Estudo de testes estatísticos para o vetor de médias em controle deprocessos multivariados sob amostragem dupla.

Abstract

In this dissertation we present an alternative method to determine Hotelling´s T2 control chart limits for the double sampling and normal process with known covariance matrix proposed by Costa and Machado (2008). The new procedure is less complex than the numeric integration and can be used in situations which more than two quality characteristics are available. Parallel, an extension of the Hayter and Tsuis test (1994) used to compare vector mean under random sampling was proposed for double sampling. Due the computation complexity, the extension of Hayter and Tsui was implemented only for the case where the covariance matrix is known. The evaluation of the tests was performed by using Monte Carlo simulation considering several settings with high and low correlation among the variables. In general, the results of the simulations pointed out that the extension of Hayter and Tsuis test presented larger power values in situations where the samples size were the same in both stages of inspection. On the other hand, Hotellings T² performed better when the correlations among the variables were higher. The comparison between the power estimates of Hotellings T² tests under the assumption of known and unknown covariance matrices showed that the power of the test decreases when the covariance matrix is estimated, particularly for situations where the shifts from the mean vector postulated under the null hypothesis and the sample sizes were smaller. In general, the results showed that in many situations the power ofHotellings T² and Hayter and Tsui tests were large, even for small samples.