6-Control Chart Concepts

Is
Process
Stable
?
The
Quality
Improvement
Model
Define
Process
Select
Measures
Collect &
Interpret
Data
Is Process Stable?
Purpose: Determine the
stability of key
measures of the
product.
Is
Process
Stable
?
No
Investigate &
Fix Special
Causes
Yes
Improve
Process
Capability
No
Is
Process
Capable
?
Yes
Use SPC to
Maintain
Current
Process
6-1
Is
Process
Stable
?
Types of Variation
Common Causes
Causes that are inherent in the
process over time, and affect all
outcomes of the process.
 Ever-present
 Create small, random fluctuations
in the process
 Lots of them
 The sum of their effects creates
the expected variability
 Predictable
Run Chart
Quality
Characteristic
Time
6-2
Is
Process
Stable
?
Types of Variation
Special Causes
Causes that are not present in the
process all the time, but arise
because of specific circumstances.
 Not always present in the process
 Can create large process
disturbances, or sustained shifts
 Relatively few in number
 Pull the process beyond the
expected level of variability
 Unpredictable
Run Chart
Quality
Characteristic
Time
Control charts help identify the presence of special causes.
6-3
Is
Process
Stable
?
Control Chart Components


Run chart of the data
Center Line (CL)


UCL
A line at the average of the
data or target of the process
Upper Control Limit (UCL)


Control Chart
A line at the upper limit of
expected variability
Lower Control Limit (LCL)

CL
A line at the lower limit of
expected variability
LCL
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Run Order
The control limits are based on data collected from the process.
6-4
Is
Process
Stable
?
Rules for Separating Common &
Special Causes
Two commonly used signals of special causes are:
Rule 1: Any point above the Upper Control Limit (UCL)
or below the Lower Control Limit (LCL)
Rule 2: 8 points in a row on the same side of the center
line (CL)
Note: Additional rules do exist.
6-5
Evaluation of Individuals Data
Is
Process
Stable
?
s
s
T
c
s
R ,n=2
s
X
•
•••
• •
• • • • • • •
• • • •
• • •
• • •• •
••
• • •• • • •
c
• •
•
•• • • • • ••
•
•
• • • • ••
• •
•
• Target
••
Order of Production
s
s
Measures Variation in All Data
Used to Estimate 'Spread'
Does Not Reflect 'Capability'
Should Not Be Used for Calculating Control Chart Limits
s
c
Measures Variation in Successive Values
Used to Estimate the Potential Capability
Should Be Used to Calculate Trial Control Chart Limits
6-6
Estimating Sigma (Standard Deviation)
Is
Process
Stable
?
n

ss =
Xi – X
2
Total s s
i=1
n–1
n

sc =
Xi – Xi–1
i=2
n–1
1.128
=
R
1.128
Short-Term
sc
In existing data, Sigma C is a better estimate of the
common cause variability… Since it eliminates variation
due to cycles, shifts, etc…(Special Causes). Therefore,
Sigma C (from edited moving ranges) is always used to
calculate control limits!
6-7
Problem: Individuals Chart Calculations
Is
Process
Stable
?
Line 1 - First 25 Points Only
CO N TR OL C HA R T F O R
X & MR
Problem #13
F req ue nc y = D ail y
D ate
T im e
O p e rato r
Line 1
Me asur em en t ( X)
Mo ving R ang e ( MR )
87.6 91.2
3.6
1
2
94.0 91.6 81.6
94.0
94.4
91.0 84.2
89.5
86.6 92.9
97.4
94.2
81.6 85.6
2.8
2.4
10.0
89.1 90.9
7.5
1.8
3.1
0.4
3.4
6.8
5.3
2.9
6.3
4.5
3.2
12.6
4.0
88.7 88.8 87.7
1.1
3.1
0.1
79.9 96.6
7.8 16.7
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
22
20
21
23
89.3
7.3
93.2
3.9
24
25
X
MR
6-8
Line 1 - First 25 Points Only
Control Chart for _______________________________
Individuals
Chart
Calculations
X & MR CHARTS - Calculation Worksheet
MR =
Current Measurement
Is
Process
Stable
?
– Previous Measurement
R =
Total of MRs
Total number MRs
X =
Total of Measurements
Total number of Measurements
=
=
UCL MR = 3.267  R
=
=
LCL MR = 0
= 3.267 
=
R =
s c = 1.128
UCL X =
X
+ 3 sc
UCL X =
+ 3(
UCL X =
+
UCL X =
1.128
=
LCL X =
)
X
– 3 sc
LCL X =
– 3(
LCL X =
–
)
LCL X =
6-9
Minitab: Creating Individuals Control Charts
• Open Minitab Software and the Line 1.MTW Worksheet.
• Create an Individuals Control Chart following the commands in the notes.
• Your output should look like the charts below:
Is
Process
Stable
?
I-MR Chart of X
U C L=103.03
Individual V alue
100
_
X=89.66
90
80
LC L=76.30
1
3
5
7
9
11
13
15
O bser vation
17
19
21
23
25
1
U C L=16.42
M oving Range
16
12
8
__
M R=5.03
4
0
LC L=0
1
3
5
7
9
11
13
15
O bser vation
17
19
21
23
25
6-10
Minitab: Creating Individuals Control Charts
Is
Process
Stable
?
•Open Problem 14.MTW located in the
Minitab Datasets folder.
•Use Minitab to create an Individuals and
Moving Range control chart for X in
column C1.
•What do you notice about the X and MR
Charts?
•What should you do to establish control
limits?
6-11
Minitab: Creating Individuals Control Charts With
Range Edited Limits
Is
Process
Stable
?
•As you noticed the moving range control chart for problem 14 has two ranges that
are above the upper control limit.
•So, a special cause source of variation is included in the limits calculation.
•The special cause needs to be removed and the limits re-calculated.
•Row 24 is the data point causing the moving ranges to be out of the limits.
•Use the brush tool to select and update the control chart or create a new column
without data point #24 (Remember to use the Backspace).
•These were taught in the Introduction to Minitab Course which is a pre-requisite
for the SPC course.
•Brush tool – Page 13 Introduction to Minitab book
6-12
Minitab: Creating Individuals Control Charts With
Range Edited Limits
Is
Process
Stable
?
•The chart below shows the updated control charts without point #24.
I-MR Chart of X_1
Individual V alue
66
1
1
U C L=65.261
65
2
64
2
2
2
2
2
_
X=63.528
63
62
LC L=61.796
1
1
5
9
13
17
21
O bser vation
25
29
33
1
37
1
1
M oving Range
2.4
1
1
U C L=2.128
1.8
1.2
__
M R=0.651
0.6
2
2
2
2
0.0
2
2
2
LC L=0
2
1
5
9
13
17
21
O bser vation
25
29
33
37
•The updated moving range chart shows more moving ranges outside of limits.
•These are caused by rows 7 and 29.
•Remove the data points and update the control charts again.
6-13
Minitab: Creating Individuals Control Charts With
Range Edited Limits
Is
Process
Stable
?
•The second updated Moving Range chart does not have any points outside of limits
I-MR Chart of X_1
65
1
U C L=64.579
Individual V alue
2
64
2
2
2
2
2
_
X=63.411
2
63
62
LC L=62.242
1
1
61
1
5
9
13
17
21
O bser vation
25
29
33
1
37
1.6
M oving Range
U C L=1.436
1.2
0.8
__
M R=0.439
0.4
0.0
LC L=0
1
5
9
13
17
21
O bser vation
25
29
33
37
•The objective is to calculate control limits that represent common cause sources of
variation only.
•However, stop editing data points once 10 to 20% of the data has been edited.
•If the initial data has this many special causes, the limits will identify plenty special
causes in the future for you to work on.
6-14
Minitab: Obtain Statistics to Calculate Limits for
Continuous Process Monitoring
Is
Process
Stable
?
Select I-MR Options in the I-MR dialog box
Choose Storage and select Means and Standard deviations
6-15
Minitab: Obtain Statistics to Calculate Control
Limits Continued
Is
Process
Stable
?
Two new columns are created
Mean1 – Average of your data
STDE1 – Sigma_C
6-16
Process Stability
Is
Process
Stable
?
Stable Process
A process in which the key measures of the output from
the process show no signs of special causes. Variation is a
result of common causes only.
Unstable Process
A process in which the key measures of the output from
the process show signs of special causes in addition to
common causes. Variation is a result of both common and
special causes.
6-17
Is
Process
Stable
?
Process Stability
STABLE v s. UNSTABLE PROCESSES
ST ABLE
s
Constant

Constant
s
Constant

Sustained Shift
s
Constant

Irregular Shift
s
Constant

Trend
s
Increase

Constant
s
Irregular

Irregular
UNST ABLE
6-18
A Stable Process
UCL
LCL
Is
Process
Stable
?
•
•
•
•
•
•
•
•
• •
•
• • •• • • • • •
•
• • •
•• •
• • • • •
• • •
•
•
•
• •• • • • • • • • • •
••
•• •
• • •
•
•
•
•
• •
•
•
•
•
•
•
•
•
• • • ••
•
•
•
Common Causes Alone Are At Work:
• Behaves in a Random Manner
• No Cycles
• No Runs
• No Trends
• No Shifts
• No Defined Patterns
6-19
A Stable Process: Sigma S = Sigma C
Lower
Spec
Upper
Spec
Is
Process
Stable
?
Centering O.K.
Capability Adequate
No Action Needed
3sc
X
3sc
CAPABILITY
SPREAD
Lower
Spec
Upper
Spec
Centering Off
Capability Adequate
Shift Centering By
Altering Aim of
Process
Lower
Spec
Upper
Spec
Centering O.K.
Capability Inadequate
Change Process
6-20
Un-Stable Process
UCL
LCL
Is
Process
Stable
?
•
••
••
•
•
• • • •
•
•
•
•
•• • •• • • •
• ••
•
•
•
•• • •
• • • • • • •• • •
•
•
• • • • •• • • •• • •• •
• • • • •
•
• •• •
• •• •
•
• •
•
•
•
•
•
Assignable Cause(s) Are Present In Addition To
Common Cause Variation
Look For:
• Points Outside the Control Limits
• Shifts
• Cycles
• Runs
• Trends
6-21
Un-Stable Process: Sigma S Not Equal to
Sigma C
Lower
Spec
Upper
Spec
Spread Within
Specifications
Determine Cause of
Instability and Correct
If Economically
Feasible
CAPABILITY
SPREAD
Lower
Spec
Is
Process
Stable
?
Upper
Spec
Spread Outside
Specifications
Capability Adequate
Determine Cause of
Instability and Correct
Lower
Spec
Upper
Spec
Spread Outside
Specifications
Capability Inadequate
Change Process Attempt to Achieve
At Least Partial
Improvement
6-22
Is
Process
Stable
?
Advantages of Stable Processes Are:
6-23
Is
Process
Stable
?
Polymer Manufacturing Data
Control Chart
b*
Histogram
LS
5
4
US
3
UCL=2.2
2
Avg=1.4
1
LCL=0.5
0
0
1
2
3
4
b*
5
20
40
60
80
Sample
100
120
140
Note: b* is a measure of yellowness
Histogram does not show whether the process is stable!
6-24
What’s Wrong With Putting Specification
Limits on Control Charts?
Is
Process
Stable
?
Case 1: (Specifications wider than Control Limits)
USL
x
UCL
x
x
x
CL
x
LCL
x
x
LSL
Case 2: (Control Limits wider than Specifications)
UCL
x
USL
x
x
x
CL
x
x
LSL
LCL
In both cases, specification limits on control charts
cause you to take the wrong action.
6-25
Histograms & Control Charts
Histograms



Plot past data
Cannot tell if process
is stable
Only useful for
prediction if the
process is stable
Is
Process
Stable
?
Control Charts



Real-time evaluation
Help identify presence
of special causes
Assess past and
present stability of
process
6-26
Is
Process
Stable
?
Pump Maintenance Data
20
18
16
Number 14
12
of
Failures 10
UCL=11.4
8
6
Avg=4.8
4
2
0
LCL=None
2
4
6
8
10
12
14
16
18
20
22
24
Week
Are there any signals of special causes? Circle them.
6-27
Is
Process
Stable
?
Driving to Work Data
55
UCL=51.6
Time
(Minutes) 50
Avg=45.9
45
LCL=40.2
40
35
5
10
15
20
25
30
35
Day
The next 5 observations are: 47, 46, 43, 52, 45. Plot them.
Are there any signals of special causes? Circle them.
6-28
Is
Process
Stable
?
Purchase Order Data
14
13
12
11
Time 10
(Days) 9
8
7
6
5
4
3
2
1
0
UCL=9.5
Avg=5.0
LCL=0.5
2
4
6
8
10
12 14
16
18
20
Week Sample Taken
Are there any signals of special causes? Circle them.
6-29
Is
Process
Stable
?
Shipping Data
0.30
0.25
p
(fraction
nonconforming)
UCL
0.20
0.15
Avg=0.123
0.10
0.05
0.00
2 4
6 8 10 12 14 16 18 20 22 24 26 28 30
LCL
Week
Are there any signals of special causes? Circle them.
6-30
Quality Improvement
Is
Process
Stable
?
Types of Control Charts
Counting Measures
p charts
np charts
c charts
u charts
Instrument Measures
x (X-bar) charts
Individuals (x) charts
Range (R) charts
Moving Range (MR) charts
Arithmetic Moving Average charts
Exponentially Weighted Moving
Average charts
Cusum charts
“When you have a problem to solve,
you want to choose the right tool.”
6-31
Is
Process
Stable
?
Exercises
Circle any signals of special causes you find in the
following control charts.
Example 1
% of
Customers
Ranking
Eastman
as #1
Supplier
•
Example 2
•
• ••
•
•• •
•
• •
•
• • •
•
•
•
Time
Monthly
Sales
•
•••
• •
• • •
•
• •
• •
Time
6-32
Is
Process
Stable
?
Skill Check - Continued
Example 3
•
•
%
Defective
•
•
•
•
•
•
•
Example 4
•
• •
•
Number
of LostTime
Accidents
•
•
•
•
•
•
•
•
Time
•
•
•
••
• •
•
•
•
•
•
Time
6-33
Exercises
Is
Process
Stable
?
1.) Your Catapult Team should complete page 9 of the
“Catapult Process” handout.
2.) Be ready to present your results in PowerPoint
Limit yourselves to 10 minutes for this exercise.
6-34