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Some Moment Inequalities for the Minimal Repair Process

Published online by Cambridge University Press:  27 July 2009

S. N. U. A. Kirmani  and
Rmaesh C. Gupta
S. N. U. A. Kirmani
Affiliation:
University of Northern lowa Cedar Falls, lowa 52242
Rmaesh C. Gupta
Affiliation:
Department of MathematicsUniversity of Maine Orono, Maine 04469
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Abstract

Some monotonicity properties and bounds on expectations of certain functions of minimal repair times and interminimal repair times are obtained under assumptions on the aging characteristics of the equipment under maintenance.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 2 , April 1992 , pp. 245 - 255
Copyright
Copyright © Cambridge University Press 1992

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References

Bartoszewicz, J. (1985). Dispersive ordering and monotone failure rate distributions. Advances in Applied Probability 17: 472–474.CrossRefGoogle Scholar
Brown, M. (1981). Further monotonicity properties for specialized renewal processes. Annals of Probability 9: 891–895.CrossRefGoogle Scholar
Gertsbakh, I.B. (1989). Statistical reliability theory. New York: Marcel Dekker.Google Scholar
Gupta, P.L. & Gupta, R.C. (1983). On the moments of residual life in reliability and some characterization results. Communications in Statistics 12: 449–461.CrossRefGoogle Scholar
Gupta, R.C. & Kirmani, S.N.U.A. (1987). On order relations between reliability measures. Communications in Statistics–Stochastic Models 3: 149–156.Google Scholar
Gupta, R.C. & Kirmani, S.N.U.A. (1988). Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probability in the Engineering and Informational Sciences 2: 475–484.CrossRefGoogle Scholar
Gupta, R.C., Kirmani, S.N.U.A., & Launer, R.L. (1987). On life distributions having monotone residual variance. Probability in the Engineering and Informational Sciences 1: 299–307.CrossRefGoogle Scholar
Kirmani, S.N.U.A. & Gupta, R.C. (1989). On repair age and residual repair life in the minimal repair process. Probability in the Engineering and Informational Sciences 3: 381–391.CrossRefGoogle Scholar
Launer, R.L. (1984). Inequalities for NBUE and NWUE life distributions. Operations Research 32: 660–667.CrossRefGoogle Scholar
Lewis, T. & Thompson, J.W. (1981). Dispersive distributions and the connection between dispersivity and strong unimodality. Journal of Applied Probability 18: 76–90.CrossRefGoogle Scholar
Marshall, A.W., Olkm, L., & Proschan, F. (1967). Monotonicity of ratios of means and other applications of majorization. In Shisha, O. (ed.), Inequalities. New York: Academic Press, pp. 177–190.Google Scholar
Ross, S.M. (1983). Stochastic processes. New York: Wiley.Google Scholar
Shaked, M. (1982). Dispersive ordering of distributions. Journal of Applied Probability 19: 310–320.CrossRefGoogle Scholar
Shaked, M. & Shanthikumar, J.G. (1988). Stochastic convexity and its applications. Advances in Applied Probability 20: 427–446.CrossRefGoogle Scholar
Shaked, M. & Shanthikumar, J.G. (1991). Dynamic multivariate mean residual life functions. Journal of Applied Probability 28: 613–629.CrossRefGoogle Scholar
Shanthikumar, J.G. & Yao, D.D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642–659.CrossRefGoogle Scholar
Van Zwet, W.R. (1964). Convex transformations of random variables. Amsterdam: Mathematisch Centrum.Google Scholar