Stochastic comparison of wear processes characterized by random linear wear rates

We consider hybrid wear processes that at random times alternately increase and decrease with random linear wear rates. We give conditions on the random alternating times and on the random wear rates such that two such wear processes are stochastically ordered. The comparison of maximum wear levels and of random failure times is also treated. We finally apply such results to the analysis of processes derived by the Goldstein-Kac telegrapher's random process, and in particular obtain bounds for the distribution of their maximum.