Reliability analysis can be performed efficiently through subset simulation. Through Markov chain Monte Carlo, subset simulation progressively samples from the input domain of a performance function (typically a computer model) to find the failure domain, that is, the set of input configurations that result in an output higher than a prescribed threshold. Recently, a probabilistic framework for numerical analysis was proposed, treating computation as a statistical inference problem. The framework, called probabilistic numerics, treats the output of a computer code as a random variable. This paper presents a generalisation of subset simulation, which enables reliability analysis for probabilistic numerical models. The advantages and challenges of the method are discussed, and an example with industrial application is presented.