Almost Sure Comparisons of Renewal Processes and Poisson Processes, with Application to Reliability Theory

摘要: If the interarrival times of a renewal process {Si, i = 0, 1, 2...} have failure rate function which is bounded away from 0 and ∞, then it possible to construct nonhomogeneous Poisson processes {Ti0, 2,...} {Ti1, on same probability space with such that {T00, T10, T20,...} ⊂ {S0, S1, S2,...} {T01, T11, T21,...} almost surely. This has applications reliability theory maintained systems. If components coherent system exponential lifetimes NWU repair times, an initially perfect will NBU distribution time until first failure. Furthermore, transient availability greater than steady-state availability.