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

 Student R Documentation

## A simulated dataset

### 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(X_i,X_j)=0.8^{|i-j|}`.

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

### Usage

``data(Student)``

A 4x5x50 array.

### Examples

``````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 July 9, 2023, 7:29 p.m.