---

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.

---

‎The boosted mixture learning method‎, ‎BML‎, ‎is an incremental method to learn mixture models for the classification problem‎. ‎In each step of the boosted mixture learning method‎, ‎a new component is added to the mixture model according to an objective function to ensure that the objective function is maximized‎. ‎Sometimes the likelihood function or equivalently information criteria are defined as the objective function of BML‎. ‎The mixture model is updated whenever a new component is added to the mixture model based on the maximum likelihood function and information criteria‎.

‎Since the information criteria does not have the ability to identify equivalent models‎, ‎therefore‎, ‎it is possible that the new mixture model and the current mixture model are equivalent‎.

‎In this paper‎, ‎the boosted mixture learning method has been corrected using Vuong's model selection test‎, ‎which has the ability to identify equivalent models‎. ‎The performance of two learning methods is evaluated over simulation data and over the U.S‎. ‎imports of goods by customs basis.‎