High operational reliability of an electronic material or a device intended for highly reliable applications (aerospace, military, long-haul communications and many other noncommercial engineering fields) is particularly critical, and cannot be assured, if the underlying physics of failure is not well understood and the never-zero probability of failure is not predicted and made adequate for the particular material, device and application. This cannot be achieved if highly focused and highly cost effective failure-oriented-accelerated-testing (FOAT) is not considered and thoroughly conducted for the most vulnerable materials and structural elements of the device of interest, and since nothing is perfect, this should be done on the probabilistic basis. FOAT is the experimental basis of the recently suggested probabilistic design for reliability (PDfR) concept and should be geared to a physically meaningful probabilistic model, such as, e.g., Boltzmann-Arrhenius-Zhurkov (BAZ) constitutive equation. Other well-known FOAT models are also indicated. FOAT significance, attributes and challenges are addressed and discussed vs. the very popular today highly-accelerated-life-testing (HALT). The general concepts are illustrated in this paper by three numerical examples: adequate heat sink, extreme response to temperature cycling, and delayed fracture ("static fatigue") of a glass-fiber test specimen.