ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
Statistical Process Control (SPC)
Variable Control Charts
Term
Definition
SPC Charts
SPC charts are used to monitor a product’s key quality characteristics.
We can
compare current performance to process history to detect special causes and to
determine if the process is stable and in statistical control.
If we see an outlier
sample, we can investigate to see why it happened, related trends, how to
prevent the anomaly, etc.
This will allow for improved economic operation.
Special Cause
(assignable) Variation
The variation can be pinpointed to one cause that can be corrected at the
machine-level
Makes up about 15% of quality problems
Ex. local faults, broken tool, tool wear, changes in raw material, and machine
slippage
Think of special causes happening at the machine level, or at a very specific
part of operations
Common Cause
(random) Variation
The variation effects all the output quality and requires a systematic change
Makes up about 85% of quality problems
Ex. system faults, poor tool maintenance, poor supervision, poor training,
inappropriate work methods, poor workstation design
Think of common causes happening at a system level - there is a larger scale
issues and possible need for system redesign
Variable Charts (
X
and R and moving
range)
Used for
variable data
(any value in a large range that is expressed as a number
(a specific measurement… ex: height, weight
Equations:
Monitoring Process Mean
Monitoring Process Standard Deviation
0
Estimated by
X
and
0
estimated by
2
d
R
X
- R charts
R
D
UCL
R
D
LCL
R
A
X
UCL
R
A
X
LCL
R
R
X
X
4
3
2
2
Moving Range Chart
(Use when a single measurement is
available – no rational subgroups of size n)
X_R
m
charts
m
Rm
m
Rm
m
X
m
X
R
D
UCL
R
D
LCL
R
E
X
UCL
R
E
X
LCL
4
3
2
2
1

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018
Problem 1:
A forging process produces Piston rings for an automotive engine. We wish to establish
statistical control of the inside diameter of the rings manufactured by this process using
x
and R
charts. 25 samples, each sample of size 5, have been taken when we think the process is in control. The
inside diameter measurement from these samples are given below.
25
1
028
.
1850
i
x
25
1
581
.
0
i
R
25
1
2350
.
0
i
S
The specification limits on this piston ring are 74.000
0.05 mm.
(a) What are the control limits for
R
X
__
chart?
(b) What is the process standard deviation?
2
=

2

ISYE 315 DISCUSSION 8 (Ch. 13 SPC and Process Capability)
Spring 2018