Life Distribution Properties of Devices Subject to a Lévy Wear Process
- 1 November 1984
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 9 (4) , 606-614
- https://doi.org/10.1287/moor.9.4.606
Abstract
Assume that a device is subject to wear. Over time the wear is assumed to be an increasing Lévy process (Xt). Suppose the device has a threshold Y with right-tail probability Ḡ. Let ζ be the failure time of the device and F̄x be its survival probability given that X0 = x. It is shown that life distribution properties of Ḡ are inherited as corresponding properties of F̄x for each x ∈ R+. Optimal replacement policies for such devices are discussed for suitably chosen cost functions when Ḡ is absolutely continuous on R+ with a bounded failure rate.Keywords
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