![]() ![]() 4.2.1) to explain that specific energy levels E i are nominally the same in all components and are distributed in a Gaussian fashion. Physical models of failure generally invoke the central limit theorem ( Sect. Electronic components have wear-out hazard functions that do not rise monotonically, and this partially accounts for the utility of the lognormal distribution. This is distinct from the Weibull distribution, which simply shows a monotonic increase with time. The lognormal distribution is characterized by a failure rate λ( t) that has a single maximum, with λ equal to zero at both zero and infinite time. Milton Ohring, in Reliability and Failure of Electronic Materials and Devices, 1998 4.5.4 Physics of the Lognormal Distribution The Mathematics of Failure and Reliability ![]() In contrast to electronic devices, the longevity of humans cannot be predicted with any accuracy through a physical examination. In addition, random external variables, e.g., bacteria, viruses, accidents, addiction to cigarettes, alcohol, or drugs, become increasingly life-threatening as the recuperative powers of the body wear out. ![]() For example, loss of a kidney does not cause death in humans. Furthermore, the presence of redundancy at many levels complicates the form of the hazard function. For living species, internal aging processes apparently generate species-specific biological clocks with increasing hazard functions as t → ∞. There is an interesting inequivalence between the lognormal description of electronic components and the increasing hazard function for human lifetimes. Explicit expressions for the reduction of the electroluminescent efficiency were derived and had the form of the lognormal function. In a specific application, Jordan has discussed the aging degradation of GaP red LEDs in terms of diffusion and accumulation of point defects in the p–n junction region. Since the spread in product life is primarily a function of manufacturing variability, it is possible to predict lifetimes on the basis of reliability testing. Service environments of electronic products are relatively benign and vary little among populations. Since degradation is directly related to the occupancy of such levels according to the Maxwell–Boltzmann factor, exp , the logarithm yields E i/ kT, which is normally distributed hence the lognormal distribution. Physical models of failure generally invoke the central limit theorem (Section 4.2.1) to explain that specific energy levels E i are nominally the same in all components and are distributed in a Gaussian fashion. Milton Ohring, Lucian Kasprzak, in Reliability and Failure of Electronic Materials and Devices (Second Edition), 2015 4.5.4 Physics of the Lognormal Distribution The Mathematics of Failure and Reliability ![]()
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