1 Introduction

This is a document that shows an np chart for the number of defects in each lot of wafers. There are 50 consecutive lots of \(n=200\) wafers that have been collected. We are going to use the package qcc in doing so.

library(qcc)

We load the number of defects in each lot of 200 wafers in 50 consecutive lots:

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)

2 NP Chart

We would like to create an np chart for this data.

2.1 Formulas for NP Chart

The NP chart has the following equations for control limits:

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

\[ CL = np \]

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

2.2 QCC Output

The qcc object for the np chart is given below:

np <- qcc(defects, type = "np", sizes = 200, title = "NP Chart of Wafer Lot Defects", ylab = "Number of Defects", xlab = "Wafer Lot")

2.3 QCC NP Chart Interpretation

The data remains within the control limits (UCL: 15.01, LCL: 0) and fluctuates randomly around the center, or the average number of defects, of 7.14. This indicates that the process is statistically in control.

3 Complete R Code

#install.packages("qcc")
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)