In this work we develop a study of positive periodic solutions for a mathematical model of the dynamics of computer virus propagation. We propose a generalized compartment model of SEIR-KS type, since we consider that the population is partitioned in five classes: susceptible (S); exposed (E); infected (I); recovered (R); and kill signals (K), and assume that the rates of virus propagation are time dependent functions. Then, we introduce a sufficient condition for the existence of positive periodic solutions of the generalized SEIR-KS model. The proof of the main results are based on a priori estimates of the SEIR-KS system solutions and the application of coincidence degree theory. Moreover, we present an example of a generalized system satisfying the sufficient condition.

The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution, and its multivariate extension. The proposed test is consistent against any fixed alternative. It is also able to detect local alternatives converging to the null at the rate $n^{-\frac{1}{2}}.$ The bootstrap can be employed to consistently estimate the null distribution of the test statistic. Through a simulation study we investigated the goodness of the bootstrap approximation and the power for finite sample sizes.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér–von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

This paper is about the use of the Statistical Process Control (SPC) to detect problems generated by the variability inside Automatic Process Control (APC). This paper tries to find a successful tool regarding to detect values out of control in automatic system. This kind of tool afford evaluated the control strategy and will be useful for the decision makers. Statistical process control, monitoring no only the quality variables but also, variables in the automatic processes that are controlling the quality. In order to test this tool, it will be tested checking the status of moisture control in a medium density fiberboard (MDF) line, this process, is one of the most important in this type of industry. Furthermore, this useful statistical tool could be use to evaluated the performance of any process inside of an organization to help in the improvement cycles.