Statistical Process Control
(SPC) Overview
SixSigmaTV.Net
SixSigmaTV.Net 2 Statistical Process Control (SPC) Workshop
SPC - Agenda
Statistical Process Control History
Review fundamentals of Control Charts
Understand the impact of variation within
your process
Construct and interpret Control Charts to
monitor process performance
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Control Charts: A Brief History
• Dr. Shewhart of Bell Laboratories introduced Control Charts in 1924.
He developed a theory of variation that states there are two
components to variation:
1. Common cause - the collection of conditions inherent in any process
2. Special cause - identifiable causes or conditions directly responsible for process
shifts
• Dr. Shewhart is credited with the development of the standard
control chart based on 3 standard deviation limits to separate
common cause variation from special cause variation.
• Control Charts became widely used by the US Military during World
War II.
• Dr. Deming introduced Control Charts to the Japanese in the 1950s.
They consider this their turning point to re-building Japan after the
war and making them a formidable leader in the industrial world.
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Control Charting
• What is it?
– A technique for applying statistical analysis to measure, monitor
and control processes
• When do I apply it to my process?
– To establish a baseline of performance.
– To determine if a process is stable and predictable.
– To determine if a shift has taken place.
– To avoid tampering.
– To identify impacts of process variation.
– To monitor and control critical Xs, Ys & implemented solutions.
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Control Charting
• What is it?
– A technique for applying statistical analysis to measure, monitor
and control processes
• When do I apply it to my process?
– To establish a baseline of performance.
– To determine if a process is stable and predictable.
– To determine if a shift has taken place.
– To avoid tampering.
– To identify impacts of process variation.
– To monitor and control critical Xs, Ys & implemented solutions.
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Control Charts - Purpose
• Provide feedback on process performance
– Shows the natural variation of the process
– Provides process monitoring / feedback
– Measures the health of the process
• Identify when process performance changes
– Due to deterioration and neglect
– Due to the introduction of outside influences (“special” causes)
• Allows timely action for process adjustments
Note: Eliminating special cause variation can be one of the easiest ways to reduce variation and improve the process performance.
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Control Charts – When to Use
• Define Phase – To establish a baseline of current
process performance (metrics)
• Analyze Phase – After data collection & MSA, control
charts are used to determine process variation (spread /
standard deviation), location, normality and stability
• Control Phase – To ensure improvements have positively
impacted process variation, location and stability. Also,
monitor sustained gains over long term
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Control Chart Terminology
• Control - operating within natural limits without undue impact
from outside, extraneous, or “special” causes
• Control Limits - statistically calculated boundaries within which a
process in control should operate. – Identify the natural bounds of the process
– Based on the Voice of the Process
– Unrelated to customer specifications
• Control Chart - a sequential time plot tracking process
performance
2.18
7.05
11.93
1.96
3.96
5.96
7.96
9.96
11.96
13.96
0 5 10 15 20
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Control Chart Terminology
• Common Cause Variation – natural variation of a process – Consistent, stable, random variability within the process
– Requires fundamental (systemic) improvement to reduce; usually more difficult to reduce
• Special Cause Variation – variation that is not natural to a process due to an outside influence (“special cause”) that may temporarily or permanently alter the process performance unless identified and addressed. – Identified by changes in process performance, outliers, or unusual patterns in the data
– Requires identifying process changes; usually easier to address and eliminate
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Control Chart - Illustration
{ Normal or expected range of measures
10.04
17.58
25.11
5.40
10.40
15.40
20.40
25.40
30.40
0 5 10 15 20
Out-of-control point
Time plot of sequential process measurements
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Control Limits vs. Spec Limits
Control Limits
Defined based on process
performance (+/- 3 estimated
standard deviations from the
mean).
Help determine if your process is
“in control” (without special
cause variation).
Plotted on control charts.
Change when there is a verified,
significant change to your
process.
Represent the voice of the
process.
Customer Spec Limits
Defined based on feedback
from the customer(s).
Help determine if your process
is producing defects.
Plotted on histograms (not
control charts).
Change when your customers
say they do!
Represent the voice of the
customer.
Determine product functional
requirements
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Control Charts – Data Types
Variable/Continuous ( Measurable ) • Processing Cycle Time ( days, weeks, months )
• Customer Wait Time ( seconds, minutes, hours )
• Can you think of other variable data types in your organization?
Attribute / Discrete ( Defects ) • Number of Errors on Patient Records ( missing or incorrect
information )
• Can you think of other attribute data types in your organization?
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Control Chart: Illustration
Common Cause Variation
Sample
Sa
mp
le M
ea
n
332925211713951
400
300
200
100
__X=262.4
UC L=408.5
LC L=116.3
Sample
Sa
mp
le R
an
ge
332925211713951
600
450
300
150
0
_R=200.5
UC L=457.4
LC L=0
Xbar-R Chart of Distance
Subgroup Variation
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The Family of Control Charts
• Continuous/Variable data
• X-bar/R charts for sample averages
• ImR charts for individual items
• X-bar/S charts for large samples using standard deviation
• Always measurable with a tool
– Examples: stopwatch, caliper, scale
• Attribute/Discrete
• p-chart for percent or proportions of defective items
• np-chart for number of defective items
• u-chart for defects per unit
• c-chart for number of defects
• Operational definitions are always required
– Examples: good/bad, pass/fail, correct/incorrect
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Guidelines for Determining Control Chart Usage
Type Appropriate Data Examples of Use
c-Chart
u-Chart
c = counts of relatively infrequent events. To chart defects with
constant subgroup size.
u = counts of relatively infrequent events. To chart defects per
unit with constant or variable subgroup size.
Number of miss applied payments.
Number of lost checks.
Number of miss applied payments per week @
FC.
Number of fields missing info. on loan app.
p-Chart
np-Chart
p-Chart: To chart proportion or percent defective with subgroup
size constant or variable.
np-Chart: To chart number of defective units with constant
subgroup size. (Note: A defective may contain many defects.)
p-Chart: percent defective, percent of mis-routed
mail items from FC (sample sizes may vary),
percent of late loan payments.
np-Chart: Number of defective applications per
batch (sample sizes are constant).
I-Chart
I-MR Chart
Measurable data collected on individual items (i.e. the subgroup
size is one at any one time).
Individual charts are some of the easiest to create, and can be used
in a wide variety of situations but require larger shifts to highlight
or detect a change. Based on the standard normal distribution.
Cycle time for a process (the item may be a
single loan).
Amount of money used in the ATM per day.
Loan interest rates per day.
X bar and
Range Charts
X-Bar: displays the subgroup average. Based on standard normal
distribution.
R: range (variation) within & between the subgroups.
X-Bar and R Charts should be used in conjunction to determine
whether a process is in control.
X-Bar:
Average length of time customers wait to be
served (multiple customers used).
Cycle time for a process (in this case, a group of
loans may be monitored and the average time and
range tracked).
Control Chart Roadmap D
iscre
te D
ata
C
ontinuous D
ata
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Discrete/Attribute Chart Decision Tree
C Chart defect
count
U Chart,
defects/ unit
NP Chart, #
defective
P Chart, % or
proportion
Count or Classification
(Discrete/Attribute Data)
Defects
Fixed
sample sizes
Variable
sample sizes
Defective Units
Fixed
sample sizes
Variable
sample sizes
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Continuous/Variable Chart Decision Tree
Measurement
(Continuous/Variable Data)
Subgroup Size of 1
I-Chart / I-MR
Subgroup Size
2-10
X-bar & R
Subgroup Size
> 10
X-bar & S
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P-Chart
• Used whenever monitoring proportion or percent
defective
• Some uses of the p-chart in transactional applications
are:
– Account errors
– Defective patient records
– Proportion of statements with errors
– Missing items
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P-Chart: Exercise
A Registrar processes patient records and sends them over to Pre-Op. Construct a p-chart and see what percent of records are defective.
Day 1 2 3 4 5 6 7 8 9 10
Records 28 34 21 30 25 31 40 29 30 32
Bad 7 8 7 9 9 11 14 6 8 10
As the Patient Registrar Manager,
what are your next steps?
Day 11 12 13 14 15 16 17 18 19 20
Records 28 29 33 39 23 29 42 29 33 27
Bad 8 8 11 14 6 8 16 6 7 8
P-Chart for Errors
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0.295751634
0.032260581
0.559242687
-0.100
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
P -
bad
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U-Chart
• Used whenever monitoring number of
defects per unit.
• Some uses of the U-Chart in transactional applications
are:
– Number of account errors per customer or batch.
– Number of defects on each application processed.
– Number of errors on each patient record processed .
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U-Chart: Exercise
Now that you now the percent of defective patient records being received from your Registrar, how many defects per record are we getting?
Day 1 2 3 4 5 6 7 8 9 10
Records 28 34 21 30 25 31 40 29 30 32
Defects 37 18 27 19 14 21 34 16 28 40
Day 11 12 13 14 15 16 17 18 19 20
Records 28 29 33 39 23 29 42 29 33 27
Defects 18 28 41 45 16 18 26 16 27 38
As the Pre-Op Manager,
what are your next steps?
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U-Chart: Exercise
0.861
0.325
1.397
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.100
1.200
1.300
1.400
1.500
U -
defe
cts
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I-MR Chart (Individual and Moving Range)
Usage when:
There is no basis for
subgrouping.
Each measurement represents
one batch.
Production rate is slow such that
measurements are easy to
gather or widely spaced in time.
I-MR chart is appropriate for continuous data and focuses
on the variation between individual measures.
0Subgroup 50 100
5
10
15
Ind
ivid
ua
l V
alu
e
Mean=10.04
UCL=16.25
LCL=3.831
0
1234
567
89
Mo
vin
g R
an
ge
1
R=2.334
UCL=7.627
LCL=0
I and MR Chart for Processing Time
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ImR-Chart: Exercise
Now that you now how many defects per record you are getting, how much time is your team spending per week reworking the mistakes?
Day 1 2 3 4 5 6 7 8 9 10
Records 28 34 21 30 25 31 40 29 30 32
RW Time (hours)
2 8 6 5 3 4 6 3 2 3
Day 11 12 13 14 15 16 17 18 19 20
Records 28 29 33 39 23 29 42 29 33 27
RW Time (hours)
8 5 5 3 2 4 4 6 3 6
As the Pre-Op Manager,
what are your next steps?
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ImR-Chart: Exercise – RW Time
Mean CL: 4.40
-1.199104143
9.999104143
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
Ind
ivid
uals
: R
W T
ime
2.105263158
0
6.87849944
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
MR
: R
W T
ime
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Xbar-R Chart
R chart:
Shows changes in the "within"
subgroup variation.
Asks "Is the variation in the
measurements within
subgroups stable?"
X-bar chart:
Shows changes in the average
value of the process.
Asks "Is the variation between
the averages of the subgroups
more than that predicted by
the variation within the
subgroups?"
Xbar-R chart is appropriate for continuous data when it is
practical to collect frequent samples of subgroups.
0Subgroup 10 20 30
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
Sa
mple
Me
an
Mean=10.09
UCL=13.08
LCL=7.108
0
5
10
Sa
mp
le R
an
ge
R=4.099
UCL=9.351
LCL=0
Xbar/R Chart for Processing Time
Most sensitive (powerful) chart for
tracking changes in the mean.
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