Consider two systems, labeled system 1 and system 2, each with m components. Suppose component i in system k, k = 1, 2, is subjected to a sequence of shocks occurring randomly in time according to a non-explosive counting process {Γi(t), t > 0}, i = 1, ···, m. Assume that Γ1, ···, Γm are independent of Mk = (Mk,1, ···, Mk,m), the number of shocks each component in system k can sustain without failure. Let Zk,i be the lifetime of component i in system k. We find conditions on processes Γ1, ···, Γm such that some stochastic orders between M1 and M2 are transformed into some stochastic orders between Z1 and Z2. Most results are obtained under the assumption that Γ1, ···, Γm are independent Poisson processes, but some generalizations are possible and can be seen from the proofs of theorems.
