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In this work, we consider two sets of dependent variables 
$\{X_{1},\ldots,X_{n}\}$ and 
$\{Y_{1},\ldots,Y_{n}\}$, where 
$X_{i}\sim EW(\alpha_{i},\lambda_{i},k_{i})$ and 
$Y_{i}\sim EW(\beta_{i},\mu_{i},l_{i})$, for 
$i=1,\ldots, n$, which are coupled by Archimedean copulas having different generators. We then establish different inequalities between two extremes, namely, 
$X_{1:n}$ and 
$Y_{1:n}$ and 
$X_{n:n}$ and 
$Y_{n:n}$, in terms of the usual stochastic, star, Lorenz, hazard rate, reversed hazard rate and dispersive orders. Several examples and counterexamples are presented for illustrating all the results established here. Some of the results here extend the existing results of [5] (Barmalzan, G., Ayat, S.M., Balakrishnan, N., & Roozegar, R. (2020). Stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under Archimedean copula. Journal of Computational and Applied Mathematics 380: Article No. 112965).
$\chi_{\alpha}^{2}$ divergence measure
The purpose of this paper is twofold. The first part is to introduce relative-
$\chi_{\alpha}^{2}$, Jensen-
$\chi_{\alpha}^{2}$ and (p, w)-Jensen-
$\chi_{\alpha}^2$ divergence measures and then examine their properties. In addition, we also explore possible connections between these divergence measures and Jensen–Shannon entropy measure. In the second part, we introduce 
$(p,\eta)$-mixture model and then show it to be an optimal solution to three different optimization problems based on 
$\chi_{\alpha}^{2}$ divergence measure. We further study the relative-
$\chi_{\alpha}^{2}$ divergence measure for escort and arithmetic mixture densities. We also provide some results associated with relative-
$\chi_{\alpha}^{2}$ divergence measure of mixed reliability systems. Finally, to demonstrate the usefulness of the Jensen-
$\chi_{\alpha}^{2}$ divergence measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that the Jensen-
$\chi_{\alpha}^{2}$ is an effective criteria for quantifying the similarity between two images.
In this paper, several linear two-dimensional consecutive k-type systems are studied, which include the linear connected-(k, r)-out-of-
$(m,n)\colon\! F$ system and the linear l-connected-(k, r)-out-of-
$(m,n)\colon\! F$ system without/with overlapping. Reliabilities of these systems are studied via the finite Markov chain imbedding approach (FMCIA) in a novel way. Some numerical examples are provided to illustrate the theoretical results established here and also to demonstrate the efficiency of the developed method. Finally, some possible applications and generalizations of the developed results are pointed out.
