## 1 Introduction
Reliability modeling based on performance-degradation theory cannot be separated from the application of competitive failure; moreover, the interactions between shock and degradation processes cannot be ignored. [PERSON] et al. [17] reported that reaching the performance-degradation threshold caused the decline of the hard-failure threshold. One study considered the delta shock in a reliability model, proposing that the shock causes degradation increment. [PERSON] et al. [18] modeled the multidegradation process using the copula function, considering that the performance-degradation process was affected when the degradation was sufficiently large. [PERSON] et al. [19] proposed two models; one considered that the arrival of effective shocks considerably increases degradation, and one considered that it accelerates the degradation process. These models have practical significance and cannot ignore the interactions between failure modes. However, few studies have considered the self-recovery of specific products. Most contemporary stochastic process reliability models focus on the continuous degradation process, and few models discussed the impact of the shock process on performance degradation [20; 21]. For example, semiconductor products are used in different working environments; thus, it is unreasonable to use only one degradation process model. The semiconductor industry has various unique production processes, so there are many restrictions for indices such as priority, production time, and storage time. The duration of the product inventory directly influences cumulative degradation before the working stage; thus, the initial degradation rate and inventory time should be analyzed. Therefore, to solve the above-mentioned problems, in this study, semiconductor products with self-recovery properties are the research object, meaning that the small failures of the semiconductor could be recovered through the intervention of a control unit or associated component to ensure that the semiconductor products continued to work normally, and to reduce the failure rate of products. Considering that there are two degradation processes during the service life of a product, a three-stage, stochastic-process, competitive-failure, reliability-evaluation model is proposed. In this paper, the performance-degradation and self-recovery properties of products at the storage stage are considered, and the shock process was integrated into the study. A reliability-evaluation model of products in the whole life cycle is proposed that was verified with a simulation. The proposed model could describe the competitive failure process more accurately, and effectively prevent the product reliability from being over- or underrated due to the incompleteness of considering the product degradation features. The article is organized as follows. The modeling description and basic derivation are presented in Section 2. The specific derivation process and results of this model are outlined in Section 3. In Section 4, a numerical example is presented to illustrate and verify the proposed model. Conclusions and the scope for future research are discussed in Section 5.