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Further results related to variance past lifetime class & associated orderings and their properties

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  • Mahdy, Mervat

Abstract

If the random variable T denotes the lifetime of a unit, then the random variable T(t)=[t−T∣T≤t], for a fixed t>0, is known as the past lifetime. In this study, we present some new properties of the mean and variance for past lifetime classes (orderings). In addition, we consider an (n−r+1)-out-of-n system with identical components where it is assumed that the lifetimes of the components are i.i.d. We assume that the system fails before time x,x>0. Under these conditions, we are interested in studying the variance time elapsed since the failure of the components. Several properties of this function are studied and an example is provided.

Suggested Citation

  • Mahdy, Mervat, 2016. "Further results related to variance past lifetime class & associated orderings and their properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1148-1160.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1148-1160
    DOI: 10.1016/j.physa.2016.06.066
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    References listed on IDEAS

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    1. Mahdi Tavangar & Majid Asadi, 2010. "A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 59-73, July.
    2. Majid Rezaei & Behzad Gholizadeh & Salman Izadkhah, 2015. "On Relative Reversed Hazard Rate Order," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(2), pages 300-308, January.
    3. S. M. Sunoj & S. S. Maya, 2008. "The role of lower partial moments in stochastic modeling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 223-242.
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    Cited by:

    1. Jafar Ahmadi & H. N. Nagaraja, 2020. "Conditional properties of a random sample given an order statistic," Statistical Papers, Springer, vol. 61(5), pages 1971-1996, October.

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