Li, Xiaohu; Zhao, Peng Stochastic comparison on general inactivity time and general residual life of \(k\)-out-of-\(n\) systems. (English) Zbl 1162.60307 Commun. Stat., Simulation Comput. 37, No. 5, 1005-1019 (2008). Summary: This paper conducts stochastic comparison on general residual life and general inactivity time of \((n - k + 1)\)-out-of-\(n\) systems and investigates the stochastic behavior of the general inactivity time of a system with units having decreasing reversed hazard rate. These results strengthen some conclusions in both B.-E. Khaledi and M. Shaked [J. Stat. Plann. Inference 137, No. 4, 1173–1184 (2007; Zbl 1111.60012)] and Hu et al. (2007). Cited in 36 Documents MSC: 60E15 Inequalities; stochastic orderings 60K10 Applications of renewal theory (reliability, demand theory, etc.) Keywords:DRHR; hazard rate order; likelihood ratio order; reversed hazard rate order; stochastic order; SR\(_{2}\); TP\(_{2}\) Citations:Zbl 1111.60012 PDFBibTeX XMLCite \textit{X. Li} and \textit{P. Zhao}, Commun. Stat., Simulation Comput. 37, No. 5, 1005--1019 (2008; Zbl 1162.60307) Full Text: DOI References: [1] DOI: 10.1016/j.jspi.2004.08.021 · Zbl 1088.62120 · doi:10.1016/j.jspi.2004.08.021 [2] DOI: 10.1080/03610920509342434 · doi:10.1080/03610920509342434 [3] Bairamov I., Journal of Statistical Theory and Applications 1 pp 119– (2002) [4] DOI: 10.1017/S0269964899132054 · Zbl 0973.60103 · doi:10.1017/S0269964899132054 [5] DOI: 10.1017/S0269964800005064 · Zbl 0972.90018 · doi:10.1017/S0269964800005064 [6] DOI: 10.1017/S0269964801151077 · Zbl 1087.62510 · doi:10.1017/S0269964801151077 [7] DOI: 10.1111/1467-9469.00103 · Zbl 0910.62094 · doi:10.1111/1467-9469.00103 [8] DOI: 10.1002/nav.1034 · Zbl 1005.90022 · doi:10.1002/nav.1034 [9] DOI: 10.1017/S0269964807000046 · Zbl 1125.60015 · doi:10.1017/S0269964807000046 [10] Karlin S., Total Positivity (1968) [11] DOI: 10.1023/A:1014641701483 · Zbl 1078.62519 · doi:10.1023/A:1014641701483 [12] DOI: 10.1016/j.jspi.2006.01.012 · Zbl 1111.60012 · doi:10.1016/j.jspi.2006.01.012 [13] Kuo W., Optimal Reliability Modeling: Principles and Applications (2002) [14] DOI: 10.1214/aop/1176994577 · Zbl 0448.60016 · doi:10.1214/aop/1176994577 [15] DOI: 10.1239/jap/1025131440 · Zbl 1003.62089 · doi:10.1239/jap/1025131440 [16] DOI: 10.1002/asmb.507 · Zbl 1060.62115 · doi:10.1002/asmb.507 [17] DOI: 10.1109/TR.2006.879652 · doi:10.1109/TR.2006.879652 [18] DOI: 10.1016/S0167-7152(00)00137-1 · Zbl 0982.60009 · doi:10.1016/S0167-7152(00)00137-1 [19] DOI: 10.2307/3213058 · Zbl 0471.62100 · doi:10.2307/3213058 [20] DOI: 10.1016/S0378-3758(02)00157-X · Zbl 1016.62060 · doi:10.1016/S0378-3758(02)00157-X [21] Müller A., Comparison Methods for Stochastic Models and Risks (2002) · Zbl 0999.60002 [22] Raqab M. Z., IAPQR Transactions 21 pp 1– (1996) [23] Shaked M., Stochastic Orders and their Applications (1994) · Zbl 0806.62009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.