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Maintenance improvement is affected by many uncertain factors such as maintainer experience, machine deterioration state, maintenance tools and equipment, it is very hard to determine each restoration degree ahead of repair operation. Therefore, this paper considers a maintenance problem in the presence of competing risks (degradation and sudden failure) under stochastic maintenance quality for a ship pump. The degradation process of ship pump is characterized by a non-homogeneous Gamma process and the hazard rate of sudden failure is described by a proportional hazards model. We propose a two-level condition-based maintenance (CBM) policy with stochastic maintenance quality. The policy combines degradation control limit and age control limit under stochastic maintenance quality of Beta distribution, normal distribution and uniform distribution, respectively, in maintenance decision-making. Maintenance optimization problem is formulated and solved by a computational algorithm in a semi-Markov decision process (SMDP) framework, with the objective of minimizing the long-run expected average cost. The proposed model is illustrated using a numerical study and a real case study of ship pump, respectively, and comparative results show the effectiveness and superiority of our approach. • Novel competing risks model incorporating two failure processes. • Development of three stochastic maintenance models. • Development of a two-level CBM policy. • Optimization of maintenance in a SMDP framework. • Comparisons of different stochastic CBMs via case studies. [ABSTRACT FROM AUTHOR]