Life Distribution Properties of Devices Subject to a Lévy Wear Process

Abstract

Assume that a device is subject to wear. Over time the wear is assumed to be an increasing Lévy process (X t ). Suppose the device has a threshold Y with right-tail probability Ḡ. Let ζ be the failure time of the device and F̄ x be its survival probability given that X 0 = x. It is shown that life distribution properties of Ḡ are inherited as corresponding properties of F̄ x 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.