Shock models by underlying counting process
Copyright policy )Shock models by underlying counting process
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)=Σk=0∞Q̄ℙ[N(t)=k], where Q̄k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals Uk, ∊ ℕ+, are independent and NBU, and Q̄k+j ≦ Q̄k· Q̄j 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.
- Polytechnic University of Turin Italy
- University of Milan Italy
Applications of renewal theory (reliability, demand theory, etc.), shock models, ageing classes, Renewal theory, Probability distributions: general theory, counting process, NBUE and HNBUE distributions
Applications of renewal theory (reliability, demand theory, etc.), shock models, ageing classes, Renewal theory, Probability distributions: general theory, counting process, NBUE and HNBUE distributions
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