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Requirements for system availability for ultrahigh reliability electronic systems such as airborne and space electronic systems are driving the need for advanced health monitoring techniques for the early detection of the onset of damage. Aerospace electronic systems usually face a very harsh environment, requiring them to survive the high strain rates, e.g., during launch and reentry, and thermal environments, including extremely low and high temperatures. Traditional health monitoring methodologies have relied on reactive methods of failure detection often providing little or no insight into the remaining useful life of the system. In this paper, a mathematical approach for the interrogation of the system state under cyclic thermomechanical stresses has been developed for six different lead-free solder alloy systems. Data have been collected for leading indicators of failure for alloy systems, including Sn3Ag0.5Cu, Sn0.3Ag0.7Cu, Sn1Ag0.5Cu, Sn0.3Ag0.5Cu0.1Bi, Sn0.2Ag0.5Cu0.1Bi0.1Ni, and 96.5 Sn3.5Ag second-level interconnects under the application of cyclic thermomechanical loads. The methodology presented resides in the prefailure space of the system in which no macroindicators such as cracks or delamination exist. Systems subjected to thermomechanical damage have been interrogated for the system state and the computed damage state correlated with the known imposed damage. The approach involves the use of condition monitoring devices which can be interrogated for damage proxies at finite time intervals. The interrogation techniques are based on the derivation of damage proxies and system prior-damage-based nonlinear least square methods, including the Levenberg-Marquardt algorithm. The system's residual life is computed based on residual-life computation algorithms.