np Control Chart

This report uses an np chart to analyze wafer defect data from a semiconductor fabrication process.

Formulas

The center line for an np chart is

\[ CL = n\bar{p} \]

The control limits are

\[ UCL = n\bar{p} + 3\sqrt{n\bar{p}(1-\bar{p})} \]

\[ LCL = n\bar{p} - 3\sqrt{n\bar{p}(1-\bar{p})} \]

Interpretation

The np chart shows that the process appears to be in control. The points stay within the control limits, so there is no clear evidence of special cause variation. This means the defect levels look stable across the 50 lots.

Data and Code

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)

n <- 200
pbar <- mean(defects) / n

CL <- n * pbar
UCL <- n * pbar + 3 * sqrt(n * pbar * (1 - pbar))
LCL <- n * pbar - 3 * sqrt(n * pbar * (1 - pbar))

library(qcc)
## Package 'qcc' version 2.7
## Type 'citation("qcc")' for citing this R package in publications.
qcc(defects, type = "np", sizes = rep(n, length(defects)))

## List of 11
##  $ call      : language qcc(data = defects, type = "np", sizes = rep(n, length(defects)))
##  $ 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"