Abstract
Least upper and greatest lower bounds are obtained for the interval failure rate, when only the first two moments of the time-to-failure function are known.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Barlow and F. Proschan, Asymptotic Theory of Total Time on Test Processes with Application to Life Testing, North-Holland, Vol. 4 (1977), pp. 227–237.
Huang Wei-Min, “A note on the estimation of interval failure rates,” Tamkang J. Math., 16, No. 4, 59–66 (1985).
I. B. Gertsbakh, Statistical Reliability Theory, Marcel Dekker (1989).
L. S. Stoikova, “A weak necessary condition of extremum for the linear-fractional functional on a class of distribution functions,” Dop. NAN Ukr., Ser. A, No. 12, 89–96 (1993).
L. S. Stoikova, “A necessary and sufficient condition of extremum for the Lebesgue-Stieltjes integral on a class of distributions,” Kibernetika, No. 1, 72–75 (1990).
M. G. Krein and A. A. NudeFman, A Problem of Markov Moments and Extremum Problems [in Russian], Nauka, Moscow (1973).
Author information
Authors and Affiliations
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 141–150, November–December, 1999.
Rights and permissions
About this article
Cite this article
Stoikova, L.S. Using the generalized chebyshev inequalities in estimating the interval failure rate. Cybern Syst Anal 35, 965–972 (1999). https://doi.org/10.1007/BF02742289
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02742289