# Failure Rate Model for Corrosion Failure of Electronic Components

Original Publication Date: 1972-May-01

Included in the Prior Art Database: 2005-Feb-24

## Publishing Venue

IBM

## Related People

Ainslie, NG: AUTHOR [+2]

## Abstract

When a large number of nominally identical electronic or other devices are subjected to an accelerated test, the stresses applied during the test quite often result in systematic degradation of critical device parameters. Device failure occurs when the degradation of a particular parameter crosses a specification limit. Although nominally identical, each device in the population degrades at a unique rate determined by its own geometric, physical, chemical, other features. Thus, different devices cross the failure threshold at different times giving rise to an observable failure rate. Letting the rate at which the device parameter X(t) degrades be R then d X(t) over dt = R and the time-to-failure t(f) is given by (Image Omitted)

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__Page 1 of 3__**Failure Rate Model for Corrosion Failure of Electronic Components **

When a large number of nominally identical electronic or other devices are subjected to an accelerated test, the stresses applied during the test quite often result in systematic degradation of critical device parameters. Device failure occurs when the degradation of a particular parameter crosses a specification limit. Although nominally identical, each device in the population degrades at a unique rate determined by its own geometric, physical, chemical, other features. Thus, different devices cross the failure threshold at different times giving rise to an observable failure rate. Letting the rate at which the device parameter X(t) degrades be R then d X(t) over dt = R and the time-to-failure t(f) is given by

(Image Omitted)

A distribution of failure times t(f) among a population of such
devices arises, due to randomness in the variables R, X(f), and X(o).
Three cases are of interest:

CASE I.

Where X(f)-X(o) is a random Gaussian variate, and the degradation rate R(a) during an accelerated test is constant from device-to-device.

In this case the probability density function of f(t(f)) for the time-to-failure would be Gaussisn having a mean mu(t(f)) of

Thus, from an accelerated test, one measures mu(t(f)) and Var(t(f)), and, knowing R(a) from independent measurements, solves for mu(X(f)-X(o)) and Var (X(f)-X(o)) using equations 4 and 5 . The failure rate under service conditions would then be given by a Gaussian distribution of failure times whose mean mu and variance sigma/2/ are

(Image Omitted)

CASE II.

Where X(f) and X(o) are constants, and the degradation rate R(a), constant within a given device, varies from device-to-device in a Gaussian fashion during an accelerated test. From (1) X - X(o) = R(a) t 8.

Since R(a) is Gaussian, the variable X-X(o) is also Gaussian having a mean mu(X-X(o)) and variance Var (X-X(o)) of mu (X-X(o)) = t mu(R(a)) 9 (Var (X-X(o)) = t Var(R(a)) 10

The fraction F(t(f)) of devices in which X exceeds the failure criterion X(f) is given by F(t(f)) = 1 - phi(z) 11 where and phi(Z) = Cumulative of the standard normal distribution Thus, and the failure rate would be given by the probability density function of failure times of f(t(f)) f(t(f)) = dF(t(f))/dt 13.

To obtain the in-ser...