Software system developed for a specific user under contract undergoes a period of testing by the user before acceptance. This is known as user acceptance testing and is useful to debug the software in the user's operational circumstance. In this paper we first present a simple non-homogeneous Poisson process (NHPP)-based software reliability model to assess the quantitative software reliability under the user acceptance test, where the idea of an accelerated life testing model is introduced to represent the user's operational phase and to investigate the impact of user's acceptance test. This idea is applied to the reliability assessment of web applications in a different testing environment, where two stress tests with normal and higher workload conditions are executed in parallel. Through numerical examples with real software fault data observed in actual user acceptance and stress tests, we show the applicability of the software accelerated life testing model to two different software testing schemes.