Về các thứ tự tổng quát và lớp lão hóa đối với thời gian sống còn và thời gian không hoạt động tại thời điểm ngẫu nhiên

Barlow RE, Proschan F (1981) Statistical theory of reliability and life testing: probability models. Hold, Reinhart and Wiston, Inc., Silver Spring Belzunce F, Nanda AK, Ortega EM, Ruiz JM (2008) Generalized orderings of excess lifetimes of renewal processes. Test 17:297–310 Belzunce F, Riquelme CM, Mulero J (2015) An introduction to stochastic orders. Academic Press, Cambridge Cai N, Zheng Y (2009) Some results on generalized ageing classes. J Stat Plan Inference 139:4223–4230 Cai N, Zheng Y (2012) Preservation of generalized ageing class on the residual life at random time. J Stat Plan Inference 142:148–154 Dewan I, Khaledi BE (2014) On stochastic comparisons of residual life at random time. Stat Probab Lett 88:73–79 Denuit M, Lefevre C, Shaked M (1998) The \(s\)-convex orders among real random variables, with applications. Math Inequal Appl 1:585–613 Fagiuoli E, Pellerey F (1993) New partial orderings and applications. Nav Res Logist 40:829–842 Fagiuoli E, Pellerey F (1994) Mean residual life and increasing convex comparision of shock models. Stat Probab Lett 20:337–345 Gupta RC (2006) Variance residual life function in reliability studies. Metron 3:343–355 Hu T, Kundu A, Nanda AK (2001) On generalized ordering and ageing properties with their implications. In: Hayakawa Y, Irony T, Xie M (eds) System and Bayesian reliability, vol 5. World Scientific, New Jersy, pp 199–288 Hu T, Ma M, Nanda AK (2004) Characterizations of generalized ageing classes by the excess lifetime. Southeast Asian Bull Math 28:279–285 Joag-Dev K, Kochar S, Proschan F (1995) A general composition theorem and its applications to certain partial orderings of distributions. Stat Probab Lett 22:111–119 Karlin S (1968) Total positivity. Stanford University Press, Palo Alto Kass R, Van Heerwaarden AE, Goovaerts MJ (1994) Ordering of actuarial risks. Caire education series 1. CAIRE, Brussels Kayid M, Izadkhah S (2016) Some new results about the variance inactivity time ordering with applications. Appl Math Model 40:3832–3842 Kundu C, Patra A (2018) Some results on residual life and inactivity time at random time. Commun Stat Theory Methods 47(2):372–384 Li X, Xu M (2006) Some results about MIT order and IMIT class of life distributions. Probab Eng Inf Sci 20(3):481–496 Li X, Zuo MJ (2004) Stochastic comparison of residual life and inactivity time at a random time. Stoch Models 20:229–235 Mahdy M (2012) Characterization and preservations of the variance inactivity time ordering and the increasing variance inactivity time class. J Adv Res 3:29–34 Marshall KT (1968) Some inequalities in queuing. Oper Res 16:651–665 Misra N, Naqvi S (2017) Stochastic properties of inactivity times at random times: some unified results. Am J Math Manag Sci 36(2):85–97 Misra N, Gupta N, Dhariyal ID (2008) Stochastic properties of residual life and inactivity time at random time. Stoch Models 24:89–102 Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, New York Nanda AK (1997) On improvement and deterioration of a repairable system. IAPQR Trans 22:107–113 Navarro J, Hernandez PJ (2004) How to obtain bathtub-shaped failure rate models from normal mixtures. Probab Eng Inf Sci 18:511–531 Nanda AK, Jain K, Singh H (1996a) On closoure of some partial orderings under mixture. J Appl Probab 33:698–706 Nanda AK, Jain K, Singh H (1996b) Properties of moments for \(s\)-order equilibrium distribution. J Appl Probab 33:1108–1111 Nanda AK, Kundu A (2009) On generalized stochastic oredrs of dispersion-type. Calcutta Stat Assoc Bull 61:156–182 Stoyan D (1983) Comparison methods for queues and other stochastic models. Wiley, New York Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York Yue D, Cao J (2000) Some results on the residual life at random time. Acta Math Appl Sin 16:436–443