The nonhomogeneous Poisson process (NHPP) model is an important class of time-domain software reliability models and is widely used in software reliability Engineering. Traditionally, the error detection rate of NHPP models is usually assumed to be a continuous and monotonic function. In this paper, we present an exponentiated exponential growth model, which can capture the increasing or constant, decreasing nature of the failure occurrence rate per fault. The density function and hazard function of the exponentiated exponential distribution are quite similar to the density function and hazard function of the gamma or Weibull distribution. It can be used quite effectively to analyze lifetime data in place of gamma or Weibull distribution. We present an analysis of three data sets, where the underlying failure process could be efficiency described by the exponentiated exponential model, which motivated the development of the exponentiated exponential model.