Introduction and Report Description

This report aims to communicate findings regarding wafer defects in fabrication. To communicate said findings, I will construct an np control chart using the qcc package in R to confirm process stability and establish control limits for ongoing monitoring.

A fabrication facility produces wafers in lots. At the end of the photolithography stage, quality engineers inspect n = 200 wafers per lot and record the number of defective wafers in each lot. Data were collected over k = 50 consecutive lots during a period believed to represent a stable, in-control process.

NP Chart Formulas for Control Limits

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

\[ CL = np \]

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

R Code

library(qcc)
## Package 'qcc' version 2.7
## Type 'citation("qcc")' for citing this R package in publications.
#Number of defects found in each separate sample (50 samples)
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 Process Control

Referencing the generated NP Control Chart from given data, we can clearly see that the analyzed process is in control. All 50 subgroups fall within the calculated UCL and LCL. There are no violating runs and no data points exist beyond calculated limits.

UCL = 15.012

CL = 7.14

LCL = 0

Standard Deviation = 2.624

Complete R Code

library(qcc)

#Number of defects found in each separate sample (50 samples)
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)