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2019 | OriginalPaper | Chapter

7. Time-to-Failure Statistics

Author : J. W. McPherson

Published in: Reliability Physics and Engineering

Publisher: Springer International Publishing

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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. This means that not only are we interested in time-to-failure but, more precisely, we are interested in the distribution of times-to-failure. Once the distribution of times-to-failure is established, then one can construct a probability density function f(t) which will permit one to calculate the probability of observing a failure in any arbitrary time interval between t and t + dt, as illustrated in Fig. 7.1.

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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(t₅₀/t₁₆). 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.

Note that any cumulative fraction F, and its corresponding failure time, may be used in Eq. (7.8) to determine the Weibull slope. The author’s preference is to use F = 0.1 and t₁₀. However, this is only a preference, not a requirement.

A lognormal distribution was used here but a Weibull distribution could have been used and would show similar results.

A lognormal distribution could also have been used and would produce similar results.

Dhillon, B. and C. Singh: Engineering Reliability, John Wiley & Sons, (1981).

McPherson, J.: Reliability Physics. In: Handbook of Semiconductor Manufacturing Technology, Marcel Dekker, 959 (2000).

Miller, I. and J. Freund: Probability and Statistics for Engineers 2nd Ed., Prentice Hall, (1977). Nelson, W.: Accelerated Testing, John Wiley and Sons, (1990).

Title: Time-to-Failure Statistics
Author: J. W. McPherson
Publisher: Springer International Publishing
Book: Reliability Physics and Engineering
Print ISBN: 978-3-319-93682-6

Electronic ISBN: 978-3-319-93683-3

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-93683-3_7