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Biometrika 1989 76(3):626-628; doi:10.1093/biomet/76.3.626
© 1989 by Biometrika Trust
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MISCELLANEA

Maximum likelihood estimation of convex arrival rate

CHING-FAI PANG, W. A. THOMPSON, JR and HAMID FALLAHI

Department of Statistics, University of Missouri-Columbia Columbia, Missouri 65211, U.S.A.
Eastman Kodak Company Rochester, New York 14652, U.S.A.

It is commonly believed that failures of a repairable system follow a time dependent Poisson process with ‘bathtub-shaped’ arrival rate. A natural problem then is maximum likelihood estimation of arrival rate subject to the constraint that it be convex. This paper employs theoretical considerations to reduce that task to a finite dimensional nonlinear programming problem and completes the solution by computer. The resulting estimates are interesting graphical presentations of the reliability characteristics of the system.

Key Words: Arrival rate • Bathtub-shaped • Poisson process • Reliability • Repairable system • Wearout


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