Some Inequalities and Bounds for Weighted Reliability Measures

Volume 3, Issue 4, 2002

Article 60

SOME INEQUALITIES AND BOUNDS FOR WEIGHTED RELIABILITY MEASURES

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
GEORGIA SOUTHERN UNIVERSITY, STATESBORO, GA 30460
E-Mail: boluyede@gasou.edu

Received 22 October, 2001; Accepted 17 July, 2002.
Communicated by: N.S. Barnett

ABSTRACT. Weighted distributions occur naturally in a wide variety of settings with applications in reliability, forestry, ecology, bio-medicine, and many other areas. In this note, bounds and stability results on the distance between weighted reliability functions, residual life distributions, equilibrum distributions with monotone weight functions and the exponential counterpart in the class of distribution functions with increasing or decreasing hazard rate and mean residual life functions are established. The problem of selection of experiments from the weighted distributions as opposed to the original distributions is addressed. The reliability inequalities are applied to repairable systems.

Key words:
Reliability inequalities, Stochastic Order, Weighted distribution functions, Integrable function.

2000 Mathematics Subject Classification:
60E15.

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