variation, run charts and control charts powerpoint
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Colorado 5M WebExColorado 5M WebExVariation, Run Charts, Variation, Run Charts, and Control Chartsand Control Charts
Beth A. Katzenberg, EdM, MBA, CPHQBeth A. Katzenberg, EdM, MBA, CPHQDirector, Corporate Quality & ComplianceDirector, Corporate Quality & ComplianceColorado Foundation for Medical CareColorado Foundation for Medical Care
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Types of variationTypes of variation
Common causeCommon cause Always presentAlways present Inherent in processInherent in process Can predict Can predict
performance with a performance with a range of variationrange of variation
Cannot tell what Cannot tell what specifically causes specifically causes variationvariation
Special causeSpecial cause Abnormal, Abnormal,
unexpectedunexpected Due to causes not Due to causes not
inherent in processinherent in process Can be identified Can be identified
(e.g., change in (e.g., change in shift, weather, shift, weather, process)process)
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You must understand the You must understand the type of variation that is type of variation that is
occurring as this will occurring as this will determine how you determine how you
address the problem.address the problem.
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VariationVariationType of Type of
variationvariation Appropriate action to takeAppropriate action to take
Common Common causecause(predictable, (predictable, stable, in control, stable, in control, inherent in inherent in process)process)
Change the processChange the process Do not react to individualDo not react to individual differences or try to explain differences or try to explain differences between high differences between high and and low numbers low numbers
Special causeSpecial cause(unpredictable, (unpredictable, unstable, out of unstable, out of control)control)
Identify and study special Identify and study special causecause If negative, minimize or If negative, minimize or preventprevent If positive, build into processIf positive, build into process
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PitfallsPitfalls
If only If only common cause variationcommon cause variation and and treat as special cause (tampering), treat as special cause (tampering), leads to greater variation, mistakes, leads to greater variation, mistakes, defectsdefects
If If common cause and special causecommon cause and special cause, , and change the process, leads to and change the process, leads to wasted resources because the wasted resources because the change won’t workchange won’t work
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Tools to identify Tools to identify variationvariation
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Run chartsRun charts
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Run chartRun chartRun Chart
1.07 - 12.07
0
10
20
30
40
50
1.07 2.07 3.07 4.07 5.07 6.07 7.07 8.07 9.07 10.07 11.07 12.07
Time Frame(Month.Year)
Nu
mb
er
Median
Graph of data over timeGraph of data over time
Track performanceTrack performance
Display & identify variationDisplay & identify variation
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Run chart analysis: Run chart analysis: Common cause variation onlyCommon cause variation only
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
Common cause variation around the Common cause variation around the median:median: Only common cause variation present.Only common cause variation present. Output may or may not meet customer/ Output may or may not meet customer/ patient requirementspatient requirements
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Run chart analysis: RunsRun chart analysis: Runs
Run = one or more consecutive data Run = one or more consecutive data points on the same side of the medianpoints on the same side of the median
Excludes data points on the medianExcludes data points on the median
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11 runs
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Expected number of runsExpected number of runs# data pts not
on median
Smallest run
count
Largest run
count
# data pts not
on median
Smallest run
count
Largest run
count
10 3 8 26 9 1811 3 9 27 9 1912 3 10 28 10 1913 4 10 29 10 2014 4 11 30 11 2015 4 12 31 11 2116 5 12 32 11 2217 5 13 33 11 2218 6 13 34 12 2319 6 14 35 13 2320 6 15 36 13 2421 7 15 37 13 2522 7 16 38 14 2523 8 16 39 14 2624 8 17 40 15 2625 9 17 41 16 26
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High probability High probability of special cause variation:of special cause variation:
Too few runsToo few runsToo many runsToo many runs
= 0.05)(
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Run chart analysis: Run Run chart analysis: Run lengthlength
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
Special cause—run length:Special cause—run length:
<20 data points<20 data points (not on median): A run of (not on median): A run of 77 data points on one side of the median data points on one side of the median (either above or below) (either above or below)
20+ data points20+ data points (not on median): A run of (not on median): A run of 88 data points on one side of the median data points on one side of the median
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Run chart analysis: TrendsRun chart analysis: Trends
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
Special cause—Special cause—trends:trends: Consecutive points all Consecutive points all going up or all going going up or all going down. May cross the down. May cross the median. Ignore 2+ median. Ignore 2+ consecutive points that consecutive points that are the same.are the same.
Total # data points on Total # data points on chartchart
# Consecutive points all # Consecutive points all increasing or decreasingincreasing or decreasing
5 to 85 to 8 44
9 to 209 to 20 55
21 to 10021 to 100 66
101 or more101 or more 77 (Pyzdek, 2003)
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Run chart analysis: FreaksRun chart analysis: Freaks
0
2
4
6
8
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
Freaks:Freaks: The presence of more than one The presence of more than one or two dramatic spikes suggests the or two dramatic spikes suggests the process is out of control.process is out of control.
Run charts not as sensitive in identifying, Run charts not as sensitive in identifying, thus may fail to detect.thus may fail to detect.
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Run chart analysis: CyclingRun chart analysis: Cycling
Cycling:Cycling: A zigzag or saw-tooth pattern A zigzag or saw-tooth pattern with 14+ points in a row alternating up with 14+ points in a row alternating up or down. or down.
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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Run charts tipsRun charts tips
How many data points?How many data points?15-20 minimum is preferable15-20 minimum is preferable
Median = 50%/50% split pointMedian = 50%/50% split pointPrecisely half of the data set will be Precisely half of the data set will be
above the median and half below itabove the median and half below it
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Control chartsControl charts
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Control chartControl chart
Time
Qu
alit
y C
ha
rac
teri
sti
c
Low
High
UCL
An indication of a special cause
LCL
X
Run chart with control limitsRun chart with control limits
Determines type of variationDetermines type of variation
Is process stable? Predictable?Is process stable? Predictable?
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Dividing control chart into Dividing control chart into zoneszones
Zone AZone A
Zone BZone B
Zone CZone C
Zone CZone C
Zone BZone B
Zone AZone A
Each zone is 1
sigma wide
UCL
LCL
X
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Identifying special causesIdentifying special causes
Apply independently to each side of the Apply independently to each side of the center line:center line:1 point outside the 3 sigma limit1 point outside the 3 sigma limit2 out of 3 consecutive points in zone A or beyond2 out of 3 consecutive points in zone A or beyond4 out of 5 consecutive points in zone B or beyond4 out of 5 consecutive points in zone B or beyond<20 total data points:<20 total data points: 7 consecutive points in 7 consecutive points in
zone C or beyond on one side of center line zone C or beyond on one side of center line 20+ total data points:20+ total data points: 8 consecutive points in 8 consecutive points in
zone C or beyond on one side of center linezone C or beyond on one side of center line(continued)(continued)
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Identifying special causes, Identifying special causes, cont.cont.
Apply this test to entire chart:Apply this test to entire chart:<21 total data points:<21 total data points: 6 or more points 6 or more points
in a row steadily increasing or decreasingin a row steadily increasing or decreasing21+ total data points:21+ total data points: 7 or more points 7 or more points
in a row steadily increasing or decreasingin a row steadily increasing or decreasing14 consecutive points alternating up and 14 consecutive points alternating up and
down in saw-tooth patterndown in saw-tooth pattern15 consecutive points in zone C (above 15 consecutive points in zone C (above
and below center line)and below center line)
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Deciding which control chart to Deciding which control chart to useuse
Decide on type of data
Continuous (Variables, measurement) data(Values on continuous scale; e.g., time, temperatures, cost)
Attributes (count, discrete) data
(Values in discrete categories; e.g., % waste, # falls, # errors,
% incomplete charts)
More than one observation per
sub-group?NoYes
Fewer than 10 observations
per sub-group?
Are there equal areas of opportunity?
Are the subgroup
sizes equal?
Can both occurrences and non-occurrences
be counted?
NoYes
X -R chart X -S chart XmR chart
NoYes
No NoYes Yes
c-chartp-chartnp-chart u-chart
Average & range chart
Average & standard deviation
(sigma) chart
Individual & moving range
chart
Source: Carey, R. C. and Lloyd, R. C. Measuring Quality Improvement in Healthcare: A Guide to Statistical Process Control Applications, 1995
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Types of dataTypes of dataCount/attributeCount/attribute Measurement/Measurement/
continuouscontinuousCount observations or Count observations or incidents falling into incidents falling into categoriescategories
Whole numbers onlyWhole numbers onlyCannot be converted Cannot be converted to measurementto measurement
Take on values on a Take on values on a continuous scalecontinuous scaleWhole numbers and Whole numbers and decimals decimals Can be converted to Can be converted to countcount
Yes/noYes/no Dead/aliveDead/alive Infected/not infectedInfected/not infected On time/lateOn time/late
Time in minutes or Time in minutes or hourshours Weight in gramsWeight in grams Length of stayLength of stay Blood sugar levelsBlood sugar levels
% c-sections% c-sections % incomplete charts% incomplete charts # pt falls# pt falls # medication errors# medication errors
CostsCosts TemperatureTemperature
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Control chart example 1Control chart example 1
CBC Turn Around Time
40
50
60
70
80
90
100
110
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Day (Not Counting Weekends)
CB
C T
urn
Aro
un
d T
ime
(M
inu
tes)
UCL = 114.6
LCL = 51.9
X = 83.3
Common cause variation only
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Control chart example 2Control chart example 2
Luggage Reported Missing on Flights into Center CityMarch 7 through April 10
0
2
4
6
8
10
12
Day
# P
iece
s M
issi
ng UCL = 9.5
LCL = None
X = 3.2
new hiresnowstorm
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Control chart example 3Control chart example 3
Net Operating Margin for Hospital A 1/05-9/06
-4
-2
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Month
Per
cen
t
UCL = 12.1
X = 4.6
LCL = -2.9
(From: Carey, R. G. & Lloyd, R. C. Measuring Quality Improvement in Healthcare
Common cause variation only; can predict will stay within control limits, if no changes
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Control chart example 4Control chart example 4
Net Operating Margin for Hospital B1/92-9/93
-4
-2
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Month
Per
cen
t
UCL = 9.25
X = 4.60
LCL = -.04
(From: Carey, R. G. & Lloyd, R. C. Measuring Quality Improvement in Healthcare
Out of control, unpredictable
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Just because a process is under Just because a process is under control (common cause variation control (common cause variation only), it does not mean that the only), it does not mean that the
process is meeting expectations. process is meeting expectations.
It just means that the process is It just means that the process is predictable and you are getting predictable and you are getting
consistent performance.consistent performance.
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Control charts tipsControl charts tips
Control limits are not specifications limits Control limits are not specifications limits (specification limits related to customer (specification limits related to customer requirements)requirements)
After removing special causes and After removing special causes and recalculating chart, continue to plot new data recalculating chart, continue to plot new data on this chart, without recalculating control on this chart, without recalculating control limits.limits.Recalculate control limits only when a Recalculate control limits only when a
permanent, desired change has occurred in the permanent, desired change has occurred in the process and only using data process and only using data afterafter the change the change occurredoccurred
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Share the dataShare the data
Team meetingsTeam meetingsPost in break-roomsPost in break-roomsNewslettersNewslettersIntranetIntranet
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Examples of SoftwareExamples of Software
QI Macros QI Macros www.qimacros.comwww.qimacros.comStatSoft StatSoft www.statsoft.comwww.statsoft.comMinitab Minitab www.minitab.comwww.minitab.com
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ReferencesReferences
Carey, R.G. & Lloyd, R.C. Carey, R.G. & Lloyd, R.C. Measuring Quality Improvement in Healthcare: A Measuring Quality Improvement in Healthcare: A Guide to Statistical Process Control Applications, Guide to Statistical Process Control Applications, Quality Resources, 1995.Quality Resources, 1995.
Pyzdek, R. Pyzdek, R. The Six Sigma Handbook: A Complete Guide for Green Belts, Black The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, Belts, and Managers at All Levels, 2003.2003.
The Six Sigma Memory Jogger II, The Six Sigma Memory Jogger II, GOAL/QPC, 2002.GOAL/QPC, 2002.
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Beth Katzenberg, EdM, MBA, CPHQBeth Katzenberg, EdM, MBA, CPHQDirector, Corporate quality & complianceDirector, Corporate quality & compliance
Colorado Foundation for Medical CareColorado Foundation for Medical [email protected]@cfmc.org