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Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

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  • Bo H. Lindqvist
  • Francisco J. Samaniego

Abstract

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.

Suggested Citation

  • Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:5:p:430-438
    DOI: 10.1002/nav.21849
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    References listed on IDEAS

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    1. Navarro, Jorge, 2018. "Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 264-268.
    2. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, February.
    3. Manuel Franco & M. Ruiz & José Ruiz, 2003. "A note on closure of the ILR and DLR classes under formation of coherent systems," Statistical Papers, Springer, vol. 44(2), pages 279-288, April.
    4. Nanda, Asok K. & Jain, Kanchan & Singh, Harshinder, 1998. "Preservation of some partial orderings under the formation of coherent systems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 123-131, August.
    5. Jorge Navarro & Yolanda del Águila & Miguel A. Sordo & Alfonso Suárez‐Llorens, 2014. "Preservation of reliability classes under the formation of coherent systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 444-454, July.
    6. Abouammoh, A. & El-Neweihi, E., 1986. "Clusure of the NBUE and DMRL classes under formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 4(5), pages 223-225, August.
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    Cited by:

    1. 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.
    2. Gámiz, Maria Luz & Nozal-Cañadas, Rafael & Raya-Miranda, Rocío, 2020. "TTT-SiZer: A graphic tool for aging trends recognition," Reliability Engineering and System Safety, Elsevier, vol. 202(C).

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