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In this paper, we investigated the performance of the multivariate exponentially weighted moving average (MEWMA) control chart under highly asymmetric gamma distributions. Simulation procedures were used to obtain probabilistic control limits of the chart using a specific underlying distribution with known parameters (Phase II). The performance of the chart was evaluated under three different mean vector shifts, and the best values for the smoothing constant were identified. Results were compared with the existing proposal of using normal limits. Our results suggested that for three or more variables, probabilistic control limits lead to a better performance of the chart. We extended the analysis to the T2 chart and compared the efficiency of both strategies. MEWMA chart performance was better than T2 chart in all the cases analysed. A real application with Phase I reference data is described. The parameters of the marginal gamma distributions were estimated and a specific algorithm was then employed to determine the appropriate values of the smoothing constant and upper control limit of the MEWMA chart (Phase II). The relevance of this method lies in the fact that it can be adapted to any practical situation in which gamma model is suitable. [ABSTRACT FROM AUTHOR]

Multivariate hypothesis testing in studies of vegetation is likely to be hindered by unrealistic assumptions when based on conventional statistical methods. This can be overcome by randomization tests. In this paper, the accuracy and power of a MANOVA randomization test are evaluated for one and two factors with interaction with simulated data from three distributions. The randomization test is based on the partitioning of sum of squares computed from Euclidean distances. In one-factor designs, sample size and variance inequality were evaluated. The results showed a high level of accuracy. The power curve was higher with normal distribution, lower with uniform, intermediate with lognormal and was sensitive to variance inequality. In two-factor designs, three methods of permutations and two statistics were compared. The results showed that permutation of the residuals with Fpseudo is accurate and can give good power for testing the interaction and restricted permutation for testing main factors. [ABSTRACT FROM AUTHOR]