#' Hotelling T2 Statistic for Phase II. #' #' Calculate the Hotelling T2 statistic for multivariate observations at phase #' II , to be used to build the corresponding control chart. #' #' Before using this function it is necessary to execute the function #' "stats"(that calculate the auxiliary statistics involved in the T2 formula) #' and the function "data.2" (or other way to supply the data). #' #' @param datum2 The data set for the phase II. Shoul be a vector. #' @param estat The values of the auxiliary statistics. Should be a list with a #' matrix with the means, mean of the means and mean of the standard deviation. #' @param n The size of each sample used previously in data.2. If they are #' individual observations, use n = 1. #' @return Return a vector with the Hotelling T2 statistics. #' @export #' @author Daniela R. Recchia, Emanuel P. Barbosa #' @seealso \link{T2.1},\link{stats}, \link{data.2}, \link{cchart.T2.2} #' @references Montgomery, D.C.,(2008)."Introduction to Statistical Quality #' Control". Chapter 11. Wiley. #' @examples #' #' mu <- c(5.682, 88.22) #' Sigma <- symMatrix(c(3.770, -5.495, 13.53), 2) #' #Example with individual observations #' datum <- data.1(50, 1, mu, Sigma) #' estat <- stats(datum, 50, 1, 2) #' datum2 <- data.2(estat, 1, p = 2) #' T2II <- T2.2(datum2, estat, 1) #' #Example with subgroup observations #' datum <- data.1(20, 10, mu, Sigma) #' estat <- stats(datum, 20, 10, 2) #' datum2 <- data.2(estat, 10, p = 2) #' T2II <- T2.2(datum2, estat, 10) #' T2.2 <- function(datum2, estat, n) { if(n == 1) { T2 <- (t(datum2 - estat[[1]]) %*% solve(estat[[2]]) %*% (datum2 - estat[[1]])) } if(n > 1) { media <- colMeans(datum2) T2 <- n * (t(media - estat[[1]]) %*% solve(estat[[2]]) %*% (media - estat[[1]])) } return(T2) }