## 1 Introduction  
As one of the key functional components of computer numerical control (CNC) machine tools, the reliability of motorized spindles has an important impact on the reliability of CNC machine tools [1]. For complex electromechanical and hydraulic products, such as motorized spindles, a reliability test is the only way to verify the reliability level of a motorized spindle and expose its weak links. Because the reliability level of a motorized spindle is high, it is usually necessary to carry out accelerated tests to evaluate its reliability. However, the traditional accelerated life test (ALT) [2] aims to obtain the failure data, and then evaluate the reliability of the product, and improve the reliability design according to the evaluation results, so as to improve the reliability of the product. However, with the development of science and technology, the reliability level of motorized spindles is constantly improving. This traditional accelerated life test method has been unable to obtain enough fault data of motorized spindle in a short time, and then cannot obtain an accurate reliability level for motorized spindles. ADT can product failure or performance degradation in a short time by applying higher-than-normal stress in the test, and evaluate the reliability of the product under normal stress levels by analyzing and processing the data [3, 4]. ADT not only overcomes the disadvantages of the traditional ALT, but also overcomes the disadvantage that ALT only records fault data, so that a reliability evaluation can be carried out under the condition of zero fault [5]. Although ADT has a high test efficiency, in order to obtain higher efficiency and reduce test costs, it is usually necessary to optimize the test factors in ADT before test, including sample size, stress level, test time and constraint conditions. In 1962, [PERSON] [6] first carried out research on the optimization design of accelerated tests. He studied the optimization design of constant stress accelerated test schemes with an exponential distribution of product life, and gave a theoretical framework for the optimization design of accelerated tests. On the basis of this theoretical framework, [PERSON] and [PERSON] [4; 7; 8; 9; 10; 11] introduced model constraints into the optimization model to improve the theoretical framework of the optimization method. By studying the variation in stress level, sample ratio and asymptotic variance with the model parameters in the experiment, they obtained an optimization scheme which is insensitive to model parameters. However, these studies assume that an object is subjected to a single stress, but a product is often subject to multiple stresses in practice. Therefore, in recent years, scholars have expanded the research content from single stress to multiple stresses. [PERSON] [12] applied the idea of single stress optimal design (two stress levels) to an object under the action of two kinds of stresses, researched the optimal design of life distribution obeying the generalized Eyring law, and obtained an optimal scheme based on the factor arrangement of the test points method. [PERSON] [13] used the same method to obtain an optimal scheme under the proportional risk model. However, the optimization scheme obtained by this method is highly sensitive to changes in model parameters, and this method only contains two stress levels, which cannot meet the needs of application. Therefore, [PERSON] [14] extended stress levels in SSADT from two to more, and proved the effectiveness of this method under the condition of constraints. [PERSON] [15] studied the validity between model parameters and stress variables, and obtained a method of how to select stress levels in an accelerated test scheme with multiple stress levels. [PERSON] [16] studied the selection of stress levels for multi-stress SSADT under the constraints of test samples and test times.