PurposeThe purpose of this paper is to optimize the degradation test for products subject to multiple types of inherent stresses and external random shocks. The mechanism that shows how the variables to be optimized influence the considered multiple objectives is also aimed to be explored by using the grey incidence analysis (GIA) model.Design/methodology/approachThe Gamma process is employed to model the influences of different types of stresses and external random shocks. The GIA model is introduced to transfer multiple considered objectives as a comprehensive degree of grey incidence. The particle swarm optimization is integrated to search the globally optimal value of the characteristic variables to be optimized.FindingsThe acceleration of tested stresses and external random shocks both make the engineering systems become more vulnerable to the inherent degradation. And, the Kriging model can provide guidance of searching the optimal values of test characteristic variables and mitigate the computation burden. The grey incidence model can make the optimization focused and improve the optimality of objective values.Originality/valueThe proposed method can effectively overcome the drawbacks brought by the limitation of test data and can specify the dependence strength between the inherent degradation and external random shock. The computation cost and accuracy of optimization can be simultaneously ensured by the proposed model.