SPC & MSA Using Minitab
I Chart for C1
39
Individual Value
3.0SL=37.36
34
X=30.60
29
24
-3.0SL=23.84
0
5
10
15
20
25
30
35
Observation Number
L. GOCH – FEBRUARY 2011
AGENDA
Continuous & Attribute Data
 IMR Charts
 Xbar & R Charts
 Xbar & S Charts
MSAs
 Using Xbar & S Charts for MSAs
 Non-Destructive Variable MSAs
(NOTE: Minitab will also Analyze Destructive Variable
MSAs & Attribute MSAs)
THE BASIC CONTROL CHART
KEY COMPONENTS
MONITORED
CHARACTERISTIC
Control Limits are NOT Spec Limits
UCL
Plotted Data
Center Line
LCL
DATA PLOTTED OVER TIME
UCL = Upper Control Limit
/
LCL = Lower Control Limit
COMMON CAUSES VS SPECIAL CAUSES
Individual-X &
Moving Range Chart
CONTROL CHARTS
INDIVIDUAL /MOVING RANGE



Use:
 When only have 1 measurement per time period
 When want to chart Counts.
 When want to chart Percentages (%’s).
Do NOT use P-Charts if the values are <10% or
subgroup sample size >100 since it violates basic
P-Chart assumptions.
Need a minimum of 10 data points
Variation
 Short Term: Measures relatively rapid changes over
time (Moving Range chart)
 Long Term: Measures relatively gradual changes over
time(Individuals chart)
Charts are Based on a Subgroup Size of 1
I / MR CHART: STAT > CONTROL CHARTS > I-MR

I-MR Chart analyzes individual
data over time.
Open worksheet
Exh_QC.mtw
I / MR CHART: STAT > CONTROL CHARTS >
RUN CHART
Rule #1
MINITAB EXERCISE
INDIVIDUALS / MOVING RANGE OUTPUT
I-MR Chart of Weight
1050
1
1
1
Individual Value
1
U C L=1010.9
6
1000
6
2
2
2
950
900
2
6
6
2
2
2
2
2
2
2
2
2
6
2
2
5
LC L=862.8
5
1
850
1
_
X=936.9
2
9
13
1
17
21
25
O bser vation
29
33
37
41
45
1
M oving Range
100
U C L=91.0
75
50
__
M R=27.8
25
LC L=0
0
1
5
9
13
17
21
25
O bser vation
29
33
37
41
45
Is there a shift at Observation # 25?
MINITAB EXERCISE
INDIVIDUALS / MOVING RANGE OUTPUT
Group
Column
Added
MINITAB EXERCISE
INDIVIDUALS / MOVING RANGE OUTPUT
Press <Ctl> e
MINITAB EXERCISE
INDIVIDUALS / MOVING RANGE OUTPUT
I-MR Chart of Weight by Group
1
1050
2
U C L=1041.8 5
Individual Value
5
1000
_
X=973.3
U C L=974.4
950
6
_
X=905
900
5
1
LC L=904.8
850
LC L=835.6
1
5
9
13
17
1
21
25
O bser vation
U C L=85.23
29
33
37
2
41
45
U C L=84.13
M oving Range
80
60
40
__
M R=26.09
__
M R=25.75
20
0
LC L=0
1
5
9
13
17
21
LC L=0
25
O bser vation
29
33
37
41
45
Xbar & R Chart
CONTROL CHARTS
X BAR / R CHART


Advantages
Sensitive to changes in data
Limitation
Unlike the Individual Chart, the Xbar Chart
control limits do not represent the overall data
range. They represent the range of the subgroup
averages.
CONTROL CHARTS
X-BAR / R CONTROL CHARTS


GATHERING DATA
 Define rational basis for subgrouping
 Select sample size for the subgroups
 Select sampling frequency
 Need a minimum of 10 subgroups
VARIATION
Short Term: Measures the variation within the Subgroups
based on the subgroup range (Range chart)
 Long Term: Measures the variation between the
Subgroups based on the subgroup average (X Bar chart)

XBAR-R CHARTS: STAT > CONTROL CHARTS >
VARIABLES CHARTS FOR SUBGROUPS > XBAR-R
Open worksheet
Camshaft.mtw
MINITAB EXERCISE - XBAR / R CHARTS OUTPUT
Xbar-R Chart of Length
Sample M ean
602
U C L=601.722
601
_
_
X=600.072
600
599
LC L=598.422
1
598
1
3
5
7
9
11
Sample
13
15
17
19
U C L=6.048
Sample Range
6.0
4.5
_
R=2.860
3.0
1.5
LC L=0
0.0
1
3
5
7
9
11
Sample
13
15
17
19
What do the Charts tell us?
We need to look at the individual suppliers.
MINITAB EXERCISE - XBAR / R CHARTS
o Stack Data:
Stack the 2 Suppliers so the data can be
looked at together on the same chart
MINITAB EXERCISE - XBAR / R CHARTS
Xbar-R Chart of Lengths by Supplier
S upp1
S upp2
1
Sample M ean
1
U C L=602.474
602
_
_
X=600.23
U C L=600.321
_
_
X=599.548
600
LC L=598.775
598
6
1
5
9
13
17
21
Sample
S upp1
25
29
LC L=597.986
33
S upp2
37
U C L=8.225
Sample Range
8
6
_
R=3.890
4
U C L=2.835
_
R=1.341
2
0
LC L=0
1
5
9
13
17
LC L=0
21
Sample
25
29
33
37
Xbar & S Chart
CONTROL CHARTS
X BAR / S CHART


Advantages
 Very sensitive to changes in data.
 Also, the center line of the S-Chart provides a
good estimate for the data’s standard
deviation.
Limitation
The Xbar Chart control limits do not represent
the overall data range. They represent the range
of the subgroup averages.
CONTROL CHARTS
X-BAR / S CONTROL CHARTS


GATHERING DATA
 Define rational basis for subgrouping
 An S-Chart is typically used when the subgroup’s
sample size is > 9
 Select sampling frequency
 Need a minimum of 10 subgroups
VARIATION
Short Term: Measures the variation within the
Subgroups based on the subgroup stddev (S chart)
 Long Term: Measures the variation between the
Subgroups based on the subgroup average (X Bar chart)

XBAR-S CHARTS: STAT > CONTROL CHARTS >
VARIABLES CHARTS FOR SUBGROUPS > XBAR-S
Open worksheet
Bloodsugar.mtw
MINITAB EXERCISE - XBAR / S CHARTS OUTPUT
Xbar-S Chart of Glucoselevel
U C L=130.72
Sample M ean
120
_
_
X=101.03
100
80
LC L=71.35
1
3
5
7
9
11
Sample
13
15
17
19
U C L=50.67
Sample StDev
50
40
_
S =28.77
30
20
10
LC L=6.88
1
3
5
7
9
11
Sample
13
15
17
19
What do the Charts tell us?
We need to look at the individual people.
MINITAB EXERCISE - XBAR / S CHARTS
o Sort Data:
Sort the data by SubjectID & Reading
MINITAB EXERCISE – I-MR CHARTS
I-MR Chart of Glucoselevel by SubjectID
Individual Value
1
2
3
4
1
5
6
7
8
9
200
6
6
150
5
6
1111
86
100
151
65
1
55
5
8
1
1
6
5
1
66
50
1
1
19
1
60
37
2
55
3
73
91
109
O bser vation
4
5
6
127
7
145
8
163
9
1
M oving Range
1
1
45
1
30
1
1
1
1
1
1
15
0
1
19
37
55
73
91
O bser vation
109
127
145
163
Xbar & S Charts used
for MSA’s
MSA: X BAR / S CHART


Advantages
 Pictorial look at MSA results
 Measurement error can easily be calculated

% R&R and %P/T can easily be calculated

Daily Calibration Data can be used
Limitation
 Will NOT detect measurement that varies by
nominal value (e.g. large parts having more or less
measurement error than small parts)
MSA: X-BAR / S CHART


GATHERING DATA
 Need Multiple measurements per time period
 Can use 1 or more Parts
 Need a minimum of 10 subgroups
VARIATION
S Chart: Displays the Measurement Error. A good
measurement system will be in-control
 Xbar Chart: Displays any Drift over time in the average
measurements. A good measurement system will be incontrol for each individual Part.

MSA: X-BAR / S CHART
Open worksheet
Daily Calibration
Data.mtw




Multiple
Measurements per
Day on most Days.
1 Calibration Part
per Facility
3 Facilities
Sorted by Facility
Date & Time
XBAR-S CHARTS: STAT > CONTROL CHARTS >
VARIABLES CHARTS FOR SUBGROUPS > XBAR-S
Open worksheet
Daily Calibration
Data.mtw
MSA: X-BAR / S CHART OUTPUT
Xbar-S Chart of Actual Measurement by Facility
DHM
DSM
Sample Mean
UCL=604.2
UCL=594.3
600
550
_
_
X=511.8
_
UCL=560.2
_
X=538.8
_
_
X=500.8
500
1
LCL=517.5
450
LCL=429.3
400
LCL=397.4
Nov-02
100
Sample StDev
GSO
1
Nov-09
Nov-19
DHM
Nov-29
UCL=101.4
Nov-04
Nov-13
Date
Nov-26
DSM
Nov-03
Nov-09
Nov-16
Nov-23
GSO
1
UCL=89.8
75
_
S=31.0
50
25
1
0
Nov-02
Nov-09
Nov-19
LCL=0
Nov-29
1
_
S=27.5
Nov-04
Nov-13
LCL=0
Nov-26
UCL=26.2
_
S=8.0
2 2
Nov-03
Nov-09
2 2
Nov-16
Date
Tests performed w ith unequal sample sizes
Need to add the Measurement Error.
LCL=0
Nov-23
MSA: X-BAR / S CHART RESULTS
Facilitly
~Sbar
Multiplier
~ Meas Error %P/T
DHM
31.0
2.575
+/- 80
80/50 = 160%
DSM
27.5
2.575
+/- 71
71/50 = 142%
GSO
8.0
2.575
+/- 21
21/50 = 42%

Comments
 Spec is +/- 50.
 %P/T target is < 30%
 None of Facilities meet the measurement error
target
 Daily Calibration Check procedures need
investigated since producing dramatically
different results
Variables MSA
(Non-Destructive Testing)
VARIABLES MSA:
STAT > QUALITY TOOLS> GAGE
STUDY > GAGE R&R STUDY (CROSSED)

Minimum Requirements
 Minimum 10 parts: ~3 at low end of spec,
~4 parts in middle of Spec, ~3 parts at
high end of spec (NOTE: some parts should be out of
spec)

3 Operators (NOTE: if only 1 operator measures parts,
1 operator may be used for MSA)

3 Repeated Measurements
VARIABLES MSA:
STAT > QUALITY TOOLS> GAGE
STUDY > GAGE R&R STUDY (CROSSED)
VARIABLES MSA:
STAT > QUALITY TOOLS> GAGE
STUDY > GAGE R&R STUDY (CROSSED)
VARIABLES MSA: GRAPH RESULTS
Gage R&R (ANOVA) for Measurement
G age name:
Date of study :
Reported by : Lisa G och
Tolerance:
8-16
M isc:
G age 1
F eb 18. 2011
Components of Variation
Measurement by Part
96.0%
100
Percent
67.1%
% R&R
% P/T
50
14
12
27.9%
19.5%
18.4%
12.9%
20.9%
14.6%
10
0
Gage R&R
Repeat
Reprod
1
Part-to-Part
2
3
B
Sample Range
UCL=0.880
14
0.5
_
R=0.342
12
0.0
LCL=0
10
A
B
C
UCL=12.551
_
X=12.201
Average
Sample Mean
9
10
C
Operator
A
B
C
14
LCL=11.852
10
8
Operator * Part Interaction
14
12
7
B
Operator
Xbar Chart by Operator
A
6
Measurement by Operator
C
1.0
5
Part
R Chart by Operator
A
4
12
10
1
2
3
4
5
6
Part
7
8
9
10
VARIABLES MSA:
SESSION WINDOW RESULTS
Both the Part &
the Operator
significantly
effect the part
measurements.
Measurement Error: +/- 0.78
(i.e. 1.55721/2 = 0.78)
SPC/MSA - SUMMARY
The reliability of Control Charts are dependent
on the selection of Rational Subgroups. Pick the
wrong subgroup and the results can be very
misleading.
The reliability of MSAs are dependent on the
selection of the actual Parts. Pick Parts with too
much or too little variation between them and the
results can be very misleading.