This research presents a case study were existing physics-of-failure models and Bayesian statistical methods are used in conjunction to quantify the test-time compression achieved during accelerated temperature cycling tests on leadless solder joints. Different combinations of substrate materials and package styles are evaluated with physics-of-failure models and calculable information is obtained from a relatively small population of test specimens under accelerated stresses, because the critical variables are identified, and their influences on the stress magnitude are quantified. Bayesian statistical analysis is employed to obtain an acceleration transform, determine the confidence on the calculations, and determine which outliers are contaminating the database. In addition to accelerating the stress levels, the total test time is further minimized by tailoring the stress drivers in each sample such that multiple stress levels can be achieved under a single loading, which eliminates the need for repeating the test at multiple load levels. This research presents the details of how the models and statistical methods are applied, the results of evaluating different material combinations and package styles, problems encountered during the test, and a summary of the acceleration transforms obtained from the test. Analytical predicative models for life predictions are essential and will obviously result in significant savings of cost and time. The methods used in this are general enough to be applied to screening, qualification, and reliability enhancement tests of a wide range of new or existing electronics assemblies.