X-bar Chart for Etch Rate Data

1 Introduction

This is a document that shows an X-bar chart for Etch Rate data. There are 20 subgroups of \(n=5\) that have been collected over time. We are going to use the package qcc in doing so.

library(qcc)

We load the dataset EtchRateRetroData.csv:

df <- read.csv("EtchRateRetroData.csv", header=FALSE)

2 X-bar Chart

We would like to create an X-bar chart for this data. The X-bar chart has the following control limits:

\[ UCL = \bar{\bar{X}} + \frac{3\sigma}{\sqrt{n}} \]

\[ CL = \bar{\bar{X}} \]

\[ LCL = \bar{\bar{X}} - \frac{3\sigma}{\sqrt{n}} \]

3 QCC Output

The qcc object for the X-bar chart is given below:

qcc(df, type = "xbar")

## List of 11
##  $ call      : language qcc(data = df, type = "xbar")
##  $ type      : chr "xbar"
##  $ data.name : chr "df"
##  $ data      : num [1:20, 1:5] 4.8 5.6 4.4 4.9 5.8 4.3 4.2 4.2 4.2 4.8 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics: Named num [1:20] 4.76 4.56 4.68 4.82 4.92 4.46 4.32 4.58 4.58 4.54 ...
##   ..- attr(*, "names")= chr [1:20] "1" "2" "3" "4" ...
##  $ sizes     : int [1:20] 5 5 5 5 5 5 5 5 5 5 ...
##  $ center    : num 4.52
##  $ std.dev   : num 0.58
##  $ nsigmas   : num 3
##  $ limits    : num [1, 1:2] 3.74 5.3
##   ..- attr(*, "dimnames")=List of 2
##  $ violations:List of 2
##  - attr(*, "class")= chr "qcc"

4 Complete R Code

library(qcc)

df <- read.csv("EtchRateRetroData.csv", header=FALSE)

qcc(df, type = "xbar")