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Preservation of unimodality under shock models

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  • Mini N. Balu
  • S.V. Sabnis

Abstract

A number of results pertaining to preservation of aging properties (IFR, IFRA etc.) under various shock models are available in the literature. Our aim in this paper is to examine in the same spirit, the preservation of unimodality under various shock models. For example, it is proved that in a non‐homogeneous Poisson shock model if {pk}K≥0, the sequence of probabilities with which the device fails on the kth shock, is unimodal then under some suitable conditions on the mean value function Λ (t), the corresponding survival function is also unimodal. The other shock models under which the preservation of unimodality is considered in this paper are pure birth shock model and a more general shock model in which shocks occur according to a general counting process. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 952–957, 1999

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  • Mini N. Balu & S.V. Sabnis, 1999. "Preservation of unimodality under shock models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(8), pages 952-957, December.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:8:p:952-957
    DOI: 10.1002/(SICI)1520-6750(199912)46:83.0.CO;2-2
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    References listed on IDEAS

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    1. A-Hameed, M. S. & Proschan, F., 1973. "Nonstationary shock models," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 383-404, October.
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    Cited by:

    1. Nader Ebrahimi & S.N.U.A. Kirmani & Ehsan S. Soofi, 2011. "Predictability of operational processes over finite horizon," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 531-545, September.

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