This paper extends the existing one-stage weighted-out-of-model to two-stage weighted-k-out-of-models with components in common. Algorithms are developed to calculate the system reliability, and generate the minimal cuts & minimal paths of two-stage weighted-k-out-of-systems. Reliability bounds for systems with-dependent component failures are investigated based on the generated minimal cuts & minimal paths. Two types of two-stage weighted-k-out-of-models, the SW-k-out-ofmodel, and the PW-k-out-of-model, can be applied to investigate reliability issues in network applications, such as the project management, and the shortest path problems. Examples are provided to demonstrate the developed models & algorithms.
Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials' long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition.Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing).Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.
In the paper, a novel color image encryption scheme is proposed by use of the threedimensional chaotic maps and some data reconstruction techniques. In the diffusion process of the encryption algorithm, the three-dimensional chaotic Logistic map is introduced to changes the pixel value of the plain image. Meanwhile, in the confusion process, the three-dimensional chaotic Cat map is applied to deal with the position of the image pixels. Moreover, some data reconstruction techniques are employed for the better encryption result. Furthermore, the corresponding decryption algorithm is also given. The significant advantages of our method are the effectiveness and simplicity, and our proposed method breaks the correlation between image pixel layers, offers a large key space and against differential and statistical attacks effectively. Finally, the superiority of the proposed algorithm will be shown by the experimental results, security analysis, and the corresponding comparisons with literature.
Many complex multi-component systems suffer from dependent competing risks. The reliability modeling and maintenance planning of repairable dependent competing risks systems are challenging because the repair of the failed component can change the lifetime of the other components when multiple components fail dependently. In this paper, we first propose a generally dependent latent age model to capture the dependence of competing risks under general component repairs. Based on the proposed reliability model, both system and component level periodic inspection-based maintenance polices are considered for repairable multi-component systems that are subject to dependent competing risks. Under the system level maintenance policy, the entire system is restored to as good as new once a failure is detected.While under the component level maintenance policy, only the failed component is repaired imperfectly. We obtain the optimal solution of the system level policy by using renewal theory.The optimal solution of the component level policy, however, cannot be obtained analytically, due to its complex failure and repair characteristics. In this paper, we developed a simulation-based optimization approach with stochastic approximation to solve the optimization A c c e p t e d M a n u s c r i p t 2 problem for the component level policy. The developed methods are illustrated by using a cylinder head assembling cell that consists of multiple stations.
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