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On the role of dependence in residual lifetimes

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  • Longobardi, Maria
  • Pellerey, Franco

Abstract

Consider a vector (X,Y) that describes the failure times of two non-independent components of a system. Assuming that the first component has survived up to a given time t>0, i.e., assuming X>t, one can define the corresponding residual lifetime under different assumptions on the failure of the second component, having lifetime Y. In particular, one can observe that the second component has not failed before a time s≥0 (maybe different from t), thus the conditioned residual lifetime X˜t=[X−t|X>t,Y>s] can be considered, or one cannot observe Y, and in this case the conditioned residual lifetime Xt=[X−t|X>t] has to be studied. This note deals with conditions on the survival copula of (X,Y) such that X˜t and Xt are comparable according to the main reliability stochastic orders. Similar conditions, based on the connecting copula of (X,Y), are described also for the conditioned inactivity times X˜t=[t−X|X≤t,Y≤s] and Xt=[t−X|X≤t].

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  • Longobardi, Maria & Pellerey, Franco, 2019. "On the role of dependence in residual lifetimes," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 56-64.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:56-64
    DOI: 10.1016/j.spl.2019.05.010
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    References listed on IDEAS

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    Cited by:

    1. Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    2. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    3. Li, Chen & Li, Xiaohu, 2021. "On stochastic dependence in residual lifetime and inactivity time with some applications," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    5. Jorge Navarro & Camilla Calì & Maria Longobardi & Fabrizio Durante, 2022. "Distortion representations of multivariate distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 925-954, October.

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