and S. C. Kochar. 2000. Some new results on stochastic comparisons of parallel systems. Journal of Applied Probability 37 (4):1123–8.
   Web of Science ®Google Scholar
• Kochar, S. C., and M. Xu. 2007. Stochastic comparisons of parallel systems when components have proportional hazard rates. Probability in the Engineering and Informational Sciences 21:597–609.
   Web of Science ®Google Scholar
• Kochar, S. C., and M. Xu. 2009. Comparisons of parallel systems according to the convex transform order. Journal of Applied Probability 46 (2):342–52.
   Web of Science ®Google Scholar
• Lehmann, E. L. 1953. The power of rank tests. Annals of Mathematical Statistics 24:23–43.
   Google Scholar
• Marshall, A. W., and I. Olkin. 2002. Life Distributions. New York: Springer-Verlag.
   Google Scholar
• Marshall, A. W., I. Olkin, and B. C. Arnold. 2011. Inequalities: Theory of Majorization and its Applications. New York: Springer-Verlag.
   Google Scholar
• Müller, A., and D. Stoyan. 2002. Comparison Methods for Stochastic Models and Risks. New York: John Wiley & Sons.
   Google Scholar
• Nadarajah, S., and S. Kotz. 2006. The exponentiated type distributions. Acta Applicandae Mathematicae 92 (2):97–111.
   Web of Science ®Google Scholar
• Nadeb, H., and H. Torabi. 2018. Stochastic comparisons of series systems with independent heterogeneous Lomax-exponential components. Journal of Statistical Theory and Practice :1. https://doi.org/10.1080/15598608.2018.1474819.
   Web of Science ®Google Scholar
• Patra, L. K., S. Kayal, and P. Nanda. 2018. Some stochastic comparison results for series and parallel systems with heterogeneous pareto type components. Applications of Mathematics 63 (1):55–77.
   Web of Science ®Google Scholar
• Shaked, M., and J. G. Shanthikumar. 2007. Stochastic orders. New York: Springer.
   Google Scholar
• Zhao, P., and N. Balakrishnan. 2011. Some characterization results for parallel systems with two heterogeneous exponential components. Statistics 45 (6):593–604.
   Web of Science ®Google Scholar
• Zhao, P., and N. Balakrishnan. 2012. Stochastic comparisons of largest order statistics from multiple-outlier exponential models. Probability in the Engineering and Informational Sciences 26 (2):159–82.
   Web of Science ®Google Scholar
• Zhao, P., and N. Balakrishnan. 2013. Hazard rate comparison of parallel systems with heterogeneous gamma components. Journal of Multivariate Analysis 113:153–60.
   Web of Science ®Google Scholar
• Zhao, P., and N. Balakrishnan. 2015. Comparisons of largest order statistics from multiple-outlier gamma models. Methodology and Computing in Applied Probability 17 (3):617–45.
   Web of Science ®Google Scholar