Shock models by underlying counting process

1994/03/01 by Franco Pellerey
Mathematics · Computer Science · #Statistical Distribution Estimation and Applications #Bayesian Methods and Mixture Models #Statistical Methods and Inference

paper · doi:10.2307/3215243

Abstract

Suppose that a device is subjected to shocks governed by a counting process N = N ( t ), t ≧0. The probability that the device survives beyond time t is then H̄( t )=Σ k=0 ∞ Q̄ℙ[ N ( t )= k ], where Q̄ k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals U k , ∊ ℕ + , are independent and NBU, and Q̄ k+j ≦ Q̄ k · Q̄ j holds whenever k, j ∊ ℕ. Similar results hold for the classes of the NBUE and HNBUE distributions. We show that some other ageing classes have similar properties.

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