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Coherent structures and unimodality

  • S. V. Sabnis (a1) and Mini R. Nair (a1)

Abstract

This paper is concerned with the preservation of unimodality under coherent structures of independent components having a common life distribution function. This result in a way generalizes a result of Alam [1], as Alam's result indirectly also deals with preservation of unimodality for (ni + 1)-out-of-n systems of independent and identically distributed components. The usefulness of this property of coherent systems in obtaining sharper upper bounds on the reliability of the concerned system has been illustrated below for a bridge structure with components having a gamma life distribution function.

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Postal address: Department of Mathematics, Indian Institute of Technology, Bombay, India.

References

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[1] Alam, K. (1972) Unimodality of the distribution of an order statistic. Ann. Math. Statist. 43, 20412044.
[2] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
[3] Chaudhuri, G., Deshpande, J. V., Dharmadhikari, A. D. (1991) Some bounds on the reliability of coherent systems of IFRA components. J. Appl. Prob. 28, 709714.
[4] Dharmadhikari, S. and Joag-Dev, K. (1988) Unimodality, Convexity, and Applications. Academic Press, New York.

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Coherent structures and unimodality

  • S. V. Sabnis (a1) and Mini R. Nair (a1)

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