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Remarks on a univariate shock model with some bivariate generalizations

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  • William S. Griffith

Abstract

In a 1973 paper J. D. Esary, A. W. Marshall, and F. Proschan [5] considered a shock model giving rise to various nonparametric classes of life distributions of interest in reliability theory. A number of authors have extended these results in a variety of directions. In this paper, alternative proofs of the increasing failure rate (IFR) and decreasing mean residual life (DMRL) results are given which do not make use of the theory of total positivity. Some bivariate extensions are then obtained using a shock model similar to that originally used by H. W. Block, A. S. Paulson, and R. C. Kohberger [2] to unify various bivariate exponential distributions.

Suggested Citation

  • William S. Griffith, 1982. "Remarks on a univariate shock model with some bivariate generalizations," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(1), pages 63-74, March.
    • Handle: RePEc:wly:navlog:v:29:y:1982:i:1:p:63-74
    DOI: 10.1002/nav.3800290107
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