Balancing burn-in and mission times in environments with catastrophic and repairable failures

In a system subject to both repairable and catastrophic (i.e., nonrepairable) failures, ‘mission success’ can be defined as operating for a specified time without a catastrophic failure. We examine the effect of a burn-in process of duration τ on the mission time x, and also on the probability of mission success, by introducing several functions and surfaces on the (τ,x)-plane whose extrema represent suitable choices for the best burn-in time, and the best burn-in time for a desired mission time. The corresponding curvature functions and surfaces provide information about probabilities and expectations related to these burn-in and mission times. Theoretical considerations are illustrated with both parametric and, separating the failures by failure mode, nonparametric analyses of a data set, and graphical visualization of results.