On Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution

The stress – strength model is one of the models that are used to compute reliability. In this paper, we derived mathematical formulas for the reliability of the stress – strength model that follows Rayleigh Pareto (Rayl. – Par) distribution. Here, the model has a single component, where strength Y is subjected to a stress X, represented by moment, reliability function, restricted behavior, and ordering statistics. Some estimation methods were used, which are the maximum likelihood, ordinary least squares, and two shrinkage methods, in addition to a newly suggested method for weighting the contraction. The performance of these estimates was studied empirically by using simulation experimentation that could give more varieties for different-sized samples for stress and strength. The most interesting finding indicates the superiority of the proposed shrinkage estimation method.

Reliability Estimation for the Remained Stress-Strength Model under the Generalized Exponential Lifetime Distribution

A stress-strength reliability model compares the strength and stresses on a certain system; it is used not only primarily in reliability engineering and quality control but also in economics, psychology, and medicine. In this paper, a novel extension of stress-strength models is presented. The mew model is applied under the generalized exponential distribution. The maximum likelihood estimator, asymptotic distribution, and Bayesian estimation are obtained. A comprehensive simulation study along with real data analysis is performed for illustrating the importance of the new stress-strength model.

Strength Model of Backfill-Rock Irregular Interface Based on Fractal Theory

In the two-step open stope subsequent filling mining method, the determination of the strength model for the backfill-rock interface is of great engineering significance to study the stress distribution and stability of the backfill in the stope. Considering the deformation mechanism of the interface and the interaction of the asperities, a strength model for backfill-rock with irregular interface has been proposed based on fractal theory, which can effectively describe the shear mechanical behavior of interfaces with random roughness. The model has been compared with the two-body mechanistic model and good agreements have been achieved. The results show that the shear strength of the interface changes non-linearly with increasing fractal dimension D, when the fractal dimension D is in the range of 1∼1.12. The complete relationship between the interface shear strength and the fractal dimension is given, as the fractal dimension increases from 1 to 2 based on the presented model. At the same time, the quantitative relationship between the interface and backfill friction angles during direct shear testing is analyzed.

Theoretical Analysis for Stability Evaluation of Rock Mass Engineering Structure under Combined Compression-Shear Loading: A Case Study of Inclined Pillar

An inclined pillar is a typical support structure under compression and shear loads for underground mining. The shear load caused by the inclination of the ore-body affects the bearing capacity of the pillar. At present, there is no systematic investigation on the influence of shear load on the stress state evolution and bearing capacity of the inclined pillar. Additionally, there is still a lack of effective evaluation of the bearing capacity of the inclined pillar in the presence of additional shear load. In this research, the theoretical analysis method is used to solve these problems. First, the compressive and shear load components on the inclined pillar were calculated by the tributary area method, and the average stress state of the inclined pillar, considering the influence of the shear load, was characterized by a series of generalized stress circles. The factors that affect the shear load, such as the area extraction ratio, the inclination of the ore-body, and the in-situ stress ratio, were analyzed, and it reveals that there are three kinds of stress paths of the inclined pillar and their trajectories are straight line, circle, and curve, respectively. Then, a shear strength model was proposed to evaluate the bearing capacity of inclined pillars. The expression of this model is multiplied by a vertical pillar strength model and a dimensionless coefficient that is named the contribution factor of shear load (CFSL). Some cases of inclined pillars were employed to verify the rationality of this model. Finally, the factors that affect the bearing capacity of pillars were analyzed. This investigation presents that the shear load affects the stress path and determines the bearing capacity of the pillar. Therefore, the shear load should not be neglected in pillar design and stability analysis.

Investigation of the deformation and strength characteristics of the thread connection in the manufacture of products from fur waste

By the method of mathematical planning of the experiment, regression equations were obtained for the breaking load and the breaking relative elongation of the thread connection of a special furrier’s seam in the manufacture of products from fur waste. As input factors were taken: the number of stitches in 1 cm., Thread thickness, needle diameter. The features of the behavior of the strength model of this thread connection are revealed.