Results for burn-in of systems under external shocks

Recently, Cha and Finkelstein (IEEE Transactions on Reliability, 2011) have proposed and studied the new burn-in procedures for systems operating in an environment with shocks. The systems were characterized by the strength, which in this context is the capability of the system to survive a shock of a given magnitude. That work implicitly assumed that the impacts of environmental shocks on a system in field usage are statistically independent. However, in reality, each subsequent survived shock updates the distribution of the system's strength, introducing certain dependence, and this was overlooked in the original paper. In the current paper, we develop the new stochastic approach, and modify the failure model of Cha and Finkelstein (IEEE Transactions on Reliability, 2011) accordingly to account for the described statistical dependence. We obtain rather general results that, most importantly, justify practical application of shocks of the controlled magnitude as a new method of burn-in. Specifically, we show that the probability of failure under an environmental shock is decreasing with time, and with the controlled magnitude of the burn-in shock. We also discuss the corresponding optimization problems.