## 1 Introduction
However, during the storage process, due to the influence of environmental stresses such as temperature, humidity, and salt spray, the degradation process of individual products is uncertain. At this time, reliability models based on degradation trajectories perform poorly in describing and explaining the randomness of product degradation paths. Stochastic process models have good performance in describing the time-varying uncertainty of products, so they are widely used in product performance degradation analysis. Specifically, [PERSON] et al. studied parameter estimation methods based on intermediate data using the Wiener process, and the lifetime distribution function estimation method proposed is more accurate than both the standard and modified maximum likelihood estimation (MLE) methods [16]. The Wiener process is suitable for describing non-monotonic performance degradation processes with increasing or decreasing trends, while the Gamma process and Inverse Gaussian (IG) process are suitable for describing monotonic continuous degradation processes. Aiming at monotonic continuous degradation processes, [PERSON] et al. proposed the MLE method based on the IG model and used the EM algorithm to calculate estimates of the unknown parameters [17]. [PERSON] et al. also used the IG process model for modeling energy pipelines. At the same time, considering the possibility of detection errors in the detection results, Bayes was used to estimate the model parameters [18]. On this basis, [PERSON] et al. proposed a general Bayesian framework for the degradation analysis of IG process models and focused on the applicability of Bayesian methods in the degradation analysis of IG process models [19]. [PERSON] et al. proposed a nonlinear Gamma process model based on the time transfer function and used the MLE method to estimate model parameters [20]. [PERSON] et al. focused on the randomness of product degradation paths and proposed a novel assessment method based on the IG process to analyze and predict the results of the SDSADT [21]. From the above literature, it is known that stochastic process models are widely applied and have achieved certain successes in ADT data processing. However, existing methods rarely consider the following two situations: First, the detection equipment is affected by noise and disturbance, and the detection results have detection errors. Second, the degradation paths of different products exhibit randomness and difference. In addition,due to the low initial stress level of the SSADT, the rate of performance decline at the beginning of the test is slow. This greatly reduces the efficiency of the accelerated test. By applying high stress to the product at the beginning of the SDSADT, the reliability information of the product can be obtained in a shorter time and the test efficiency can be improved. Based on this, this article proposes a storage life assessment method for the SDSADT that considers random effects and detection errors and applies it to the SDSADT data from a specific missile tank to assess its storage life. The main contributions of this article are as follows. 1. This article proposes a new method for assessing storage life under the SDSADT to solve the problem of slow product performance degradation at the beginning of the step-stress ADT. This article mainly focuses on the assessment method for the storage life of high-reliability and long-life products under the SDSADT. 2. A new IG performance degradation model is proposed. This model introduces the Gamma distribution to characterize the randomness of and difference in the degradation paths of different products and uses the normal distribution to describe the detection errors of performance parameters. This model can solve the problem of the product storage life assessment caused by random effects and detection errors. 3. The Monte Carlo (MC) technique is employed to estimate the unknown parameters in the IG model to solve the problem that the calculation of the likelihood function is complicated and there is no explicit expression.