Aluminum powders with different concentrations of TiC ceramic particles were applied to an AZ31B magnesium alloy by laser cladding. Due to differences in coefficients of thermal expansion, the distribution of TiC ceramic particles in the cladding layer was not uniform. The results show that the degree of TiC ceramic particle agglomeration in the cladding layer increases with increasing TiC content. The phases of cladding metal mainly consisted of Al, γ-Al12Mg17, β-Al3Mg2, and TiC. The γ-Al12Mg17 phase mainly distributed to the bottom of the cladding layer, and the β-Al3Mg2 phase distributed to the middle and surface areas. The existence of the γ-Al12Mg17 phase enhanced the hardness of the fusion zone. The microhardness of the cladding layer increased with increasing TiC ceramic particle content. An appropriate TiC content improved the wear resistance of the cladding layer. When the TiC content was excessive, the agglomeration behavior of TiC ceramic particles strongly affected the wear resistance of the coatings.
In this paper, we consider a redundancy allocation problem in a series-parallel system with uncertain component lifetimes of multiple states, which involves multitype components and mixed redundancy strategy. We develop a distributionally robust redundancy allocation model using state-dependent ambiguity set, which describes the mean, expected cross-deviation, and the support conditional on each state of the component lifetime distribution. Our structural analysis of the worst-case system reliability function identifies a concave equivalent for the conditional worst-case reliability function in each state and achieves an averaged finite piece-wise affine representation for the overall worst-case system reliability function, which enjoys valuable operational insights for reliability evaluation and scalable optimization of the redundancy designs. Furthermore, we analyze the reliability guarantees for the worst-case reliability in optimality under possible misspecification of ambiguity-set parameters, which admit the structure of "Reliability Target + Target Surplus + Estimated Elasticity," and insightfully imply that the auxiliary dual variables obtained via solving the design problem can be regarded as the scale of elasticity. Computationally, the redundancy design problem can be linearized and reformulated as a mixed 0-1 second-order cone program. Exploiting the above finite piece-wise affine structure of the worst-case reliability function, the design problem also admits a practical iterative decomposition scheme with finite convergence, which is more scalable especially for the possible situations of large number of states in practice. Finally, numerical experiments including a case with real-life data of braking system components well justify the value of state information incorporated by our model in producing favorable cost-effective redundancy designs for reliability operations.
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