8.
Assessing Product Reliability
8.1. Introduction


When changing stress is equivalent to multiplying time to fail by a constant, we have true (physical) acceleration 
Physical Acceleration (sometimes called True Acceleration or just Acceleration) means that operating a unit at high stress (i.e., higher temperature or voltage or humidity or duty cycle, etc.) produces the same failures that would occur at typicaluse stresses, except that they happen much quicker. Failure may be due to mechanical fatigue, corrosion, chemical reaction, diffusion, migration, etc. These are the same causes of failure under normal stress; the time scale is simply different. 

An Acceleration Factor is the constant multiplier between the two stress levels  When there is true acceleration, changing stress
is equivalent to transforming the time scale used to record when failures
occur. The transformations commonly used are linear, which means
that timetofail at high stress just has to be multiplied by a constant
(the acceleration factor) to obtain the equivalent timetofail at
use stress.
We use the following notation:
Then, an acceleration factor \(AF\) between stress and use means the following relationships hold:


Each failure mode has its own acceleration
factor
Failure data should be separated by failure mode when analyzed, if acceleration is relevant Probability plots of data from different stress cells have the same slope (if there is acceleration) 
Note: Acceleration requires that there be
a stress dependent physical process causing change or degradation that
leads to failure. In general, different
failure modes will be affected differently by stress and have different
acceleration factors. Therefore, it is unlikely that a single acceleration
factor will apply to more than one failure mechanism. In general, different
failure modes will be affected differently by stress and have different
acceleration factors. Separate out different types of failure when analyzing
failure data.
Also, a consequence of the linear acceleration relationships shown above (which follows directly from "true acceleration") is the following: The Shape Parameter for the key life distribution models (Weibull, Lognormal) does not change for units operating under different stresses. Probability plots of data from different stress cells will line up roughly parallel.These distributions and probability plotting will be discussed in later sections. 