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Methodologies for prognostication and health monitoring (HM) can significantly impact electronic reliability for applications in which even minimal risk of failure may be unbearable. Presently, HM approaches such as the built-in self-test are based on reactive failure diagnostics and unable to determine residual-life (RL) or estimate residual-reliability. Prognostics health-monitoring (PHM) approach presented in this paper is different from state-of-art diagnostics and resides in the prefailure-space of the electronic system, in which no macro-indicators such as cracks or delamination exist. Applications for the presented PHM framework include, consumer and defense applications such as automotive safety systems including front and rear impact protection systems, chassis-control systems, x-by-wire systems, and defense applications such as avionics systems, naval electronic warfare systems. The presented PHM methodologies enable the estimation of prior damage in deployed electronics by the interrogation of the system state for systems in which the prior stress-history may be unknown or unavailable. The primary focus is on thermo-mechanical stresses. The presented methodologies will trigger repair or replacement, significantly prior to failure. The approach involves the use of condition monitoring devices which can be interrogated for damage proxies at finite time-intervals. The system's residual life is computed based on residual-life computation algorithms. Previously, we have developed several leading indicators of failure. In this paper, a mathematical approach has been presented to calculate the prior damage in electronics subjected to cyclic and isothermal thermo-mechanical loads. Electronic components operating in a harsh environment may be subjected to both temperature variations in addition to thermal aging during use-life. Data have been collected for leading indicators of failure for 95.5Sn4Ag0.5Cu first-level interconnects under both single and sequential - - applications of cyclic and isothermal thermo-mechanical loads. Methodology for the determination of prior damage history has been presented using non-linear least-squares method based on interrogation techniques. The methodology presented used the Levenberg-Marquardt Algorithm. The test vehicle includes various area-array packaging architectures soldered on immersion Ag finish, subjected to thermal cycling in the range of -40 οC to 125 οC and isothermal aging at 125 οC.