Model for failure rate curves

Abstract

The failure rate of electronic components is determined by the initial distribution of the critical parameters and by the nature of the degradation mechanism. Assuming the mechanism to be determined by a first order differential equation with respect to time it turns out that a simple relation exists between the life histories of components with different initial conditions. With only one failure mechanism and a (truncated) normal distribution function, with average μ and standard deviation σ, it is shown that the shape of the failure rate curve is determined by a dimensionless characteristic parameter b = n( σ/ μ) 2, in which n is typical for the underlying failure mechanism. For b < 1 4 a “bath tub” like failure rate curve will occur in general; for b > 1 4 the failure rate decreases continuously as a function of time. By considering the complete failure rate curve, including the rejects during testing, a relation between yield and failure rate can be indicated. A prediction about the temperature-dependence of the failure rate curve is given. The effect of stress testing at elevated temperature can be made quantitative by a simple scaling rule.