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Section XI, Control
Concepts
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What is SPC?
Description: Involves the use of statistical signals to identify sources of variation, to maintain or improve performance to a higher quality level, typically through the use of control charts.
Process ControlStatistical
“Quality control by statistical methods is now so extensively applied in all lines of industry, and in all sections of the United States, that everyone who is interested in manufacturing should also have a definite interest in the methods.”
-Control Charts, E.S. Smith - 1947
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Statistical control - shows if the inherent variability of a process is being caused by common causes of variation, as opposed to assignable causes.
Why only common cause variation?
Assignable Cause?
Assignable Cause?
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1. Minimize cost by making economical decisions
2. Attain a consistent process or improve a process
3. Identify when a process has changed
4. Allow everyone to contribute to process improvement
Goals of SPC
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A control chart is simply a distribution of values, turned 90 degrees on its side...
How distributions relate to control charts
Distribution of values
This gives the advantage of seeing when an event occurs. It is highly recommended to use a histogram and control chart together.
…and stretched out over time.
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Warning indicators a.k.a Natural Process Limits (NPL) Usually drawn on the chart at +3
(UCL) and -3 (LCL) from the process average.
Defines the process boundaries of your measured subgroups
Signals you if your process is operating in a state of statistical control, or if it is out of control
Control limits
UNPL - Upper Natural Process LimitUCL - Upper Control Limit
LNPL - Lower Natural Process LimitLCL - Lower Control Limit
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Control chart example
Is there special cause variation present? Does it look normal?
Is there a pattern?Is the process in control?
When do I make a change to the process?
Remember Walter Shewhart? He is credited with the control chart. We will refer to
these as the Shewhart Methods.
I n d i v i d u a l s C h a r t
U C L = 0 . 3 8 6 4
L C L = - 0 . 0 8 1 4
C E N = 0 . 1 5 2 5
- 0 . 2- 0 . 1
00 . 10 . 20 . 30 . 40 . 5
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0
M o v i n g R C h a r t
U C L = 0 . 2 8 7 2 7
L C L = 0 . 0
C E N = 0 . 0 8 7 9 3
- 0 .1
- 0 . 0 5
00 . 0 5
0 . 1
0 . 1 5
0 . 20 . 2 5
0 . 3
0 . 3 5
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0
Is measurement variation having a big effect?
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Control Charts vs. Histograms
0
1
2
3
4
5
6
7
8
18.0 to <= 18.8 18.8 to <= 19.6 19.6 to <= 20.4 20.4 to <= 21.2 21.2 to <= 22.0
# O
bser
vatio
ns
Weekly Mileage
Histogram
15
16
17
18
19
20
21
22
23
24
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Weeks
Gas
Mile
age
Histogram of gas mileage data
Control chart based on gas mileage
data
Same data shown using different tools
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1. Analyze where SPC should be done.
2. Decrease any obvious variability3. Verify Gage R&R is acceptable4. Create sampling plan with rational
subgroups5. Create control chart – allow only
common cause variability6. Run the process and verify control7. Calculate process capability8. Monitor process or improve if
necessary9. Pre-control10. Continue to monitor or improve
How to apply SPC to a process
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You always need to take random samples.
1. At random times2. At regular intervals
◦ Time based◦ Quantity based
3. Use “Rational Subgroups”◦ Small variation within groups◦ Large variation between groups
(sources of variation that occur over time)
When do I get the data?
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Let’s remember the assumptions: normal, homogeneous, need rational subgroups1. Typical Shewhart methods will
state rational subgroups of 4, 5, or 6 if you have a lot of data recorded periodically, or 100% for small sample sets
2. Based on process capability
How much data do I need?
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Control chart decision tree
Mea
sure
men
ts
Counts
Median, RangeAverage, Range
Average, sigma
Run chart
IX control chart
np control chart
p control chart
c chart
u chart
n = 2 to 9
n = 10 or more
n = 1non-normal data
normal data
n fixed
n varies
n fixed
n varies
Count pieces
or units
Count occurences
Varia
bles
Attributes
Mea
sure
men
ts
Counts
Median, RangeAverage, Range
Average, sigma
Run chart
IX control chart
np control chart
p control chart
c chart
u chart
n = 2 to 9
n = 10 or more
n = 1non-normal data
normal data
n fixed
n varies
n fixed
n varies
Count pieces
or units
Count occurences
Varia
bles
Attribu
Mea
sure
men
ts
Counts
Average, Range
Average, sigma
Run chart
IX control chart
np control chart
p control chart
c chart
u chart
n = 2 to 9
n = 10 or more
n = 1non-normal data
normal data
n fixed
n varies
n fixed
n varies
Count pieces
or units
Count occurences
Varia
bles
Attributes
Variable: data provides the most information
Attribute: Needs a lot of data
Control chart – The basic tool of SPC
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1. Select a process measurement2. Stabilize process and decrease
obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the
points8. Calculate the control limits and
analyze for control9. Calculate the capability and
analyze for capability10. Monitor the process11. Continuous Improvement
11 step procedure for Average and Range control charts
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Average and Range Chart exercise
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Pronounced “individual x and moving range”
The most common chart used with limited data
Each point on the chart represents an individual value
Used when subgroup samples need to be 1
Works well with processes that have trends that develop and disappear quickly
What is an IX and MR chart?
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1. Select a process measurement2. Stabilize process and decrease
obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the
points – at least 10 measurements before calculations
8. Calculate the control limits and analyze for control - histogram
9. Calculate the capability and analyze for capability
10. Monitor the process ( )11. Continuous Improvement
11 step procedure for IX-MR control charts
andRx
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How to calculate control limits
For the moving range control chart:
For the individual control chart:
RMDLCLRMDUCL
LimitsControl
nMR
RrangeAverage
MR
MR
3
4
M
RMExLCLRMExUCL
LimitsControl
nx
xx
Average
x
x
2
2
estimate s by UCL-LCL 6
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The data below was collected as part of a development process
The tolerance is .655 to .645
IX & MR exercise data
0.6480.6460.6490.6500.6480.6510.6500.6490.6460.652
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1020
1525
3530
0
RUCLXUCL LCL
PART
#
DATE
FEAT
URE
INDI
VIDU
ALS
X &
MOV
ING
RANG
E CH
ART
OPE
RATO
R
OP.
#
ORD
ER #
MAC
H.
SPEE
D
MAT
.
FEED
TOO
L / W
HEEL
TYPE
RUN
CHAR
T
CONT
ROL
CHAR
T
CPK
CR
Comments Section
S/N
or P
air #
Individuals X Chart Moving Range Chart
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1. Select a process measurement2. Stabilize process and decrease
obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the
points*8. Calculate the control limits and
analyze for control*9. Calculate the capability and
analyze for capability*10. Monitor the process11. Continuous Improvement
11 step procedure for p control charts
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7. Chart the points◦ Sets scales for control chart◦ Calculate each subgroup’s
proportion nonconforming◦ Plot the proportion
nonconforming on the chart8. Calculate control limits and
analyze for control◦ Plot your control limits
p chart control limits
npppUCLp
)1(3
npppLCLp
)1(3
You can use these equations – but it’s better to let the computer do it.
nnp
p
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9. Calculate the capability and analyze for capability
◦ Capability is based on average defective
◦ Is UCL or LCL within your goal value? If UCL > USL or LCL < LSL then
Cpk<1 If UCL < USL or LCL > LSL then
Cpk>1
p chart control limits
nnp
p
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This data represents the number of errors found in purchase orders over a 30 week period.
p chart example
1. Complete a p chart.
2. What can you tell from the data?
3. Complete a np chart.
4. What can you tell from the data?
5. How are these charts different?
# of P.O's ErrorsWeek 1 54 7Week 2 34 5Week 3 54 6Week 4 47 9Week 5 67 7Week 6 54 6Week 7 39 13Week 8 36 2Week 9 46 15Week 10 56 11Week 11 55 12Week 12 47 9Week 13 39 6Week 14 60 8Week 15 48 4Week 16 43 14Week 17 47 5Week 18 52 9Week 19 57 5Week 20 43 4Week 21 49 6Week 22 67 3Week 23 55 2Week 24 45 1Week 25 49 2Week 26 67 3Week 27 56 4Week 28 45 0Week 29 55 1Week 30 67 0
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PART
#FE
ATUR
E
ATTR
IBUT
E CO
NTRO
L CH
ART
Order # & DateOP
ERAT
ION
CHAR
T TY
PE:
P (
Perc
ent D
efec
tive)
Sub
Grou
p #
Sam
ple
Size
No. o
fDe
fect
ives
Prop
ortio
nDe
fect
ive
UCL
LCL
Proportion Defective Units
.0.10
.20
.30
.40
.50
.60
110
98
76
54
32
1116
1514
1312
2322
2120
1918
1730
2928
2726
2524
3635
3433
3231
37
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Normal Distribution50%50%
-1-2-3 +1 +2 +30
± .68261
± .9973 3
± .95462
z value = distance from the center measured in standard deviations
ZonesA B C C B A
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The process creating the data on the control chart is operating under statistical control.
Produces a graphic that will have a high center, and sloping sides.
The points tend to cluster around the center of the chart, show random variation, with only a few points spreading out toward the control limits.
Points look random – good but not too good ◦ Here is an example of a process running
in statistical control:
Normal Patterns
Normal Pattern.4005
.3985
.3990
.3995
.4000
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Data that fluctuates excessively and fails to center itself around the centerline is characteristic of assignable or non-normal variation.
Several of these patterns have been classified. ◦ aka “The Western Electric Rules”
The next few pages describe the most common patterns seen in processes.
Not necessarily a bad thing.◦ Heading in right direction◦ Result of improvement
Non-normal Patterns
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A random part located outside of the control limits (1 point outside of zone A)
Occurs for a number of reasons Any reason requires investigation before
continuing to run the job.
Reasons to occur: ◦ An incorrect machine adjustment that is
immediately noticed and fixed◦ Errors in measurement or plotting◦ A cutting tool that “caught a chip”◦ May be normal variation
Random Parts Out of Control – Freaks (Rule 1)
Random Patterns.1254
.1246
.1248
.1250
.1252
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Occurs when the points occur in clusters
Can be done visually Can be done statistically (2 of
3 points in zone A or beyond – 4 of 5 points in zone B or beyond)
Grouping can be caused by: ◦ Differences in setups◦ Tools moving◦ Method problems
Grouping (Rule 2 and 3)
Grouping.7510
.7490
.7495
.
.7505
.7500
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Set of seven or more consecutive points that are all on one side of the center line indicating the center has changed (8 or more points in zone C or beyond, all on one side of the center line)
Usually temporary / sudden A sudden shift in the level of parts shown
on a chart can be good or bad◦ Good: if the shift is bringing the parts back to
split limit◦ Bad; if the shift is taking the parts away from
split limit Sudden shifts can be caused by:
◦ A change of material, new operator or inspector, an offset change, two or more machines/suppliers on one chart
Sudden Shift in Level – Shifts(Rule 4)
Sudden Shift in Level.0950
.0930
.0935
.0940
.0945
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Defined as consecutive points on a control chart that are steadily increasing or decreasing in value (6 or more consecutive points that either increase or decrease in value – also, 10 out of 11 consecutive points that either increase or decrease in value )
Usually gradual Trends can be caused by:
◦ Air, coolant, or part temperatures that are steadily increasing or decreasing.
◦ Tool wear that allows a part to steadily increase or decrease in size
◦ A fixture that is constantly wearing, causing the parts to steadily increase or decrease in size.
◦ Operator fatigue
Trends – Runs (Rule 5)
Trends.3140
.3120
.3125
.313
.3135
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There are no number rules to identify cycles
Cycles are defined as repeated patterns in a process
Cycles can be caused by: ◦ Machines that are continually heating up
and cooling down◦ Air temperatures in the shop that rise to
a certain point, then are reduced quickly as cooling systems are activated
◦ Tool wear that allows a part to increase or decrease in size until an offset is made
◦ Seasonal
Cycles
Cycles.5005
.4985
.4990
.4995
.5000
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Can be identified by looking for a majority of parts hugging the center line. (15 or more consecutive points inside zone C)
Will have a "sawtooth" look to it.
Stratification can be caused by: ◦ Gaging concerns (rule of 10s)◦ Honest reporting?
Stratification (Rule 6)
Mixtures.4785
.4765
.4770
.4775
.4780
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Can be identified by looking for a majority of parts falling very close to the control limits, with very few in the center of the chart. (5 or more consecutive points outside zone C)
Will have a "sawtooth" look to it. Typically, this type of situation is
actually a combination of two separate distributions within a process, one at high limit, and one at low limit.
Mixtures can be caused by: ◦ Two different gages being used◦ Output from two or more machines mixed
together on the same chart.◦ Gaging concerns (rule of 10s)◦ Honest reporting?
Mixtures (Rule 7)
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Use the right level of control that brings long term stability to the process that you are improving.
There will most likely be a tradeoff between the effectiveness, effort and cost of the control technique.
Poka-Yoke (Mistake Proofing)
Statistical Process Control (SPC)
Verbal Instructions (Training, Sounds, etc….)
Written Procedures (SOPs, FMEAs, etc….)
Finding The Right Level Of Control
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SOP as the control Exercise:Draw a rectangle.
Draw a semi- circle along the left edge.
Draw another rectangle along the right edge of the rectangle.
Draw a trapezoid along the right edge of that rectangle.
Draw a rectangle along the right edge of the trapezoid.
What is your result?
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Class Exercise
2 1 3 4 5
Draw the described figure
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A Control Plan is simply a plan that documents your process◦ Intended to make the process
robust◦ Assures that we meet our customer
expectations ◦ It contains Key Input and Output
Variables◦ Data comes from process map,
fishbone (C-N-X), standard operating procedures, FMEA and error proofing
The Control Plan
Initial: Modified:Date (Orig):Date (Rev):
Size Freq.Oper Process Output
Verification Methods
Tol.Process Name / Operation
Description
Final:Plan StatusControl Plan No:Part Number:
Process Champion:Process Owners:
Process Owners / Responsibilities
Ow
ner B
Ow
ner C
Ow
ner D
Ow
ner E
Part Name: Black Belt
Ow
ner A
Evaluation Method / Verifier
SampleControl Method / Specification
Reaction Plan for when Control Methods Failed
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Example Control Plan
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