# A Probable Approach to Reliability Assessment of Reinforced Plates
## 1 Introduction
The empirical probability of failure of multilayer materials with transverse layers was the highest for the layer predicted by the deterministic analysis. With an increase in the input parameters' variation, a rapid decrease was observed. The general significance of considering the tensile strength and thickness of the composite material layer as random variables was shown. The significance of randomness in the orientation of layers for laminates with balanced and corner layers was analyzed. In [5], bistable composite laminates are considered. They can be used in the design of engineering structures because of their low density and deformation properties. An analysis of their reliability was carried out via the Monte Carlo simulation method. Several types of uncertain parameters, geometry, and material properties were considered random variables. It was shown that the thickness and thermal expansion coefficient of the studied composite material mostly affect the bistability behavior compared to the other input parameters. The research results were validated by comparing them with the results obtained by the finite element method. Paper [6] proposed a method for studying the crack resistance of composite materials. The structure of the composite was represented by an embedded cell near the crack tip. The rest of the composite under study was modeled as an anisotropic elastic body. Experimental data on transverse cracking of the matrix as a result of tests for three-point bending with one notch were used. The effectiveness of the microstructure in increasing the fracture toughness due to the disruption of the bond between the fiber and the matrix, fiber rupture, and crack deflection was shown. An increase in fracture toughness due to the disruption of the bond between the fiber and the matrix, fiber rupture, and crack deflection has been studied. It was shown that the research results are an important aspect of the development of composites with high crack resistance. Paper [7] investigated the reliability of composite plates made using the process of vacuum transfer casting resin based on carbon fiber/epoxy resin. An assessment was made of the change in the volume fraction of fibers in different parts of a plate made of a composite material. The effective orthotropic properties of the composite are numerically calculated for the various volume fractions of fibers by the homogenization method using periodic boundary conditions. The problem of predicting the failure probability of a composite beam with a double cantilever was considered. The accuracy and efficiency of the proposed approach are demonstrated by the study of meta-model stability. In [8], adaptive multipoint modeling with actively damaged areas of composite materials using high-precision 3D brick elements and discrete cracks, while dormant and inactive areas are considered with lower values, is proposed. The criteria for the transition between the two levels of modeling were studied to ensure the efficiency of calculations. The obtained results were comparedto the experimental data known in the scientific literature on the tension of transverse-layer and quasi-isotropic composite materials and the results of a high-precision simulation. The article is another variation on the strength of composite materials with internal type inclusions/holes which has been studied since 1950-60. It must be agreed that there has been no significant progress in this area since the indicated data. Mathematical ideas ([PERSON] and co-authors [9; 10], [PERSON] and co-authors [11]) have not yet been implemented. [PERSON] and co-authors [12; 13] have made some progress in calculating random compositions with rigorous mathematical methods, but not exactly of the class considered in this article.