l16: beyond statistical process control: advanced charts ... · l16: beyond statistical process...

11/18/2009

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Note: we are assuming excel skills…so buddy up withsomeone who has strong skills if yours are not as strong …thanks!

L16: Beyond Statistical Process Control: Advanced Charts for Healthcare

l d i i

API and CT Concepts, 2009

Lloyd P. Provost, Associates in Process Improvement

Sandra Murray, CT Concepts

L16: Beyond Statistical Process Control: Advanced Charts for Healthcare

This session will explore some of the more advanced uses for statistical process control (SPC) charts for health care data. Some issues to be discussed include how to tell if anything has improved when “yucky” events are already rare; why some control charts have such narrow limits with all of the data outside the limits; and how to factor in seasonalwith all of the data outside the limits; and how to factor in seasonal impacts on data. Our journey will include the use of T and G charts for rare events data, Prime charts for dealing with over dispersion in data, adjustments for autocorrelation, using changing center lines on control charts, and the use of the CUSUM control chart.

Session Objectives: • Select the appropriate SPC chart for rare events data

Id if h i i i CUSUM l h


2

• Identify when it is most appropriate to use a CUSUM control chart

• Describe when to use a prime chart for over‐dispersion in data

• Identify autocorrelation and describe how to deal with it using a Shewhart control chart

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Introduction

Our Process– Will provide some context for Shewhart Charts

– Then address each 4 of objectives

– We will use case studies and Excel on your PC’s to give you practice building the charts


3

SHEWHART CHART:What Is It?

• The Shewhart chart is a statistical tool used to distinguish between variation in a measure due to common causes and variation due to special causes. • Commonly called “control chart.” • A more descriptive name might be “learning charts” or “system performance charts”

• Format:•Data is usually displayed over time•Data usually displayed in time order


•Shewhart chart will include:•Center line (usually mean)•Data points•Statistically calculated upper and lower limits

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What Does a Shewhart Chart Look Like? Coding Errors per 20 Records12 10 14 12 19 8 15 10 8 6 21 10 5 9 11 6 7 10 13 11 9 3 7 6 10Defects

c‐chart Set 1: UCL=19.60, Mean=10.08, LCL=0.56 (n=1)

25

30

Straight limits indicate equal subgroup size

# Co

ding

Errors

10

15

20 UCL

Mean

API and CT Concepts, 2009Sequential Subgroups of 20 Records

#

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

0

5

LCL

% of C-Sections Performed Due to Fetal DistressJan4015

Feb8015

Mar7020

Apr6520

May8525

Jun7015

Jul6520

Aug5510

Sep10011

Oct5515

Nov7010

Dec8012

Jan350

Months# C-SecFetal Ind

p chart

40

45

50

Varying limits indicate unequal subgroup size

20

25

30

35

UCL = 36.70

Mean = 21.61

API and CT Concepts, 2009Jan

Feb Mar AprMay Ju

n Jul

Aug Sep OctNov Dec Ja

n0

5

10

15

LCL = 6.52

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What do we use a Shewhart chart for?

• Learn how much variation exists in processA t bilit d d t i i t• Assess stability and determine improvement strategy (common or special cause strategy)

• Monitor performance and correct as needed • Find and evaluate causes of variation• Tell if our changes yielded improvementsS if i t “ ti ki ”


• See if improvements are “sticking”

Shewhart’s Theory of Variation

• Common Cause: causes that are inherent in the process, over time affect everyone working in the process, and affect all outcomes of the process– Process stable predictableProcess stable, predictable– Action: if in need of improvement must redesign

• Special cause: causes that are not part of the process all the time, or do not affect everyone, but arise because of special circumstances


– Process unstable, not predictable– May be evidence of improvement (change we tested working)

– Action: go investigate special cause and take appropriate action

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Standard Rules for Detecting Special Cause


Unplanned Returns to Ed w/in 72 HoursM

41.7817

A43.89

26

M39.86

13

J40.03

16

J38.01

24

A43.43

27

S39.21

19

O41.90

14

N41.78

33

D43.00

20

J39.66

17

F40.03

22

M48.21

29

A43.89

17

M39.86

36

J36.21

19

J41.78

22

A43.89

24

S31.45

22

MonthED/100Returns

u chart

1.0

1.2

How Do We Detect Special Cause?

Rat

e pe

r 100

ED

Pat

ient

s

0.6

0.8

UCL = 0.88

Mean = 0.54

API and CT Concepts, 20091 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190.0

0.2

0.4

LCL = 0.19

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ACEI for LVSD: All Data Within Limits But Still Special Causep char t

90

100

110

UCL = 101.98

Per

cent

Com

plia

nce

70

80

90Mean = 88.55

LCL = 75.12


J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M

50

60

Type of Data

Count or Classification (Attribute Data) Qualitative data in terms of an integer (# errors #

Continuous (Variable Data) Quantitative data in the form of a measurement

Shewhart Chart Selection Guide

-

Qualitative data in terms of an integer (# errors, # nonconformities or # of items that passed or failed) Discrete: must be whole number when originally collected (can’t be fraction or scaled data when originally collected)This data is counted, not measured

Count (nonconformities)1,2,3,4, etc.

Classification (nonconforming)either/or, pass/fail, yes/no

Equal area of Unequal area Unequal or equal

Quantitative data in the form of a measurementTime, money, scaled data i.e. length, height, weight, temperature, mg. and throughput (volume ofworkload/ productivity)

Subgroup sizeUnequal or equal subgroup

Each subgroup is composed of a single data value

Each subgroup has more than one data value


Equal area ofopportunity

Unequal area of opportunity

Unequal or equal subgroup size

Subgroup size of 1 (n=1)

equal subgroup size (n>1)

C Chart U Chart P ChartI Chart (also known as X Chart) X Bar and S

Number of nonconformities

Nonconformities per unit

Percent nonconforming

Individual measurement Average and standard deviation

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T and G Charts for Rare Events

• The problem and examples

• Intro to template

• Work Case Study – (10)

• Debrief ‐ Tips, issues, references


The Problem: How do we tell if we are improving when undesirable events are rare anyway?

Month # Med Errors # Doses #Doses/1000 Notes

N 06 3 24222 24.222D 1 23616 23 616A D 1 23616 23.616J 07 4 23072 23.072F 2 19439 19.439M 2 24568 24.568A 3 21020 21.02 Chg 1 test and Imp, Ch 2 testM 2 28754 28.754 Chg 2 TestJ 2 23390 23.39 Chg 2 ImpJ 1 28475 28 475 Chg 3 Lg Test

AverageBefore=3

Average


J 1 28475 28.475 Chg 3 Lg TestA 2 22079 22.079 Chg 3 ImpS 0 29206 29.206O 1 23390 23.39N 0 28475 28.475D 1 23390 23.39

Average After=1.3

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The Problem: when undesirable events are rare even a standard run or Shewhart control chart may not be very helpful

Harmful Medication Error Rate per 1000 Doses Dispensedu chart

nd Im

p, C

h 2

test

Chg

2 T

est

Chg

2 Im

p

Chg

3 L

g Te

st

Chg

3 Im

p0.4

rror R

ate/

1000

Dos

es

UCL = 0.23

Chg

1 te

st a

n0.2

0.3


Med

E

Mean = 0.07

N 06 D J 07 F M A M J J A S O N D

0.1

0.0

How Do You Know You Need to View Data Differently?

• Have too many zeros (>25% of data points 0)

• Have no lower limitPercent C‐Sections

p‐chart (%) Mean=15.84100

Percen

t

40

50

60

70

80

90

UCL

API and CT Concepts, 2009Sequential Months

P

Mo

95/1

95/2

95/3

95/4

95/5

95/6

95/7

95/8

95/9

95/10

95/11

95/12

96/1

96/2

96/3

96/4

96/5

96/6

96/7

96/8

96/9

96/10

96/11

96/12

97/1

97/2

97/3

97/4

97/5

97/6

97/7

97/8

97/9

97/10

97/11

97/12

98/1

98/2

98/3

98/4

98/5

98/6

98/7

98/8

98/9

98/10

98/11

98/12

99/1

99/2

99/3

99/4

99/5

99/6

99/7

99/8

99/9

99/10

99/11

99/12

00/1

00/2

00/3

00/4

00/5

00/6

00/7

00/8

00/9

0

10

20

30

Mean

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When Will This Happen?Classification Data: Guidelines for Selecting Subgroup Size for an Effective P chart

Average PercentNonconforming

Units (pbar)

Minimum Subgroup Size (n) Required to Have

< 25% zero for p'sMinimum Subgroup Size

Guideline(n>300/pbar)

Minimum Subgroup Size Required to Have

LCL > 00.1 1400 3000 90000.5 280 600 18001.0 140 300 9001.5 93 200 6002 70 150 4503 47 100 3004 35 75 2205 28 60 1756 24 50 1308 17 38 104

10 14 30 8112 12 25 66


12 12 25 6615 9 20 5120 7 15 3625 5 12 2830 4 10 2240 3 8 1450 2 6 10

Note: for p>50, use 100‐p to enter the table (e.g. for p=70% use table p of 30%, for p=99% use table p of 1%, etc.) Source: The Data Guide: L Provost and S. Murray, 2009

When Will This Happen?For Count Data

(U chart: errors or occurrences per unit: rate data)

• If center line less than 9 will be no lower limit• If center line less than 9 will be no lower limit

• If center line less than 1.4 will have too many 0’s

• What Can We Do?


What Can We Do?– Increase subgroup size

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One Way to Transform Data: Limits: Appropriate Vs. Too Small Subgroup SizeAggregate Level: Total C‐Section Rate By Quarter

80

90

100

p‐chart (%)

% C‐Sections By Month % C‐Sections Quarter

80

90

100p‐chart (%)

60

70

%

30

40

50

UCL

C‐Section Ra

te%

30

40

50

60

70

UCL

%

API and CT Concepts, 2009 Sequential Quarters

95/1

95/2

95/3

95/4

96/1

96/2

96/3

96/4

97/1

97/2

97/3

97/4

98/1

98/2

98/3

98/4

99/1

99/2

99/3

99/4

00/1

00/2

0

10

20Mean

30

Sequential Months

Mo

95/1

95/2

95/3

95/4

95/5

95/6

95/7

95/8

95/9

95/10

95/11

95/12

96/1

96/2

96/3

96/4

96/5

96/6

96/7

96/8

96/9

96/10

96/11

96/12

97/1

97/2

97/3

97/4

97/5

97/6

97/7

97/8

97/9

97/10

97/11

97/12

98/1

98/2

98/3

98/4

98/5

98/6

98/7

98/8

98/9

98/10

98/11

98/12

99/1

99/2

99/3

99/4

99/5

99/6

99/7

99/8

99/9

99/10

99/11

99/12

00/1

00/2

00/3

00/4

00/5

00/6

00/7

00/8

00/9

0

10

20Mean

What Can We Do?

• Increase subgroup size

L k t ti t ( ti t i it• Look at time or count (cases, patients, visits, etc.) between an event


11/18/2009

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Alternative: Plot Time or Count Between Occurrences of Rare Events

Instead of plotting the number of incidences

Number of Incidences Per Month

1

2

mbe

r

each month, plot the time (or number of cases, patients, visits, etc) between incidences. Cases Between an Event

500

0

1

Jan-

01

Mar

-01

May

-01

Jul-0

1

Sep

-01

Nov

-01

Jan-

02

Mar

-02

May

-02

Jul-0

2

Sep

-02

Nov

-02

Jan-

03

Mar

-03

Num


Plot a point each time an incidence occurs

0

100

200

300

400

Feb-01

Apr-01

Jun-01

Aug-01

Oct-01

Dec-01

Feb-02

Apr-02

Jun-02

Aug-02

Oct-02

Dec-02

Feb-03

# C

ases

Use Special Shewhart Charts for Rare EventsType of Data

Count or Classification (Attribute Data)‐Qualitative data such as # errors, # nonconformities or # of items that passed or failed) ‐ Discrete: must be whole number when originally collected (can’t be fraction or scaled data when originally collected)‐This data is counted, not measured

Continuous (Variable Data) ‐Quantitative data in the form of a measurement‐Requires a measurement scale ‐Time, Money, Scaled Data (i.e. length, height, weight, temperature, mg.) and Throughput (volume of workload/ productivity)

Count (Nonconformities)1,2,3,4, etc.

Classification (Nonconforming)Either/Or, Pass/Fail, Yes/No

Equal Area of Opportunity

Unequal Area of Opportunity

Unequal or Equal Subgroup Size

SubgroupSize of 1(n=1)

Unequal Or Equal SubgroupSize (n>1)

C Chart U Chart P ChartI Chart (also known as an X chart)

X‐Bar and S


P Chart an X chart)

Number ofNonconformities

NonconformitiesPer Unit Percent

NonconformingIndividual Measures Average and Standard

Deviation

Other types of control charts for count/classification data:1. NP (for classification data)2. T-chart [time (or event, items, etc.) between rare events]3. Cumulative sum (CUSUM)4. Exponentially weighted moving average (EWMA)5. Geometric distribution chart (G chart for count data) 6. Standardized control chart

Other types of control charts for continuous data:7. X‐bar and Range8. Moving average9. Median and range10. Cumulative sum (CUSUM)11. Exponentially weighted moving average (EWMA)12. Standardized control chart

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g‐Chart for Rare Occurrences• Alternative to p‐chart, c‐chart, or u‐chart for count or classification data

when the measure is the number of cases between the incident or non‐conformity of interest.

• This chart allows the evaluation of each occurrence to be evaluated rather than having to wait to the end of a time period before the data is plotted. The g chart is g p p galso particularly useful for verifying improvements (such as reduced SSIs) and for processes with low rates.

• The number of units (surgeries, insertions, admissions, etc) between an incidence can often be modeled by the geometric distribution.

Calculation of control limits:g = number units between incidencesg‐bar= average of g’s


g bar average of g sUL = ĝ + 3[ĝ * (ĝ +1)]1/2

LL = ĝ ‐+ 3[ĝ * (ĝ +1)]1/2 , (<0, so no LCL for this g chart)

CL = 0.693* g‐bar (median of g’s)

Notes: 1. The UL is approximately 4x the CL (for quick visual analysis)2. Use median for centerline to get data symmetric around CL for run rules

G chartU Chart - Infections per 100 ICU Admissions

10

15

20

25

30

35

Infe

ctio

n R

ate

UCL

CL = 7.2

Good

ComparisonOf U h t

Number of ICU Admissions Between Infections

30

35

40

45

50

ons

UCL = 39.7

0

5

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Good G Chart

Good

Of U chart and G chart for infections in the ICU


0

5

10

15

20

25

30

Jan Feb Feb Mar Apr May Jun Aug Oct Nov Nov Jan Mar Jun

# of

adm

issi

o

CL = Median = 9.6

Mean = 13.8

11/18/2009

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T‐Chart for Time Between Rare OccurrencesAlternative to p‐chart, c‐chart, or u‐chart for count or classification data when the

measure is the time (continuous variable) between the incident or non‐conformity of interest.

This chart allows the evaluation of each non‐conformity or non‐confirming unit to be evaluated rather than having to wait to the end of a time period before the data is plotted. If the rate of occurrence can be modeled by the Poisson distribution then the times between occurrences will becan be modeled by the Poisson distribution, then the times between occurrences will be exponentially distributed. The exponential distribution is highly skewed, so plotting the times would result in a control chart that is difficult to interpret. The exponential can be transformed to a symmetric Weibull distribution by raising the time measure to the 1/3.6 = 0.2777 power or

[y = t 0.2777]. Calculation of control limits:

t = time between incidences, y = transformed timeMR’ = average moving range of y’s

ŷ = average of y’s (center line)UL = ŷ + 2.66 * MR’

ŷ


LL = ŷ ‐ 2.66 * MR’

Transform the limits back to time scale before plotting chart: t = y3.6

Notes: 1. Conduct the usual screening of MR’s to calculate the average moving range.2. Need to be careful about 0’s in the data (try to increase precision (hrs vs. days) when

near zero.3. LL < 0, there is no LL for this measure

Source: The Data Guide

T Chart for FallsChris McCarthy: Time Between [email protected]

12

Sam

ple

Coun

t

5

4

3

2

1

_C=1.385

UCL=4.915

C C ha r t o f # of F a l ls pe r M onth

Days Between

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 MoreBin

Freq

uenc

y = days ** 0.2777

6

Sa mple2421181512963

0


0

1

2

3

4

5

6

1 1.4 1.8 2.2 2.6 3 More

Bin

Freq

uenc

11/18/2009

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MRSA R

ate/

1000

Bed

Day

s

MRSA Rate per 1000 Occupied Bed Days.491

5.442

4.318

5.312

5.409

5.271

3.278

2.211

2.260

1.341

2.398

1.275

3.244

1#OBD/1000

# MRSAu c har t

UCL = 25.07

15

20

25

30

M Mean = 9.18

M/07 A M J J A S O N D J/08 F M A M

5

10

MRSA-Days Between4 1 8 7 10 10 3 12 7 1 10 6 9 7 6 3 7 9 3 4 11 5 2 8 6 13 15 16 17 23 20 15 21 19 18 17 10 19Days

t char t

UCL = 30 78

35

40

45


Day

s

UCL 30.78

Mean = 5.57

LCL = 0.19

3/2/07 3/

63/7

3/15

3/22 4/

14/11

4/14

4/26 5/

35/3

5/13

5/19

5/28 6/

46/10

6/14

6/21

6/30 7/

37/7

7/18

7/23

7/25 8/

28/8

8/21 9/

59/21

10/8

10/31

11/20 12

/512

/26

1/14

/08 2/

12/18

2/28

3/19

0

5

10

15

20

25

30

Let’s Practice

• Lets look at Template and Excel Database

• Make a T or G chart– You will need to copy and paste the data into the appropriate template

• May make both charts if time allows


11/18/2009

15

Cardiac Arrests per Monthc chart

4

5

What’s the problem with this chart??Good

# A

rrest

s

UCL = 3.12

2

3


Mean = 0.67

J-02F M A M J J A S O N DJ-03F M A M J J A S O N DJ-04F M A M J J A S O N DJ-05F M A M J J A S O N DJ-06F M A M J J A S O N DJ-07F M A M J J A S OM DJ-08F M A M J J A0

1

ADEs per 1000 Doses Dispensedu chart

UCL = 0.22

0.25

0.30

No statistical signal of improvement

AD

E R

ate

0.10

0.15

0.20


CTL = 0.06

N 06 D J 07 F M A M J J A S O N D J08 F M A M J J A S0.00

0.05

11/18/2009

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Debrief• Both t chart and g chart can use all 5 rules for detecting special cause

– That is why g chart uses median as center line

• Resources:• The Data Guide. Provost and Murray, 2009. API‐Austin, Austin, TX, Chapter 7.

• Jackson, J. E. , “All Count Distributions are not Alike”, Journal of Quality Technology, Vol 4 (2), pp 86‐92, 1972.

• Yang, S., et al, “On the Performance of Geometric Charts with Estimated Control Li it ” J l f Q lit T h l V l 34 N 4 448 458 O t b 2002


Limits” Journal of Quality Technology, Vol 34, No.4, pp 448‐458, October, 2002.

• Wall, R., et al, “Using real time process measurements to reduce catheter related bloodstream infections in the ICU, Qual. Saf. Health Care 2005;14;pp. 295‐302.

• Nelson, L., “A Control Chart for Parts‐Per‐Million Nonconforming Items”, Journal of Quality Technology, Vol 26, No. 3, pp. 239‐240, July, 1994.

Cumulative Sum Control Charts

• Problem (5)

• Examples, Intro to template (7)


• Debrief ‐ Tips, issues, references (5)


11/18/2009

17

Some Advanced Control Charts

• Shewhart control charts plot information from only the last subgroup.

• The sensitivity of the chart can be improved by i ti i d t i h l tt d i t Thincorporating previous data in each plotted point. The moving average and moving range are two examples of this.

• Other effective alternatives to the Shewhart control charts are the cumulative sum (CUSUM) control chart and the exponentially weighted moving average(EWMA) control chart


(EWMA) control chart. • Especially useful when it is important to detect small

shifts in the measure of interest.

Warning: With these Advanced Control Charts, Can Not Use Standard Rules 2‐5 for Determining a Special Cause

OK


SPC-

11/18/2009

18

Data Used to Calculate Plotted Point (after 5 data points)

x1 x2 x3 x4 x5 x6 x7 x8 x9 x10

Run Chart or 0 0 0 0 1 0 0 0 0 0Run Chart or Control Chart

0 0 0 0 1 0 0 0 0 0

Cusum .2 .2 .2 .2 .2 0 0 0 0 0

Moving Average (3)

0 0 .33 .33 .33 0 0 0 0 0

Moving Average (5)

.2 .2 .2 .2 .2 0 0 0 0 0


EWMA λ = 0.2 .09 .17 .24 .3 .2 0 0 0 0 0

EWMA λ = 0.1 .1 .2 .25 .35 .1 0 0 0 0 0

Data Used to Calculate Plotted Point (After 8 Data Points)

x1 x2 x3 x4 x5 x6 x7 X8 x9 x10

Run Chart or Control Chart

0 0 0 0 0 0 0 1 0 0

Cusum .125 .125 .125 .125 .125 .125 .125 .125 0 0

Moving Average (3)

0 0 0 0 0 .33 .33 .33 0 0

Moving Average (5)

0 0 .0 .2 .2 .2 .2 .2 0 0


EWMA λ = 0.2 .05 .06 .09 .12 .14 .16 .18 .2 0 0

EWMA λ = 0.1 .06 .09 .11 .13 .15 .17 .19 .1 0 0

11/18/2009

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CUSUM

The cumulative sum statistic (S) is the sum of the deviations of the individual measurements from a target value, for example:

Si = S i‐1 + (Xi ‐ T), Xi = the ith observation,T = Target (often from historical average)


Si = the ith cumulative statistic.

CUSUM Calculation – Patient Satisfaction Data

Month %Sat(X) Target (Average) X-Target (Si) CUSUM CUSUM + Target

J-02 82 88.296 -6.296 -6.296 82

F 79 88.296 -9.296 -15.592 72.704

M 84 88.296 -4.296 -19.888 68.408

A 82 88.296 -6.296 -26.184 62.112

M 92 88.296 3.704 -22.48 65.816

J 80 88.296 -8.296 -30.776 57.52

J 94 88.296 5.704 -25.072 63.224

A 78 88.296 -10.296 -35.368 52.928

S 83 88.296 -5.296 -40.664 47.632

O 84 88.296 -4.296 -44.96 43.336


O 84 88.296 4.296 44.96 43.336

N 92 88.296 3.704 -41.256 47.04

D-02 84 88.296 -4.296 -45.552 42.744

03, 04

M 04 95 88.296 6.204 0.008 88.304

11/18/2009

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Run Chart of Patient

Satisfaction Data

% Patient Satisfaction Very Good/Ex.

80

85

90

95

100

Perc

en

CUSUM Chart

Satisfaction Data

70

75

80

J-02

F M A M J J A S O N D J-03


F M

Process Changes

CUSUM Chart: Patient Satisfaction

708090

100

Cusum Chart of


010203040506070

J-02



F M

CU

SU

Process Changes

Cusum Chart of Patient Satisfaction Data Target = Avg = 88.296

CUSUM Chart: Patient Satisfaction

2030405060708090

100

CU

SU

Target = average = 88.29CUSUM graph

sensitive t t t

CUSUM: Patient Satisfaction with 85% Target

140160180200

01020

J-02



F M

Process Changesto target selected

The Slope is Target = goal = 85%


020406080

100120140

J-02



F M

CU

SUM

pthe Focus of the Interpretation

Target = 85%

11/18/2009

21

Control Limits for CUSUM Chart – V‐Mask

0

-20

Target=0

Vmask Chart of %Sat(X)Cu

mul

ativ

e Su

m -40

-60

-80

100


Sample272421181512963

-100

-120

Moving the V‐Mask (h=5, k=0.5)

umul

ativ

e Su

m

0

-20

-40

-60

Target=0

Vmask Chart of %Sat(X)

mul

ativ

e Su

m

0

-20

-40

-60

-80

Target=0


Sample

Cu

272421181512963

-80

-100

Sample

Cum

272421181512963

-100

-120

-140

40

20

0 Target=0


100

50



Sample

Cum

ulat

ive

Sum

272421181512963

-20

-40

-60

-80

-100

Sample

Cum

ulat

ive

Sum

272421181512963

0

-50

-100

Target=0

11/18/2009

22

Alternate Form of CUSUM Control Chart Called Tabular Form

• Do not need to use V‐mask• Need to plot two statistics for each measure• Procedure:

– Let xi be the ith observation on the process– Estimate σ using screened MR’s of series– Accumulate derivations from the target μ0 above the target with one statistic, C+

– Accumulate derivations from the target μ0 below the target


g μ0 gwith another statistic, C—

– C+ and C‐‐ are one‐sided upper and lower cusums, respectively.

The Tabular CUSUM ‐ Alternate Form

The statistics are computed as follows:The Tabular Cusum

[ ]+−

+ ++μ−= 1i0ii C)k(x,0maxC

starting values areK is the reference value (or allowance or slack value)If either statistic exceed a decision interval H, the process is considered to be out of control Often taken as a H = 5σ

[ ][ ]−

−−

−

+−−μ=

μ

1ii0i

1i0ii

Cx)k(,0maxC

)(,

0CC 00 == −+


out of control. Often taken as a H = 5σ

11/18/2009

23

Cusum Control Chart for Patient Satisfaction Data

50

CUSUM Chart of %Sat(X)

Ci+

Cum

ulat

ive

Sum

25

0

-25

0

UCL=22.3

LCL=-22.3


Sample272421181512963

-50

-75

Ci-

Let’s Practice


• Make a Cusum chart– You will need to copy and paste the data into the appropriate template


11/18/2009

24

Debrief ‐ Cusum

Resources:• The Data Guide. Provost and Murray, 2009. API‐Austin, Austin, TX, Chapter 7.

• Roberts, S. W., “A Comparison of Some Control Chart Procedures”, Technometrics, Vol 8, No. 3, p. 411‐430, August, 1966.

• Lucas, J., “The Design and Use of V‐mask Control Schemes,” Journal of Quality Technology, Vol 8, No. 1, pp 1‐12, January, 1976.

• Banard, G. A. “Control Charts and Stochastic Processes”, Journal of the Royal Statistical Society B21, pp 230‐271, 1959

• Evans, W. D. , “When and How to Use Cu‐Sum Charts”, Technometrics, Vol. 5, pp. 1‐22, 1963

• Sibanda, T. and Sibanda N., “The CUSUM chart method as a tool for continuous monitoring of li i l t i ti l ll t d d t ” BMC M di l R h M th d l 2007


clinical outcomes using routinely collected data”, BMC Medical Research Methodology 2007, 7:46 doi:10.1186/1471‐2288‐7‐46

• Noyez, Luc, “A review of methods for monitoring performance in healthcare Control charts, Cusum techniques and funnel plots”, Interact Cardiovascular Thoracic Surg 2009; 9:494‐499;

• Biau, D., “Quality control of surgical and interventional procedures: a review of the CUSUM”, Qual Saf Health Care 2007;16:203–207. 2006

Over‐dispersion and Prime Charts

• The problem and examples

• Intro to template




11/18/2009

25

Problem of Over dispersion with a P chart

P‐chart: Health Plan Management of Patients by Phone

50

55

60patients

ULCL

30

35

40

45

Jan‐07 Mar ‐07 May‐07 Jul ‐07 Sep‐07 Nov‐07 Jan‐08 Mar‐08 May‐08

% of all active

p

LL

CL


“Are all these points outside the limits due to special causes, or is something else going on here?”

Month J‐07 F‐07 M‐07 A‐07 M‐07 J‐07 J‐07 A‐07 S‐07 O‐07 N‐07 D‐07 J‐08 F‐08 M‐08 A‐08Members 8755 9800

17000

16400

19500

19800

21200

22300

21600

20500

18700

18900

14300

14800

14500

14600

Mng by Phone 3852 4100 7083 7339 9406 9310 7250

10400 9250 9950 9846 9854 8034 8162 8122 8200

percent 44.0 41.8 41.7 44.8 48.2 47.0 34.2 46.6 42.8 48.5 52.7 52.1 56.2 55.1 56.0 56.2

Over dispersion: Prime Charts

• Sometimes Shewhart charts look weird!

• This can happen when subgroup sizes large– Limits on charts for attribute data impacted by subgroup size

– Larger subgroup size means tighter limits

– May be issue when subgroup > 5000


May be issue when subgroup > 5000

• We have an alternative: Prime charts

»P’ or U’

11/18/2009

26

Alternative to the P chart: the P’‐ChartP ‐ c h a r t : H e a l t h P l a n M a n a g e m e n t o f P a t i e n t s b y P h o n e

4 5

5 0

5 5

6 0

all active patients

L L

U LC L

3 0

3 5

4 0

Ja n ‐0 7 M a r ‐0 7 M a y ‐0 7 Ju l ‐0 7 S e p ‐0 7 N o v ‐0 7 Ja n ‐0 8 M a r ‐0 8 M a y ‐0 8

% of a


U’ Chart for Medications Errors

U Chart for Medications Errors

20

30

40

50

60

ros per 1000 en

tries

UL

CL

Data obtained from a screening of computer order entry of prescriptions in the hospitals for one month.

0

10

0

A F I N H S U B M D L J T O P R V Q W K C X G EHospital

Err

LL

CL

U' Chart for Medications Errors

40

50

60

0 en

tries

UL

Subgroup sizes (number of prescription entries for the month) ranges from 4,467 to 27,203.

Hospitals on the u chart from the smallest to largest denominator (e.g. funnel plot format).

Th i t f h lf f th

*


0

10

20

30

A F I N H S U B M D L J T O P R V Q W K C X G EHospital

Erros per 1000

LL

CL

The points for one-half of the hospitals were outside the limits.

Based on conversation with the subject matter experts (and the very large subgroup sizes), the quality analyst created the u’.

*Hospitals rationally ordered from smallest to largest

*

11/18/2009

27

Guidance for Attribute Charts• First develop the appropriate chart (p or u).

• If the limits “appear too tight” and very large subgroupIf the limits appear too tight and very large subgroup sizes are involved:

1. Look for ways to further stratify the data• monthly into weekly or daily subgroups• organization data into department subgroups• Overall clinic data subgrouped by clinician

2. If you still end up with large subgroup sizes and a chart that is full of special causes, spend time with the subject


that is full of special causes, spend time with the subject matter expert trying to identify and understand the special causes.

3. If you are not able to learn from the special causes, then constructed a modified attribute chart (P’ or U’ ).

Guidance for Attribute ChartsStep 1 – calculate the p chart (getting pi and σpi for each subgroup).

Step 2 – convert the individual p values to z-values usingStep 2 convert the individual p values to z values using zi = [ pi – p-bar] / σpi.

Then use the I chart calculation of moving ranges to determine the sigma for Z-values: σzi = screened MRbar divided by 1.128.(note: as with any I chart, it is very important to screen the moving ranges for special caused prior to calculating the average moving range).

Step 3: Transpose the z-chart calculations back to p values to get the


Step 3: Transpose the z chart calculations back to p values to get the limits for the p' chart by multiplying the theoretical sampling sigma (σpi) by the between subgroup sigma (σzi ) as follows:

CL = pbar (same as original p chart)UCL = pbar + 3 σpi σziLCL = pbar - 3 σpi σzi

11/18/2009

28

Let’s PracticePercent ANC Tested

30260

23,528

27477

21,504

25529

19,760

26046

22,700

26734

23,229

24989

20,166

27112

23,864

23990

21,797

24288

20,955

25076

21,421

22528

18,213

21844

16,899

26487

23,531

23985

19,898

26391

21,153

23479

20,465

22564

21,195

21232

18,648

Total ANCTested

p chart

95

100

%

UCL = 84.90CTL = 84.20LCL = 83.51

80

85

90

95


1/1/20082/1/2008

3/1/20084/1/2008

5/1/20086/1/2008

7/1/20088/1/2008

9/1/2008

10/1/2008

11/1/2008

12/1/20081/1/2009

2/1/20093/1/2009

4/1/20095/1/2009

6/1/20097/1/2009

8/1/20099/1/2009

10/1/2009

11/1/2009

12/1/200965

70

75

Debrief: Cautions in using the Prime modification to p and u charts

1. Don’t consider the adjustment unless the subgroup i lsizes are very large.

2. In cases where average subgroup sizes are very large (>5000), first try using different subgrouping strategies to the stratify the data into smaller rational subgroups.

3 Spend time with subject matter experts trying to


3. Spend time with subject matter experts trying to understand and learn from the initial indications of special causes on the attribute chart before considering the modification to these charts.

11/18/2009

29

Improper use of P’ Chart

Very important to not just automatically switch to a these modified charts until the source of the o e di pe ion h been

P‐chart: Percent of Diabetic Patients with Self‐Management Goals

0102030405060708090100

I B H L K C N M E A J D F G

% of patients with goals

LL

CL

UL

Clinic

P'‐chart: Percent of Diabetic Patients with Self‐Management Goals200

*over-dispersion has been thoroughly investigated.

Only when subgroup sizes are above 2000 should the adjustment be even considered.

The purpose of

‐150

‐100

‐50

0

50

100

150

200


% of patients with goals

UL

CL

LL

Clinic

note: the l imits calculated below 0% and above 100% are shown here to clarify the impact of the P'chart calculation

P' h t P t f Di b ti P ti t ith S lf M t G l*


The purpose of Shewhart’s method is to optimize learning, not get rid of special causes.

See problem Example. Subgroup sizes range from 180 to 1845.

P'‐chart: Percent of Diabetic Patients with Self‐Management Goals

% of p

atients with goals

0

50

100


CL

Clinic

*Clinics rationally ordered from smallest to largest

*

References for Over dispersion with Attribute charts1. The Data Guide. Provost and Murray, 2009. API‐Austin, Austin, TX, Chapter 8.

Debrief

2. Heimann, P.A., “Attributes Control Charts with Large Sample Sizes”, Journal of Quality Technology, ASQ, 1996, Vol 28, pp 451‐459.

3. Spiegelhalter D. “Handling overdispersion of performance indicators”. Journal of Quality and Safety in HealthCare, BMJ, 2005;14:347–51.

4. Laney DB. “Improved Control Charts for Attribute Data”. Quality Engineering, 2002; Vol. 14, p. 531–7.


5. Mohammed, M. A. and D Laney,” Over dispersion in health care performance data: Laney’s approach”, Journal of Quality and Safety in Health Care, 2006; Vol. 15, pp.383–384.

11/18/2009

30

Autocorrelation

• Autocorrelated – use registry data

• Problem

• Examples, Intro to template



59


Autocorrelation

A basic assumption in determining the limits for Shewhart charts is that the data for each subgroup arecharts is that the data for each subgroup are independent, that is the data from one subgroup does not help us predict another period.

The most common way this assumption is violated is when special causes are present.

Then subgroups associated with the special causes tend to be more alike than subgroups affected only by special


be more alike than subgroups affected only by special causes.

The result is that these subgroups show up as “special”, exactly what the chart was designed to do.

11/18/2009

31

AutocorrelationBut sometimes process operations or data collection procedures result in data affected only by common causes that is not independent from subgroup tocauses that is not independent from subgroup to subgroup.

This phenomenon is called autocorrelation.

With a positive autocorrelation, successive data points will be similar. For time ordered data, subgroups l t th ill t d t b lik th


close together will tend to be more alike then subgroups far apart in time.

With negative autocorrelation, successive points will tend to be dissimilar, resulting in a saw tooth pattern.

Autocorrelation

This relationship between the plotted points would make all the additional rules used with Shewhart charts invalid.additional rules used with Shewhart charts invalid.

For the I chart and Xbar and S chart, the limits might not be accurate expressions of the common cause variation and the autocorrelation will result in an increase in false signals of special causes.


11/18/2009

32

Autocorrelation with Registry Data

The “autocorrelation problem” occurs because the data for most patients is not updated each month; only the patients whopatients is not updated each month; only the patients who come in for a visit.

If one‐third of the patients come in during the current month and have their data updated, the monthly summary will use the same data as the previous month for two‐thirds of the patients.

This creates a statistical relationship between the monthly


This creates a statistical relationship between the monthly measures – it creates autocorrelation.

Autocorrelation in Registry Data

•I chart for the average glycated hemoglobin test (HbA1c value) from a registry of about 130 adult patients with diabetes. Patients are scheduled to visit the clinic every three months, so about one-third visit each month and their registry values are updated.


•Special causes: 10 points outside limits, runs below the center line, and numerous points near the limits.

•Are these special causes or the impact of autocorrelation due to the use of the registry values? Because of the way the data are collected for this chart, autocorrelation was expected.

11/18/2009

33

Examine Autocorrelation using a Scatter Diagram – Point i vs. Point i‐1

Autocorrelation: Current Value vs. Next Value7.55

y = 0.7909x + 1.5449R2 = 0.6688

7.4

7.45

7.5

next

val

ue (i

+1)


7.25

7.3

7.35

7.25 7.30 7.35 7.40 7.45 7.50 7.55Current Value (i)

Dealing with Autocorrelation• Identify the source of the autocorrelation and take appropriate

actions to learn from it and incorporate it into improvement strategies.

• If the autocorrelation is due to the sampling or measurementIf the autocorrelation is due to the sampling or measurement strategy, modify the data collection to reduce its impact.

• Continue to learn from and monitor the process as a run chart (using only visual analysis, not using run chart rules).

• Use time series analysis to model the data series and analyze the residuals from the time series using a Shewhart chart.

• Make adjustment to the control limits to compensate for the


autocorrelation . The recommended adjustment is to increase the limits by multiplying by the factor:

___1 / √ 1‐r2 or sigma = Rbar/ [d2 * sqrt(1‐r2)]

11/18/2009

34

I Chart with Autocorrelation Adjustment

HbA1C - I chart with Limits Adjusted for Autocorrelation

7 57.55

7.67.65

c

_ UL =7.572

7.157.2

7.257.3

7.357.4

7.457.5

J05

F M A M J J A S O N D J06

F M A M J J A S O N D J -07

F M A M J J A S

Reg

istr

y A

vera

ge H

bA1

LL =7.238

CL =7.405


Control limits adjusted to compensate for the autocorrelation. The limits are increased by multiplying by the factor:

____ 1 / √ 1-r2 or sigma = Rbar/ [d2 * sqrt(1-r2)]

Let’s Practice


• Check for Autocorrelation and Adjust limits– You will need to copy and paste the data into the appropriate template


11/18/2009

35

References for Autocorrelation on Control ChartsThe Data Guide. Provost and Murray, 2009. API-Austin, Austin, TX, Chapter 8.

Debrief

Montgomery, D. C. and Mastrangelo, C. M., “Some Statistical Process Control Methods For Autocorrelated Data”, Journal of Quality Technology 23, 1991, pp. 179–193.

Wheeler, D. 1995, “Advanced Topics in Statistical Process Control”, SPC Press, Knoxville, TN, Chapter 12. (adjustment factor)

Nelson, C. R., Applied Time Series Analysis for Managerial Forecasting, Holden-Day Inc San Francisco 1973


Day, Inc. San Francisco, 1973

Note: Don’t overreact to autocorrelation. Most of the time, special causes cause the detection of autocorrelation. Spend time identifying the special causes.

Caution: Do Not Over‐react to Autocorrelation


11/18/2009

36

Examining Autocorrelation for Visit Time I Chart

• Scatterplot prepared to look at autocorrelation. • The high value of r2 (autocorrelation =• The high value of r (autocorrelation = .905) could indicate autocorrelation that must be dealt with in order to use the limits on the chart. • Receptionist noted that “it was pretty clear which of the specialists were in the office each day”. • Aware of different average cycle times for each of the doctors


for each of the doctors. • The QI team prepared a chart to show times for each of the three specialists..

I Chart Clarifying Special Causes


11/18/2009

37

Some Other Advanced Control Charts


73

Standardized Shewhart Charts• Shewhart charts with variable subgroup sizes (Xbar and S Chart, P chart, U chart) result in variable control limits.

•Sometimes this complexity in the appearance of the chart results in them not b i dbeing used.

• An alternative is called the standardized Shewhart Chart. To construct the chart, the data is transformed using:

Z = (X-u) / σ where z is the standardized value, X is the original data value; µ is the mean and σ the standard deviation of the original data.•


•• Using this transformation, data for all the types of Shewhart charts can be transformed so that the resulting chart has limits that are always:•

CL = 0 UL = 3 LL = -3

11/18/2009

38

Use of Standardized Chart

ent

Percent Unplanned Readmissionsp chart

UCL = 4.41

4

5

6

7

Standarized P-chart for Unplanned Readmissions

3

4

s

UL

Per

ce

Mean = 2.57

LCL = 0.72

LOS Reduction Testing Started

LOS Red. Lg Test

J05 F M A M J J A S O N D J-06 F M A M J J A S O N D J-07 F0

1

2

3

API and CT Concepts, 2009-4

-3

-2

-1

0

1

2

3

J05 F M A M J J A S O N D J-06 F M A M J J A S O N D J-07 F

Stan

ndar

dize

d Pe

rcen

t ras

adm

its

Data from Jan 05 - Mar 06 use to calculate limits

CL = 2.22%

LL

Control Charts with Slanted Center‐line

US Median % Obesity30

y = 0.8879x + 10.346R2=09877

10

15

20

25

Med

ian

% O

besi

ty


R = 0.9877

50 5 10 15 20 25

Year since 1989 (year1)

11/18/2009

39

Seasonal Effects on a Shewhart Chart


Seasonal Effects on a Shewhart Chart


11/18/2009

40

Selecting the Appropriate Shewhart Chart


Selecting the Appropriate Shewhart ChartType of Data











X‐Bar and S


P Chart an X chart)




Deviation



11/18/2009

41

Develop a Control Chart – Case AThe QI team wants to make a 50% reduction in the use of restraints in the hospital. The number of inpatient restraints and the total patient days each month are recorded.

Type of control chart (s)

Subgrouping Strategy


Develop a Control Chart – Case BYour clinic team is interested in the average time patients spend in the waiting area, so every day at 11:00a and 5:00p you pick the next 5 patients and measure their actual waiting time in minutes.

Type of control chart (s)Type of control chart (s)



11/18/2009

42

Develop a Control Chart – Case CThe ICU nurses want to monitor the ventilator-associated pneumonia (VAP) rate. They have data on the for each pneumonia cases, including the date the case occurred and the total number of vent days in the ICU each day. One of the nurses expressed concern that this would be difficult to track because they often go more than a month without adifficult to track because they often go more than a month without a VAP.

Type of control chart (s)



Develop a Control Chart – Case DThe clinic QI team is trying to improve evidence based care for their patients with diabetes. Each week they record the number of diabetic patients seen in the clinic and the number who received eye exams.




11/18/2009

43

Develop a Control Chart – Case EThe Chief Medical Officer’s office monitors mortality in the hospital. They feel it is very important to quickly detect any change in the system that results in an increase in mortality.




Develop a Control Chart – Case FOne of your diabetic patients records blood glucose test results at three specific times each day: 1st thing in the morning, at 11:00a before lunch, and at 1:00 after lunch. She has daily data for the past two months.

Type of control chart(s)

Subgrouping strategy?


11/18/2009

44

Making Shewhart Charts More Effective

• Guidance regarding limits on Shewhart Charts– When to make limits

– When to revise limits

• Tips for good graphical display


87

Principles for Making Limits

• If we have less than 12 data points use run chart rather than Shewhart chart– Just the data plotted as below. No limits, centerline

Is Our Volume of Net New Patients Stable?

ents 80

100

120


# of Patie

1 2 3 4 5 6 7 8 9 10 110

20

40

60

11/18/2009

45

Principles for Making Limits• When have 12 or more data points may calculate and use

the trial limitstrial limits

•• Extend trial limitsExtend trial limits

atients

Trial Limits60

80

100

120

UL 94.0



# of Pa Trial Limits

1 2 3 4 5 6 7 8 9 10 11 12 130

20

40

60

Mean 15.9

Principles for Revising Limits

1. Revise limits when moving from trial limits to i iti l li iti iti l li itinitial limits initial limits

• Use trial limits until get 20‐30 data points then revise. (If made trial limits with, for example, first 12 points don’t update trail limits with each additional point)

• When 20‐30 subgroups become available revise the trial limits to create initial limitsinitial limits


– 20 to 30 subgroups is when Shewhart chart becomes strong

11/18/2009

46


100

120


Trial Limits

100

120

UL 94.0

Initial Limits

# of Patients

40

60

80

UL 73.3

Mean 40.0

# of Patients

40

60

80

Mean 15.9

API and CT Concepts, 2009 Sequential Months1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

20

LL 6.7

Sequential Months

1 2 3 4 5 6 7 8 9 10 11 12 130

20


2. Revise when the initial Shewhart chart has special causes and there is a desire to use the calculated li it f l i f d t t b ll t d i thlimits for analysis of data to be collected in the future

• If you have 20‐30 data points and you find special cause when you calculate your initial limits then:– Investigate and address special cause – Recalculate limits without the special cause data in your i i i l li i


initial limits• Always leave data point(s) visible on chart• If you choose to remove data from limits/mean, annotate your decision

11/18/2009

47

Is Our Volume of Net New Patients Stable?8/98 9 10 11 12 1/99 2 3 4 5 6 7 8 9 10 11 12 1/00 2 3 4 5 6 760 36 48 31 52 87 64 47 24 39 35 45 29 33 30 31 41 34 24 37 33 30 39 32

MonthData

100

120

New PA hired

# of Patients

40

60

80

UL 64.4

API and CT Concepts, 2009Sequential Months1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

20

Mean 36.8

LL 9.2


100

120Is Our Volume of Net New Patients Stable?

100

120

New PA hired

# of Patients

40

60

80UL 73.3

Mean 40.0 # of Patients

40

60

80

UL 64.4

Mean 36.8

API and CT Concepts, 2009Sequential Months1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24

0

20

LL 6.7

Sequential Months1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 1718 19 20 21 22 23 24

0

20

LL 9.2

11/18/2009

48


• You have 20‐30 data points and your initial limits indicate that your process is stable

G d ti i t t d th li it d– Good practice is to extend the limits and centerline into the future and plot incoming data against these initial limits


Number of Surgical Complications

20

25

UL 18.78

# Co

mplications

10

15

Mean 9.52

Mean

API and CT Concepts, 2009Sequential Subgroups of 50 Surgeries1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 26 2728 29 3031 32 33 34 35 36 3738 39 4041 42 43 44 45 46 4748 49

0

5

LL 0.26

11/18/2009

49


3. When improvements have been made to the d h lt d i i lprocess and have resulted in special cause

• Recalculate limits that represent the new improved process.


Center DD:Time ED to OR ‐ Isolated Femur Fractures

2500

3000

Protocol change started

Minutes

1000

1500

2000

UL 1800.6


g

Sequential Cases1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

0

500Mean 540.7

11/18/2009

50

Center DD:Time ED to OR ‐ Isolated Femur Fractures

2500

3000

Minutes

1000

1500

2000

UL 274.8

API and CT Concepts, 2009Sequential Cases1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

0

500

Mean 173.8

UL 270

Mean

LL 57

Emergency Fast Track Average Length of Stay (ALOS) for Admitted PatientsEmergency Fast Track Area

April 2004 - April 2005Individuals

1200

1400

1600

AL

OS

(Min

utes

)

400

600

800

1000UCL = 1031.79

Mean = 480.29

API and CT Concepts, 2009Source: PromedWeek Ending

9/4/

2004

9/11

/2004

9/18

/2004

9/25

/2004

10/2/

2004

10/9/

2004

10/16

/2004

10/23

/2004

10/30

/2004

11/6/

2004

11/13

/2004

11/20

/2004

11/27

/2004

12/4/

2004

12/11

/2004

12/18

/2004

12/25

/2004

1/1/

2005

1/8/

2005

1/15

/2005

1/22

/2005

1/29

/2005

2/5/

2004

2/12

/2005

2/19

/2005

2/26

/2005

3/5/

2005

3/12

/2005

3/19

/2005

3/26

/2005

4/2/

2005

4/9/

2005

4/16

/2005

4/23

/2005

0

200

11/18/2009

51

%)

Percent of Total patients Admitted through Main ED- TrendstarMain ED & EFT

October 2000 - March 2005p chart

40

50

Perc

ent

of P

atie

nts

Ad

mit

ted

(%

20

30UCL = 27.04

Mean = 23.88

LCL = 20.71

API and CT Concepts, 2009Source: TrendstarWeek Ending

10/1/

2000

11/1/

2000

12/1/

2000

1/1/

2001

2/1/

2001

3/1/

2001

4/1/

2001

5/1/

2001

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0

10

Designing Effective Shewhart Charts

• Tip 1: Subgroup Size– Too small

• Classification data: see guidelines for P chart

• Count data: U chart if center line less than 9 will be no lower limit. If center line less than 1.4 will have too many 0’s

– Too large


– Too large• Over‐dispersion issue. Consider Prime charts

11/18/2009

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Guidelines for Selecting Subgroup Size for an Effective P chart

Average PercentNonconforming

Units (pbar)

Minimum Subgroup Size (n) Required to Have

< 25% zero for p'sMinimum Subgroup Size

Guideline(n>300/pbar)

Minimum Subgroup Size Required to Have

LCL > 00.1 1400 3000 90000.5 280 600 18001.0 140 300 9001.5 93 200 6002 70 150 4503 47 100 3004 35 75 2205 28 60 1756 24 50 1308 17 38 104

10 14 30 81


10 14 30 8112 12 25 6615 9 20 5120 7 15 3625 5 12 2830 4 10 2240 3 8 1450 2 6 10

Note: for p>50, use 100‐p to enter the table (e.g. for p=70% use table p of 30%, for p=99% use table p of 1%, etc.) Source: The Data Guide: L Provost and S. Murray, 2009


• Tip 2: Rounding Data: have choicesWh i t t l th– When using computer system, always err on the side of maintaining too many decimal place

– Rounding used for compliance may not be useful for learning

• E.G LOS in days for compliance may be better in minutes for learning


– Rounding center lines/ limits: keep one more decimal than the statistic plotted on the chart.

• E.g. data 11.2…center line 9.79

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• Tip 3: Formatting Charts– Put related graphs on same page


%

Know Who To Call W ith Questions

UCL = 52.5

Mean = 32.8

LCL = 13.1

Provider Gives Card Test 1 Test 3ImplementTest 2

F-07 M A M J J A S O N D J-08 F M A M J J A S O N D J-09 F M A M J J A S0

10

20

30

40

50

60

70

80

90

100

%

Received Enough Information From Provider

UCL = 62.960

70

80

90

100

Good

Good

%

Mean = 42.1

LCL = 21.4

Ask Question Test 1/2

Test 3/4

Test 5

Implement


10

20

30

40

50

%

Treated With Respect By Provider

UCL = 68.8

Mean = 47.9

LCL = 26.9

Provider Walk Pt Out Test 1Test 2 Test 4

20

30

40

50

60

70

80

90

100

Good


Provider Walk Pt. Out-Test 1Test 3 Implement


10

%

Would Recommend The Clinic

UCL = 79.3

Mean = 58.6

LCL = 37.9

Provider Gives Card

Provider Walks Pt. Out

Provider Asks Question


10

20

30

40

50

60

70

80

90

100

Good

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– Presentation:• Size matters

– ratio of horizontal to vertical of 5:2


%


UCL = 62.9

Mean = 42.1

LCL = 21.4

T t 3/4 Implement20

30

40

50

60

70

80

90

100


Test 3/4

Test 5

Implement


10


UCL = 62.960

70

80

90

100


%

Mean = 42.1

LCL = 21.4


Test 3/4

Test 5

Implement


10

20

30

40

50

11/18/2009

55



– Presentation:• Size matters

– ratio of horizontal to vertical of 5:2

• Vertical Scalei l d th li it i th iddl 50% Oth 50% f h


– include the limits in the middle 50%.Other 50% of graph space as “white space” on either side of limits. Don’t force scale to include 0 unless important to learning.

– If the data can’t go below 0 or exceed 100% don’t scale beyond these

%

% Patients Leaving Against Medical Advice (AMA)Pilot Unit (p chart)

UCL = 3.16

Mean = 2.05

LCL = 0.94

Team Formed

Change 1Change 2

Change 3

Change 4Change 5

Implementation

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Just Right

F 06 M A M A M J J A S O N D J 07 F M A M J J A S O N D J-080.0

%

Percent of Patients Leaving Against Medical Advice (AMA)Pilot Unit (p chart)

UCL = 3.16

Mean = 2.05

LCL = 0.94Change 1 Change 2

Change 3

Change 4

Change 5Implementation

F 06 M A M A M J J A S O N D J 07 F M A M J J A S O N D J-08

1.00

1.50

2.00

2.50

3.00

3.50

Percent of Patients Leaving Against Medical Advice (AMA)

Too Small a Scale


%

Percent of Patients Leaving Against Medical Advice (AMA)Pilot Unit (p chart)

UCL = 3.16

Mean = 2.05LCL = 0.94

Team Formed

Change 1Change 2

Change 3

Change 4 Change 5

Implementation

F 06 M A M A M J J A S O N D J 07 F M A M J J A S O N D J-080

2

4

6

8

10

12

14

16

18

20

Too Large a Scale

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%

% Patients with LVF Given ACEI at Discharge (p chart)

UCL = 106.07

Mean = 58.33

20

40

60

80

100

120

140

InappropriateScale

LCL = 10.60

Nov 06 D J -07 F M A M J J A S O N D J-08 F M A M J J A S O N D-20

0

20

% Patients with LVF Given ACEI at Discharge (p chart)UCL = 106.07

80

100

AppropriateScale


%

Mean = 58.33

LCL = 10.60

Nov 06 D J -07 F M A M J J A S O N D J-08 F M A M J J A S O N D0

20

40

60

InappropriateScale

%

AMI-9 Inpatient Mortality

30

40

50

60

70

80

90

100

AppropriateScale

UCL = 20.53

Mean = 8.35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260

10

20

30

AMI-9 Inpatient Mortality

25

30

35


%

UCL = 20.53

Mean = 8.35


5

10

15

20

11/18/2009

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• Tip 3: ContinuedP t ti– Presentation:

• Labels – include user friendly labels on axes, centerline, limits, and other key values (targets, baselines, requirements, etc) on chart

• Annotations: Integrate key annotations

• Gridlines‐ keep gridlines and other lines/colors/markings to a minimum


• Data‐May be helpful to display –if legible!

• Points‐ connecting the points is optional – If in time order may

– If data not time order do not connect points


80

90

100

%

UCL = 62.9

Mean = 42.1

LCL = 21.4

Test 3/4 Implement20

30

40

50

60

70

80



Test 3/4

Test 5


10

11/18/2009

58


• Tip 3: ContinuedP t ti– Presentation:

• Labels – include user friendly labels on axes, centerline, limits, and other key values (targets, baselines, requirements, etc) on chart

• Annotations: Integrate key annotations

• Gridlines‐ keep gridlines and other lines/colors/markings to a minimum


• Data‐May be helpful to display –if legible!

• Points‐ connecting the points is optional – If in time order may

– If data not time order do not connect points

AMI-9 Inpatient Mortality Nov 06

49

1

D

66

3

J -07

60

2

F

44

1

M

52

3

A

54

5

M

47

4

J

36

6

J

49

4

A

46

4

S

55

2

O

55

5

N

51

7

D

62

15

J-08

31

2

F

36

3

M

35

2

A

55

2

M

58

9

J

36

2

J

39

2

A

35

2

S

33

6

O

30

1

N DDate# Pts

Deaths

%

2.04%

3

4.55% 3.33% 2.27%

3

5.77%

5

9.26% 8.51%

6

16.67% 8.16% 8.70% 3.64%

5

9.09% 13.73%

5

24.19% 6.45%

3

8.33% 5.71% 3.64%

9

15.52% 5.56% 5.13% 5.71%

6

18.18% 3.33%

Deathspercent

UCL = 20.53

10

15

20

25

30


Mean = 8.35


5

10

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11/18/2009

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Selecting the Appropriate Shewhart ChartType of Data











X‐Bar and S


P Chart an X chart)




Deviation



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