## 7 Conclusions  
1. In this paper, under the constraint of the test cost and the actual range of test variables, taking the test stress levels \(S_{il}\), sample size \(n_{l}\) and inspection times \(m_{l}\) as optimization variables, the optimization design of multi stress step accelerated degradation test scheme for a motorized spindle is carried out. When the objective function is established, the exhaustive method is used to solve the set of alternatives to avoid the wrong optimal solution caused by improper setting of the initial conditions of the optimization algorithm. By solving all possible combinations of stress levels under different sample sizes, it is concluded that the optimal combination of stress levels with different quantities of samples is the same under the constraint conditions.
2. The drift Brownian motion is used to model the accelerated degradation process of motorized spindle under multiple stresses. By selecting the main test stress and inspection indexes of the motorized spindle, the minimum estimation variance of main stress affecting the motorized spindle is taken as the optimization objective (i.e., \(\min(\det(\left|M^{11}(\xi)\right|))\)), the optimization algorithm steps and detailed flow chart are given. Taking the accelerated degradation test of motorized spindle under two stresses as an example, the optimized test scheme is obtained, and compared with the traditional \(D\)-optimality optimization, the objective function value of the test scheme optimized by \(D_{s}\)-optimality is calculated under \(D\)-optimality, and the objective function value is only 18.5% lower than that of the optimal scheme optimized by \(D\)-optimality. Through an extended case study, it is concluded that when the proposed method is used to optimize the test scheme, the determinant value of the variance matrix of the main stress parameters is 0.59 times of that under \(D\)-optimality. It shows that this method can not only improve the evaluation accuracy of main stress parameters, but also ensure the evaluation accuracy of other stress parameters.
3. By analyzing the influence of the initial model parameter deviation on the optimization results, it is concluded that the optimization design method proposed in this paper has good stability. Since this method is based on the optimization criteria of model parameters, the range of main model parameters should be as small as possible before the test, so as to improve the accuracy of reliability evaluation of the optimized accelerated test scheme.  
Conceptualization, H.Z., Z.Y.; methodology, H.Z. and C.C.; software, H.Z.; validation, H.Z., C.C. and H.T.; investigation, X.L.; writing--original draft preparation, H.Z. and C.C.; writing--review and editing, H.Z., H.T. and S.L.; funding acquisition, H.Z. and C.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China under grant numbers 51975249 and 51675227; the Key Research and Development Plan of Jilin Province under grant numbers 20180201007 GX and 20190302017 GX; the Jilin Industry Innovation Project under grant number 2019C037-1; the Jilin Scientific Project of the Education Department under grant number JJKH20180133 KJ; and the Fundamental Research Funds for the Central Universities.  
Not applicable.  
Our deepest gratitude goes to the editors and reviewers for their constructive suggestions on the paper. We also thank the authors of the references, whose work contributed greatly to the completion of this paper.  
The authors declare no conflict of interest.