Hotelling T2 Statistic for Phase I.

Description

Calculate the Hotelling T2 statistic for multivariate observations at phase I , to be used to build the corresponding control chart.

Usage

T2.1(estat, m, n)

Arguments

Details

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.1" (or other way to supply the data).

Value

Return a vector with the Hotelling T2 statistics.

Author(s)

Daniela R. Recchia, Emanuel P. Barbosa

References

Montgomery, D.C.,(2008)."Introduction to Statistical Quality Control". Chapter 11. Wiley.

See Also

stats, data.1, cchart.T2.1

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) 
T2.1(estat, 50, 1)
#Example with sub group observations
datum <- data.1(20, 10, mu, Sigma)
estat <- stats(datum, 20, 10, 2) 
T2.1(estat, 20, 10)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(IQCC)
Loading required package: qcc
Package 'qcc', version 2.6
Type 'citation("qcc")' for citing this R package in publications.
Loading required package: MASS
Loading required package: micEcon

If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/
Loading required package: miscTools
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/IQCC/T2.1.Rd_%03d_medium.png", width=480, height=480)
> ### Name: T2.1
> ### Title: Hotelling T2 Statistic for Phase I.
> ### Aliases: T2.1
> 
> ### ** 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) 
> T2.1(estat, 50, 1)
 [1] 0.57679525 1.52618370 4.48760620 1.41572413 2.58257411 0.24814671
 [7] 1.09586309 4.51240499 1.26102548 0.09583315 6.87846390 0.37929354
[13] 0.75401733 3.86774169 0.04050108 3.80824094 1.66466617 0.73702173
[19] 1.15328105 3.63017010 4.55429759 0.29921678 0.79990624 0.58061666
[25] 1.79393908 0.06339286 2.24423755 0.51873954 0.10881320 0.43160575
[31] 0.42958063 1.36399114 1.46711150 2.92991956 0.59951447 0.06821394
[37] 3.35967844 0.14690402 1.09745858 1.00006458 0.26569371 5.18254304
[43] 0.80076302 1.28358006 1.51884935 7.25116780 1.40129833 2.00440594
[49] 0.06566077 0.32183246
> #Example with sub group observations
> datum <- data.1(20, 10, mu, Sigma)
> estat <- stats(datum, 20, 10, 2) 
> T2.1(estat, 20, 10)
 [1] 4.22269182 2.36138326 1.96361752 0.34970570 3.22983889 0.62598872
 [7] 0.40668078 1.89365645 0.74631452 0.15596703 0.15140472 3.85123893
[13] 4.76880919 0.27349115 0.09229975 1.45059342 4.07052592 2.00818692
[19] 1.93369967 0.07936566
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>