Robust Estimation in Linear Regression with Molticollinearity and Sparse Models

Consider a coherent system consisting of independent or dependent components and assume that the components are randomly chosen from two different batches, where the components lifetimes of the first batch are larger than those of the second in some stochastic order sense. In this paper, using different stochastic orders, we compare the reliability of such systems and show that the reliability of the systems increases, as the random number of components chosen from the first batch increases in different stochastics orders.  We use copula function to describe dependence structure between component lifetimes.