## 1 Introduction  
In traditional reliability analysis, the product life is considered the main research object, and the evaluation results need large amounts of supporting failure data; this method is suitable for products with low technical complexity and a short life. With advances in modern science and technology, high-quality products with a long life are developed. Moreover, reliability analysis based on performance degradation data has become a new research focus [1; 2; 3]. Unlike traditional reliability analysis, performance-degradation-based reliability analysis considers the degradation process the main cause of failure. By measuring performance-degradation data, more life-cycle information can be obtained. In contemporary research, performance-degradation data are mainly fitted using the degradation-trajectory and stochastic-process models. The degradation of a product is affected by several factors, such as material characteristics and external shocks; therefore, degradation quantity shows a random variation throughout the product's life cycle. If a product is capable of self-recovery, the degradation process is likely nonmonotonic, which complicates the analytical process. Compared with the traditional degradation-trajectory model, using the Wiener [4; 5] and gamma [6] processes for modeling is more advantageous and closer to the needs of the actual analysis. Several studies discussed the self-recovery characteristics [7] of some materials [8] and electronic devices [9; 10]; however, relatively few studies have conducted the reliability analysis of such products. Owing to the complexity of mechanical products and the various applications of new materials, the self-recovery phenomenon must be introduced into the reliability modeling of such products to assess their reliability. [PERSON] analyzed the performance degradation and self-recovery process of a semiconductor laser [11; 12]. Several studieshave verified the influence of the self-recovery process on system reliability via simulation analysis. In this study, the internal relationship between the shock interval and the self-recovery phenomenon, and the reliability modeling process with competitive failure are discussed. However, this model ignores that the degradation process of self-healing products is phased; phasing is related to changes in the working environment of the product, the characteristics of the material, and other factors. Many scholars have examined the phenomenon of phased-product degradation. [PERSON] set up two alarm thresholds related to the degradation amount in the degradation model [13]. The degradation process was divided into two different stages, and expressed with different mathematical models before and after the degradation reached the thresholds. Furthermore, after the system enters the second stage, the working time of products could lead to system failure. [PERSON] [2] established a stochastic process reliability model, considering that at the junction of two degradation stages, degradation increases significantly. [PERSON] [14] illustrated the universality of the two-stage degradation process with change points, considering lithium ion batteries, light-emitting diodes, and other electronic components as examples; they assumed that changes occurred at the degradation stage according to the cumulative degradation and the number of shocks. Another study [15] reported that the parameters of the soft failure threshold and the Wiener process drift change with changes in the degradation stage, and presented a simulation example verifying this phenomenon. [PERSON] [16] proposed a two-stage self-healing model based on cumulative and delta shocks, considering that self-recovery occurred only at the first stage of degradation. All the above-mentioned models had different definitions of phase change points. These articles, however, did not consider the fact that a product's working environment is alterable, and that such a change could cause the degradation process to enter the next stage.