#1.
p-chart (average fraction defective)
= total number of defective items / total number of items sampled
,
Ex:
The operations manager of the booking services department of Hometown Bank is concerned
about the number of wrong customer account numbers recorded by Hometown personnel. Each week a
random sample of 2500 deposits is taken, and the number of incorrect account numbers is recorded.
The results for the past 12 weeks are shown in the following table. Is the process in control? Use three
sigma control limits.
Sample Number
Wrong Account
Numbers
Sample proportion
defective
1
15
2
12
3
19
4
2
5
19
6
2
7
24
8
7
9
10
10
17
11
15
12
3
Total:
Average:
Solution:
Construct the
p-
chart, using past data to calculate
=
p
=
5

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
UCL
p
=
LCL
p
=
Is the process in control? (you can graph all points, but a quick check is to see if you have any outside
your control limits…)
6

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
#2.
np-chart (number of defectives)
d = np = # of defectives
Control limits:
Ex:
Using the data from the above problem, compute the control limits for the np-chart. Is the process
in control? Use 3 sigma control limits.
=

Is the process in control?
#3. c-chart (average number of defects in a sample)
In a sample of n items, c is the total number of defects in the sample
Control limits:
Ex:
The Woodland Paper Company produces paper for the newspaper industry. As a final step in the
process, the paper passes through a machine that measures various quality characteristics. When the
process is in control, it averages 20 defects per roll.
a.
Setup a control chart limits for the number of defects per roll. Use 3 sigma control limits
b.
The first two rolls contained 27 and 5 defects, respectively. Is the process in control?

7

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
Is the process in control?

Control Limits:
Ex:
The data set in the table given below contains the number of defects in
five sample batches, each
containing 15 items
. Assuming that the process was in control when these observations were collected,
compute the control limits of the
U
chart.
Batch #
(i)
Number of
Defects in a
Batch (c)
Average Number of
Defects per Unit
(u)
1
18
2
12
3
7
4
9
5
16
Total:
Ubar:
=
UCL
u
=
LCL
u
=
Is the process in control?
8

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
Process Capability
Term
Definition
Process Capability
The ability of a process to turn out a product that meets engineering (customer)
specifications.
We are interested in the centering and spread of a process relative
to the specification limits.
A
specification limit
is determined by the customer,
and a
control limit
is determined by the process itself (what you are producing).