Stochastic scheduling optimisation is a hot and challenging research topic with wide applications. Most existing works on stochastic parallel machine scheduling address uncertain processing time, and assume that its probability distribution is known or can be correctly estimated. This paper investigates a stochastic parallel machine scheduling problem, and assumes that only the mean and covariance matrix of the processing times are known, due to the lack of historical data. The objective is to maximise the service level, which measures the probability of all jobs jointly completed before or at their due dates. For the problem, a new distributionally robust formulation is proposed, and two model-based approaches are developed: (1) a sample average approximation method is adapted, (2) a hierarchical approach based on mixed integer second-order cone programming (MI-SOCP) formulation is designed. To evaluate and compare the performance of the two approaches, randomly generated instances are tested. Computational results show that our proposed MI-SOCP-based hierarchical approach can obtain higher solution quality with less computational effect.