Reliability projections based on failure data from high stress tests are based on assuming we know the correct acceleration model for the failure mechanism under investigation and we are also using the correct life distribution model. This is because we are extrapolating "backwards" - trying to describe failure behavior in the early tail of the life distribution, where we have little or no actual data. 

For example, with an acceleration factor of 5000 (and some are much larger than this) the first 100,000 hours of use life is "over" by 20 hours into the test. Most, or all, of the test failures typically come later in time and are used to fit a life distribution model where only the first 20 hours or less are of practical use.  Many distributions may be flexible enough to adequately fit the data at the percentiles where the points are, and yet differ by orders of magnitude in the very early percentiles (sometimes referred to as the early "tail" of the distribution). 

However, it is frequently necessary to test at high stress (to get any failures at all!) and project backwards to use. When doing this bear in mind two important points:

• Distribution models, and especially acceleration models, should be applied only to a single failure mechanism at a time. Separate out failure mechanisms when doing the data analysis and use the competing risk model to build up to a total component failure rate
• Try to find theoretical justification for the chosen models, or at least a successful history of their use for the same or very similar mechanisms. (Choosing models solely based on empirical fit is like extrapolating from quicksand to a mirage.) 

Two types of use condition reliability projections are common:

1. Projection to use conditions after completing a multiple stress cell experiment and successfully fitting both a life distribution model and an acceleration model
2. Projection to use conditions after a single cell at high stress is run as a line reliability monitor

Using the graphical model estimates for ln A and we have

T₅₀ at use = e^{-18.312 × e.808 × 11605/298.16} = e^13.137 = 507380

and combining this T₅₀ with the common sigma of .74 allows us to easily estimate the CDF or failure rate after any number of hours of operation at use conditions. In particular, the Dataplot command 

LET Y = LGNCDF((T/T50),sigma)

LET Y = LGNCDF((100000/507380),.74)

If the life distribution model had been Weibull, the same type of analysis would be done by letting the characteristic life parameter vary with stress according to the acceleration model, while the shape parameterg is constant for all stress conditions. 

The second type of use projection was used in the section on lognormal and Weibull Tests where we judged new lots of product by looking at the proportion of failures in a sample tested at high stress. The assumptions we made were: 

• we knew the acceleration factor between use and high stress
• the shape parameter (sigma for the lognormal, gamma for the Weibull) is also known and does not change significantly from lot to lot.

LET T50STRESS = T *LGNPPF(p,)
LET CDF = LGNCDF((100000/(A*T50STRESS)),)

LET ASTRESS = T*WEIPPF(p,)
LET CDF = WEICDF((100000/(A*ASTRESS)),)