Compound aftershock sequences are of special interest because the decay of secondary aftershocks contains information about the mechanisms that generate all earthquakes. If earthquakes nucleate as a result of accelerating slip, growing cracks, or any similar failure process, then the rate of decay of aftershock sequences is a direct result of that failure process, as influenced by local material properties. The aftershocks are then triggered by the mainshock, moved closer to failure, and concentrated on the curved part of loading curve, occurring earlier than they would have if the mainshock had not occurred. Secondary aftershocks, which are themselves triggered by an aftershock, are promoted toward failure twice and consequently should decay differently than primary aftershocks do. The theory behind this concept is developed, explored with numerical models, and tested with a study of the aftershocks of the Hector Mine earthquake of 1999. Because the Hector Mine mainshock occurred during the aftershock sequence of the Landers 1992 earthquake, failure-time remapping predicts a slightly different temporal distribution for the Hector Mine aftershocks than they would have had without the influence of the Landers mainshock. This prediction is testable. In this work, three different types of aftershock decay relations are applied to 94 spatial subsets of aftershocks and evaluated with two different statistical measures. Remapped aftershock decay models were superior for almost all the cases studied, regardless of the type of aftershock decay model used or the statistical measure. These results confirm previous work suggesting that the majority of aftershocks are not caused by their mainshock, only promoted toward failure, and most earthquakes nucleate through a failure process such as velocity-dependent friction or stress corrosion cracking.