Abstract
When nearly identically processed materials/devices are placed under the same set of stress conditions, they will not fail exactly at the same time. An explanation for this occurrence is that slight differences can exist in the materials' microstructure, even for materials/devices processed nearly identically.
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Notes
- 1.
Note that the lognormal distribution has the same general form as does the normal distribution in Chap. 5. The major differences are: (1) the natural logarithm of time ln(t) is used rather simply the time t; and (2) σ now represents the logarithmic standard deviation σ = ln(t 50/t 16). Also, the (1/t) in the prefactor of the lognormal distribution is needed to ensure that f(t)dt will continue to represent the probability of failure. This is due to the fact that dln(t) = (1/t)dt.
- 2.
Note that any cumulative fraction F, and its corresponding failure time, may be used in Eq. (8) to determine the Weibull slope. The author’s preference is to use F = 0.1 and t 10. However, this is only a preference, not a requirement.
- 3.
A lognormal distribution was used here but a Weibull distribution could have been used and would show similar results.
- 4.
A lognormal distribution could also have been used and would produce similar results.
Bibliography
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McPherson, J.: Reliability Physics. In: Handbook of Semiconductor Manufacturing Technology, Marcel Dekker, 959 (2000).
Miller, I. and J. Freund: Probability and Statistics for Engineers 2ndEd., Prentice Hall, (1977).
Nelson, W.: Accelerated Testing, John Wiley and Sons, (1990).
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McPherson, J.W. (2013). Time-to-Failure Statistics. In: Reliability Physics and Engineering. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00122-7_6
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DOI: https://doi.org/10.1007/978-3-319-00122-7_6
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