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T2 control charts are used to monitor a process when more than one quality variable associated with process is being observed. Recent studies have shown that using variable sample size (VSS) schemes result in charts with more statistical power when detecting small to moderate shifts in the process mean vector. This paper presents an economic- statistical design of T2 control charts with variable sample size and control limits (VSSC). We build a cost model of a T2-VSSC control chart for the purpose of economic- statistical design using the model of Costa and Rahim (2001).This cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. We optimize this model using a genetic algorithm (GA) approach. Furthermore, T2-VSSC and T2-VSS charts are compared with respect to the expect cost per unit time.

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The problem of sample size estimation is important in medical applications, especially in cases of expensive measurements
of immune biomarkers. This paper describes the problem of logistic regression analysis with the sample
size determination algorithms, namely the methods of univariate statistics, logistics regression, cross-validation and
Bayesian inference. The authors, treating the regression model parameters as multivariate variable, propose to estimate
the sample size using the distance between parameter distribution functions on cross-validated data sets.
Herewith, the authors give a new contribution to data mining and statistical learning, supported by applied mathematics.

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In the present article, an attempt has been made to provide a fully operational and useful guide regarding the implementation of two-stage cluster sampling plan in field research, which is one of the most widely used sampling plans according to the current conditions and facilities in the country. . In addition, for further use by researchers in this field, this article provides codes for implementing two-stage cluster sampling with unequal size based on probability proportional to size along with an example on two-stage cluster sampling with probability proportional to size (PPS) with hypothetical data using R software is included.