11

Colorado 5M WebExColorado 5M WebExVariation, Run Charts, and Variation, Run Charts, and Control ChartsControl 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

22

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, unexpectedAbnormal, unexpected Due to causes not Due to causes not

inherent in processinherent in process Can be identified Can be identified

(e.g., change in shift, (e.g., change in shift, weather, process)weather, process)

33

You must understand the type You must understand the type of variation that is occurring of variation that is occurring

as this will determine how you as this will determine how you address the problem.address the problem.

44

VariationVariation

Identify and study special cause If negative, minimize or prevent If positive, build into process

Special cause(unpredictable, unstable, out of control)

Change the process Do not react to individual differences or try to explain differences between high and low numbers

Common cause(predictable, stable, in control, inherent in process)

Appropriate action to takeType of variation

55

PitfallsPitfalls

If only If only common cause variationcommon cause variation and treat and treat as special cause (tampering), leads to as special cause (tampering), leads to greater variation, mistakes, defectsgreater variation, mistakes, defects

If If common cause and special causecommon cause and special cause, and , and change the process, leads to wasted change the process, leads to wasted resources because the change won’t workresources because the change won’t work

66

Tools to identify variationTools to identify variation

77

Run chartsRun charts

88

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

99

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 median:Common cause variation around the 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

1010

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

1111

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

1212

High probability High probability of special cause variation:of special cause variation:

Too few runsToo few runsToo many runsToo many runs

= 0.05)(

1313

Run chart analysis: Run lengthRun chart analysis: Run length

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 (either data points on one side of the median (either above or below) 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 mediandata points on one side of the median

1414

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—trends:Special cause—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.

45 to 8

7101 or more621 to 10059 to 20

# Consecutive points all increasing or decreasingTotal # data points on chart

(Pyzdek, 2003)

1515

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 or The presence of more than one or two dramatic spikes suggests the process is two dramatic spikes suggests the process is out of control.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.

1616

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 or with 14+ points in a row alternating up or down. 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

1717

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 point Precisely half of the data set will be above the Precisely half of the data set will be above the

median and half below itmedian and half below it

1818

Control chartsControl charts

1919

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?

2020

Dividing control chart into zonesDividing control chart into zones

Zone A

Zone B

Zone C

Zone C

Zone B

Zone A

Each zone is

1 sigma wide

UCL

LCL

X

2121

Identifying special causesIdentifying special causes

Apply independently to each side of the center Apply independently to each side of the center line:line: 1 point outside the 3 sigma limit1 point outside the 3 sigma limit 2 out of 3 consecutive points in zone A or beyond2 out of 3 consecutive points in zone A or beyond 4 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)

2222

Identifying special causes, cont.Identifying special causes, 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 in a 6 or more points in a

row steadily increasing or decreasingrow steadily increasing or decreasing 21+ total data points:21+ total data points: 7 or more points in a 7 or more points in a

row steadily increasing or decreasingrow steadily increasing or decreasing 14 consecutive points alternating up and 14 consecutive points alternating up and

down in saw-tooth patterndown in saw-tooth pattern 15 consecutive points in zone C (above and 15 consecutive points in zone C (above and

below center line)below center line)

2323

Deciding which control chart to useDeciding which control chart to use

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 data

Costs Temperature

% c-sections % incomplete charts # pt falls # medication errors

Time in minutes or hours Weight in grams Length of stay Blood sugar levels

Yes/no Dead/alive Infected/not infected On time/late

Take on values on a continuous scaleWhole numbers and decimals Can be converted to count

Count observations or incidents falling into categories

Whole numbers onlyCannot be converted to measurement

Measurement/continuousCount/attribute

2525

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

2626

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

2727

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

2828

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

2929

Just because a process is under control Just because a process is under control (common cause variation only), it does (common cause variation only), it does not mean that the process is meeting not mean that the process is meeting

expectations. 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.

3030

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 recalculating After removing special causes and recalculating chart, continue to plot new data on this chart, chart, continue to plot new data on this chart, without recalculating control limits.without recalculating control limits. Recalculate control limits only when a permanent, Recalculate control limits only when a permanent,

desired change has occurred in the process and desired change has occurred in the process and only using data only using data afterafter the change occurred the change occurred

3131

Share the dataShare the data

Team meetingsTeam meetingsPost in break-roomsPost in break-roomsNewslettersNewslettersIntranetIntranet

3232

Examples of SoftwareExamples of Software

QI Macros QI Macros www.qimacros.comwww.qimacros.com StatSoft StatSoft www.statsoft.comwww.statsoft.com Minitab Minitab www.minitab.comwww.minitab.com

3333

ReferencesReferencesCarey, R.G. & Lloyd, R.C. Carey, R.G. & Lloyd, R.C. Measuring Quality Improvement in Healthcare: A Guide to Measuring Quality Improvement in Healthcare: A Guide to

Statistical Process Control Applications, 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 Belts, and The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, Managers at All Levels, 2003.2003.

The Six Sigma Memory Jogger II, The Six Sigma Memory Jogger II, GOAL/QPC, 2002.GOAL/QPC, 2002.

3434

Beth Katzenberg, EdM, MBA, CPHQBeth Katzenberg, EdM, MBA, CPHQDirector, Corporate quality & complianceDirector, Corporate quality & complianceColorado Foundation for Medical CareColorado Foundation for Medical Care

bkatzenberg@cfmc.orgbkatzenberg@cfmc.org