  The main objective of accelerated life tests (ALTs) is to predict fraction
failings of products in the field. However, there are often discrepancies
between the predicted fraction failing from the lab testing data and that from
the field failure data, due to the yet unobserved heterogeneities in usage and
operating conditions. Most previous research on ALT planning and data analysis
ignores the discrepancies, resulting in inferior test plans and biased
predictions. In this paper we model the heterogeneous environments together
with their effects on the product failures as a frailty term to link the lab
failure time distribution and field failure time distribution of a product. We
show that in the presence of the heterogeneous operating conditions, the hazard
rate function of the field failure time distribution exhibits a range of
shapes. Statistical inference procedure for the frailty models is developed
when both the ALT data and the field failure data are available. Based on the
frailty models, optimal ALT plans aimed at predicting the field failure time
distribution are obtained. The developed methods are demonstrated through a
real life example.
