# Student: A simulated dataset In dfphase1: Phase I Control Charts (with Emphasis on Distribution-Free Methods)

## Description

This simulated data set consists in 50 subgroups, each with 5 observations, on 4 variables.

There is an isolated location shift involving only the first variable at time t=10 and a step shift, involving the third and fourth variables, starting from t=31. The in-control distribution is Student's t with 3 degrees of freedom, zero mean and such that cov(Xi,Xj)=0.8^abs(i-j).

See the example for the exact code used to simulate the data.

## Usage

 `1` ```data(Student) ```

A 4x5x50 array.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```data(Student) mphase1(Student) # # Replication of the simulation # # Generation of the in-control observations set.seed(1) m <- 50 n <- 5 p <- 4 df <- 3 Sigma <- outer(1:p,1:p,function(i,j) 0.8^abs(i-j)) Sigma xnorm <- crossprod(chol(Sigma),matrix(rnorm(p*n*m),p)) xchisq <- sqrt(rchisq(n*m,df)/(df-2)) x <- array(sweep(xnorm,2,xchisq,"/"),c(p,n,m)) # Then, we add an isolated shift at time 10 # (only for the first variable) x[1,,10] <- x[1,,10]+1 # and, a step shift starting at time 31 # (only for the third and fourth variable) x[3:4,,31:50] <- x[3:4,,31:50] + c(0.50,-0.25) dimnames(x)<-list(paste("X",1:4,sep=""),NULL,NULL) identical(x,Student) ```

dfphase1 documentation built on Feb. 17, 2021, 5:06 p.m.