© 2019 Elsevier Inc. This paper presents an approximation method for performing efficient reliability analysis with complex computer models. The computational cost of industrial-scale models can cause problems when performing sampling-based reliability analysis. This is due to the fact that the failure modes of the system typically occupy a small region of the performance space and thus require relatively large sample sizes to accurately estimate their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and subset simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset simulation is used as an integral part of the algorithm to efficiently populate those regions of the surrogate which are likely to lead to the performance function exceeding a predefined critical threshold. The emulator itself is used to inform decisions about efficiently using the original code to augment its predictions. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region is developed at a reasonable computational cost. The presented method is applied to an industrial model of a biodiesel filter.