In this paper we consider non-parametric estimation methods for software reliability assessment without specifying the fault distribution, where the underlying stochastic process to describe software fault-counts in the system testing is given by a non-homogeneous Poisson process. A comprehensive approach based on the kernel estimation is provided with several kernel functions and bandwidth estimations. Next, we develop interval estimation methods via the non-parametric bootstrap, and derive the confidence regions of several reliability measures such as the expected cumulative number of software faults, software intensity function, quantitative software reliability as well. The resulting data-driven methodology can give the useful probabilistic information on the software reliability prediction under the incomplete knowledge on fault distribution. In illustrative examples with a real software fault data, it is shown that the proposed methods provide useful software reliability measures under uncertainty from the view point of frequentist analysis.