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Accelerated Test Models

Accelerated test models relate the failure rate or the life of a component to a given stress such that measurements taken during accelerated testing can then be extrapolated back to the expected performance under normal operating conditions. The implicit working assumption here is that the stress will not change the shape of the failure distribution.

Table 3 summarizes three of the most common accelerated test models. These are not the only models that can be used. In choosing a model, the key criterion is that it accurately models the reliability or life under the accelerated conditions to the reliability or life under normal operating conditions. Great care is essential in choosing the most appropriate model, and in selecting the appropriate range of validity for the chosen model in a specific application. Documenting the rationale for these choices is important.

Table 3: Common Accelerated Test Models
Model Name Defining Equation
Inverse Power Law
Life at normal stress / Life at accelerated stress =
(Accelerated stress / Normal stress)N

where N is the acceleration factor
Arrhenius Acceleration Model
Life = Ae-(E / kT) , where:
Life = a measure of life, e.g., median life of a population of parts
A = a constant determined by experiment for the parts involved
e = the base of the natural logarithms
E = activation energy (electron volts - a measure of energy), which is a unique value for each failure mechanism
k = Boltzmann's constant = 8.62 x 10-5 eV/K
T = Temperature (degrees Kelvin)
Miner's Rule (Fatigue Damage)
Equation1
CD = cumulative range
CSi = number of cycles applied at a given mean stress Si
Ni = the number of cycles to failure under stress Si, (as determined from an S-N diagram for that specific material)
k = the number of loads applied

Assumes every part has a finite useful fatigue life and every cycle uses up a small portion of that life. Failure is likely to occur when the summation of incremental damage from each load equals unity. Miner's rule does not extend to infinity, however. It is valid only up to the yield strength of the material; beyond that point it is no longer valid.