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Life Distributions (Page 3 of 4)
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The Exponential Life Distribution
An exponential life distribution is one wherein the failure rate is constant in time. The exponential life distribution is best applied to the analysis of failures in the steady-state phase of the bath tub curve, during which the failure rate is constant. Other than this, reliability engineers don't use the exponential life distributions a lot, because there are not too many frequently-encountered critical failure mechanisms that exhibit this life distribution.
Figure 2. The f(t), F(t), and l(t) of an exponential life distribution; source: D. S. Peck and O. D. Trapp, Accelerated Testing Handbook, Technology Associates.
The Lognormal Life Distribution
The lognormal life distribution is one wherein the natural logarithms of the lifetime data, ln(t), form a normal distribution. Consequently, the life data of a lognormal distribution will also form a straight line if plotted on a lognormal plot, i.e., a plot whose x- and y-axes stand for the cumulative % of failures and the logarithmic scale of time, respectively. The failure rate curve l(t) of a lognormal life distribution starts at zero, rises to a peak, then asymptotically approaches zero again for all values of s.
The lognormal distribution is formed by the multiplicative effects of random variables. Multiplicative interactions of variables are found in many natural processes, and are in fact observed in many frequently-encountered semiconductor failure mechanisms. This characteristic of the lognormal distribution makes it a good choice for the analysis of the failure rates of many semiconductor failure mechanisms.
A notable characteristic of the lognormal distribution is the fact that its median time to failure, t50%, or the time at which 50% of the samples fail, is equal to eµ, where µ is the mean of the life data. Thus, t50% = eµ.
Figure 3. The f(t), F(t), and l(t) of a lognormal life distribution; source: D. S. Peck and O. D. Trapp, Accelerated Testing Handbook, Technology Associates.
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