A rareevent estimation of heterogeneous degradation process We study the special reliability model where preventive repair is used to prevent an instantaneous failure. The dynamic of the system is expressed in terms of the heterogeneous degradation process with successive stages, which are independent but not identically distributed. The calculating of the performance characteristics of such a systems is an important and typically challenging problem. In this paper, we focus on estimating the rareevent failure probability which is usually not analytically available. In order to evaluate the target measure, we apply a variance reduction technique using a special variant of conditional Monte Carlo approach proposed by Asmussen and Kroese in 1. The relative error of the proposed method is studied numerically. A few numerical results are presented to justify that proposed technique provides comparatively good properties of the relative error when the failure probability become small.

Bayesian Estimation Method for Storage Reliability Based on Drift Brownian Motion At present, many products have the characteristics of xe2x80x9clongterm storage, onetime usexe2x80x9d. Therefore, evaluating the storage reliability of products has become a hot topic. However, for products that are stored for a long period of time, it is difficult to determine the distribution of the product life due to lack of using data, so it is considered to analyze the storage reliability from the viewpoint of the amount of performance degradation. The performance degradation process as a continuous random process can be described by the drift Brownian motion. In view of the long storage time, variable stress accelerated experiments are usually used to obtain degradation data. The data under different stresses need to be integrated in order to calculate the final estimation value of parameters, which will inevitably cause errors in the process of the integration. The Bayesian method is an estimation method that considers prior information, thus it can be applied to the integration process of data under different stress conditions. The parameter estimation obtained under the previous stress is used as the prior information of the parameter distribution under the next stress, so as to maximize the use of experimental data to reduce the estimation error. Then, the final value of the acceleration model parameters is fitted to evaluate the storage reliability and life of the product. In the case, the solder joint is taken as the research object, and the storage reliability is evaluated by the degradation of the shear strength. The feasibility of the method is demonstrated by the application of the solder joint case.