8.7.5.1 __The Inverse Power Law
Acceleration Model__

The inverse power law states that component life is inversely
related to a power of the dominant stress.

where N is the acceleration
factor.

Assuming that an application is
within the valid operating range of the model and that the shape of the
failure distribution does not change under accelerated conditions, the inverse
power law model can be used to solve such problems as the
following.

*Example: *Suppose the mean life of a population of automobile
tires was 20,000 miles when driven at 50 miles per hour. Through testing it
has been determined that the mean life of these tires is 10,000 miles at 70
miles per hour. Thus:

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From this knowledge, we want to use life data collected at 70
mph to show that there is a 90% probability that a tire will last 10,000 miles
at 50 mph.

To solve this problem, use the life test data at 70 mph to
demonstrate, with a 90% probability, that a tire will last 10,000 miles at 50
mph.

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Desired result: 90% probability of
no failure before 10,000 miles, i.e., no more than 10% of a population fails
before 10,000 miles.

The shape of the failure
distribution is assumed to be identical at 50 and 70 mph, thus the left side
of the inverse power law equation shown above can be used to represent life at
10% failures, or:

Thus: Life at 70 mph =
10,000/2 = 5,000

Therefore, if 10% or less of the
tires tested at 70 mph fail by 5,000 test miles, we can conclude that 10% or
less of tires driven at 50 mph will fail in 10,000 miles. Thus we have a 90%
probability that a tire will last 10,000 miles at 50 mph.