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Cumulative damage processes for discrete degrading systems caused by stochastic shocks have received increasing attention. However, the degradation data is often subject to incomplete observation or censoring due to imperfect monitoring instruments or inspection strategies. In such situations, the arrival time of stochastic shocks cannot be accurately recorded. This makes a challenging task for parameter estimation and remaining useful lifetime (RUL) prognosis based on the cumulative damage process. Motivated by this fact, this article proposed a new Bayesian data augmentation approach to overcome the obstacles caused by incomplete observation. First, the proposal distribution for the occurrence number of shocks in the cumulative damage process subject to interval censoring is derived. Second, an effective data augmentation for the missing shock time is proposed by integrating rejection sampling and the order statistics technique. On this basis, multiple imputation is extended to discrete non-Gaussian stochastic processes subject to interval censoring. Finally, an RUL prognosis method of a system subject to the cumulative damage process is derived based on the Monte Carlo method. And a real case study on the head wear problem is applied to illustrate the superiority of the proposed approach, and the results show that the proposed approach can improve the estimation accuracy of RUL compared with the existing method. [ABSTRACT FROM AUTHOR]

The need for information security is self-evident. The pervasiveness of this critical topic requires primarily risk assessment and management through quantitative means. To do an assessment, repeated security probes, surveys, and input data measurements must be taken and verified toward the goal of risk mitigation. One can evaluate risk using a probabilistically accurate statistical estimation scheme in a quantitative security meter (SM) model that mimics the events of the breach of security. An empirical study is presented and verified by discrete-event and Monte Carlo simulations. The design improves as more data are collected and updated. Practical aspects of the SM are presented with a real- world example and a risk-management scenario. [ABSTRACT FROM AUTHOR]