Module5RMarkdown

Introduction

The data we are given represents the number of defective wafers out of 200 sampled wafers in the 50 consecutive lots. In this report below I will use the qcc package in R to make a np control chart to confirm process stability and establish control limits for ongoing monitoring.

np Control Chart Formulas

The center line formula is shown as : \[ CL = np \] The control limits are shown as: \[ UCL = np+3\sqrt{np(1-p)} \] \[ LCL = np-3\sqrt{np(1-p)} \]

R code

library(qcc)

## Package 'qcc' version 2.7

## Type 'citation("qcc")' for citing this R package in publications.

defects<-c(8, 7, 11, 3, 6, 11, 4, 4, 5, 8, 8,  6,  7,  6, 10,  7,  9,  5,  6,  8, 8, 10,  4, 11,  4, 11,  6,  6,  9,  5, 4,  7,  5,  7,  8,  5, 10,  9,  7,  9, 4,  9,  4,  7, 11,  8, 10,  8,  7,  5)
qcc (defects, type = "np" , sizes=200)

## List of 11
##  $ call      : language qcc(data = defects, type = "np", sizes = 200)
##  $ type      : chr "np"
##  $ data.name : chr "defects"
##  $ data      : num [1:50, 1] 8 7 11 3 6 11 4 4 5 8 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics: Named num [1:50] 8 7 11 3 6 11 4 4 5 8 ...
##   ..- attr(*, "names")= chr [1:50] "1" "2" "3" "4" ...
##  $ sizes     : num [1:50] 200 200 200 200 200 200 200 200 200 200 ...
##  $ center    : num 7.14
##  $ std.dev   : num 2.62
##  $ nsigmas   : num 3
##  $ limits    : num [1, 1:2] 0 15
##   ..- attr(*, "dimnames")=List of 2
##  $ violations:List of 2
##  - attr(*, "class")= chr "qcc"

Analysis of Control Chart

After seeing the generated np control chart, we see that all the 50 points of data points fall between the LCL=0 and UCL=15.01184.There is no extreme outliers in the set. This tells us the process is in control.

Complete R code

library(qcc)
defects<-c(8, 7, 11, 3, 6, 11, 4, 4, 5, 8, 8,  6,  7,  6, 10,  7,  9,  5,  6,  8, 8, 10,  4, 11,  4, 11,  6,  6,  9,  5, 4,  7,  5,  7,  8,  5, 10,  9,  7,  9, 4,  9,  4,  7, 11,  8, 10,  8,  7,  5)
qcc (defects, type = "np" , sizes=200)