Six Sigma ApplicationsSix Sigma Applicationsin ain a

Renal Transplantation ProcessRenal Transplantation Process

Dr. Lee PollockDr. Lee PollockKidney Transplant RecipientKidney Transplant Recipient

from thefrom theUniversity of Miami/Jackson Memorial University of Miami/Jackson Memorial

HospitalHospital

with Analysis from with Analysis from

Dr. Mark KiemeleDr. Mark KiemeleAir Academy AssociatesAir Academy Associates

2

Background StatisticsBackground Statistics• As of 4 Nov 04 in the US:As of 4 Nov 04 in the US:

– 87,249 Waiting List Candidates (85,595 on 4 Jun 04)87,249 Waiting List Candidates (85,595 on 4 Jun 04)– 15,671 Transplanted Organs (4,288 on 4 Jun 04)15,671 Transplanted Organs (4,288 on 4 Jun 04)– 8,200 Donors Jan-Feb 04 (2,221 on 4 Jun 04)8,200 Donors Jan-Feb 04 (2,221 on 4 Jun 04)

• Median Waiting Times, Based on Blood Type, are Median Waiting Times, Based on Blood Type, are Increasing Each Year:Increasing Each Year:– Heart: 39-307 DaysHeart: 39-307 Days– Intestine: 152-323 DaysIntestine: 152-323 Days– Liver: 232-1172 DaysLiver: 232-1172 Days– Heart Lung: 252-1084 DaysHeart Lung: 252-1084 Days– Kidney Pancreas: 311-650 DaysKidney Pancreas: 311-650 Days– Lung: 536-805 DaysLung: 536-805 Days– Kidney: 578-1542 DaysKidney: 578-1542 Days

• New Registrations are Outpacing Transplantation RatesNew Registrations are Outpacing Transplantation Rates• Long Term Graft Survival Rates are Excellent and Long Term Graft Survival Rates are Excellent and

Increasing Each YearIncreasing Each Year

3

Kidney Median Waiting Times Kidney Median Waiting Times 1996-20011996-2001

Source: UNOS

0

250

500

750

1000

1250

1500

1750

2000M

ed

ian

Wa

itin

g T

ime

(D

ay

s)

O

A

B

AB

O 1333 1480 1542

A 756 868 957

B 1495 1639 1803

AB 411 468 578

96-97 98-99 00-01

4

Kidney New Registrations: Kidney New Registrations: 1999-20011999-2001

0

5000

10000

15000

20000

25000

New

Reg

istr

atio

ns

Ad

ded

O

A

B

AB

O 17964 19681 21528

A 12635 13868 14742

B 5230 5867 6480

AB 1415 1648 1700

96-97 98-99 00-01

Source: UNOS

5

Graft Survival Rates - Graft Survival Rates - KidneyKidney

75

80

85

90

95

100

Gra

ft Su

rviv

al (%

)

Living Donor 91.3 91.5 92.7 92.7 92.7 94.2 94.7 94.5 94.3 94.3

Deceased Donor 82.9 82.3 84.5 86.1 87.7 88.5 88.5 89.2 88.2 89.2

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Source: UNOS

6

Kidney Transplant ProcessKidney Transplant Process

End StageRenal Disease

Imminent

PatientAdvised of

Options

Option SelectedAfter

Consultation

Transplant?

Completion ofCenter Prescribed

Pre-TransplantTests

LivingRelated

?

DialysisSelected

?

AdditionalMedication and

Dietary RegimensCommence

AlternativeProtocols

Prescribed andFollowed

A

Patient’s HealthStatus

ContinuallyMonitored

PotentialKidney

Identified

PatientNotified

PatientAdmitted to

Transplant Ctr.

ContinuousRegional

Harvesting andTissue Typing

National Liaison with

UNOS

1Access TypeIdentified and

Prepared

2

3

4

C

BYes

No

No

No

Yes

Yes

X

X

Yes

7

Kidney Transplant Process Kidney Transplant Process (Continued)(Continued)

XX

1

2

3

4

DialysisRegimen

Commences

MedicalAssessment

OfTest Results

TransplantCandidate

?

Patient ListedWith

UNOSA

MonthlyTissueTyping

Identify andComplete

Required MedicalTest

Final Donor andPatient Tissue

Typing

Match?

PatientPreparation

GraftTransplantation

C

BLife-Long

Patient Careand Follow-up

No (See Footnote)

Yes

Yes

No

Note: If living related option exists without sufficient blood and antigen matching, or the health of the living related donor is in question, transplantation is not an option. UNOS is not notified in this situation.

8

Post Kidney Transplant Post Kidney Transplant IPOIPO

Post KidneyTransplantation

Process

Prograf

Cellcept

Methyl Prednisone

Creatinine (Cr)

White Blood Count (WBC)

Blood Urea Nitrogen (BUN)

Daily Process to Treat Acute, Post Transplant Rejection

6:00 AM – Blood Test7:00 AM – Blood Results Posted8:00 AM – Surgeon Compares Blood Results

With Medication Dose Levels; Prescribes Changes

9

Transfer FunctionsTransfer Functions

Where does the transfer function come from?

• Exact transfer Function

• Approximations

- DOE

- Historical Data Analysis

- Simulation

Process y (CTC)

X1

X2

X3

s

y = f1 (x1, x2, x3)

= f2 (x1, x2, x3)

Parameters or Factors

that Influence the CTC

© 2004 Air Academy Associates LLC

10

Exact Transfer FunctionExact Transfer Function• Many transfer functions are representative of additive components:

• Loan processing involves 5 steps

Total Processing Time = y = T1 + T2 + T3 + T4 + T5

where Ti = Time to Process Step i

Bi = Height of Block i

B1

B2

B3

B4

y = Total Height = B1 + B2 + B3 + B4

Dept. 1

Dept. 2

Dept. 3

Dept. 4

Dept. 5© 2004 Air Academy Associates LLC

11

Exact Transfer FunctionExact Transfer Function• Engineering Relationships

- V = IR- F = ma

R2

R1 The equation for the impedance (Z) through this circuit is defined by:

21

21

RR

RRZ

Where N: total number of turns of wire in the solenoid: current in the wire, in amperes

r : radius of helix (solenoid), in cm : length of the helix (solenoid), in cm x : distance from center of helix (solenoid), in cmH: magnetizing force, in amperes per centimeter

2222 )x5(.r

x5.

)x5(.r

x5.

2

NH

r

x

The equation for magnetic force at a distance X from the center of a solenoid is:

© 2004 Air Academy Associates LLC

12

Purposeful changes of the inputs (factors) in order to observe corresponding changes in the output (response).

What Is a Designed What Is a Designed Experiment?Experiment?

Run

1

2

3

.

.

X1 X2 X3 X4 Y1 Y2 . . . . . . Y SY

Inputs

X1

X2

X4

X3

Y1

Outputs

.

.

.

.

.

.

PROCESS Y2

© 2004 Air Academy Associates LLC

13

Statapult

Catapulting Statistics Catapulting Statistics Into Into

Engineering CurriculaEngineering Curricula

© 2004 Air Academy Associates LLC

14

y

B

D

R

d

x0

00 x

0 y

Mg

F

mg

0

Catapulting Statistics Catapulting Statistics Into Into

Engineering Curricula Engineering Curricula (cont.)(cont.)

© 2004 Air Academy Associates LLC

15

FormulasFormulas

)sin(sin)rmgrMg(dcosins)F(rI2

10BGF

20

sin)rmgrMg(cossin)(FrI BGF0 ,

cosrd

sinrDtan

F

F

).sin(sin)rmgrMg(dcossin)F(rI2

101BGF

210

1B1B cosr21

t2

cosvx

.gt2

1t

2sinvsinry 2

1B1B

.0

2cos

)cosrR(

V2

g

2tan)cosrR(sinr

2

12

1B2B

11B1B

11B1B12

21B

B

0

2tan)cosrR(sinr

2cos

)cosrR(

r4

gI

0

1

0

1

0

).sin(sin)rmgrMg(dcossin)F(r 01BGF

© 2004 Air Academy Associates LLC

16

Run

1

2

3

4

A B A B AB Y1 Y2 Y S

Actual Factors

Coded Factors Response Values

Avg –

Avg +

Y

Statapult ExerciseStatapult Exercise(DOE demonstration)(DOE demonstration)

© 2004 Air Academy Associates LLC

17

• • Total # of Combinations = 3Total # of Combinations = 355 = 243 = 243

• • Central Composite Design: n = 30Central Composite Design: n = 30

Modeling Flight

Characteristics

of New 3-Wing

Aircraft

Pitch )

Roll )

W1F )

W2F )

W3F )

INPUT OUTPUT

(-15, 0, 15)

(-15, 0, 15)

(-15, 0, 15)

(0, 15, 30)

(0, 15, 30)

Six Aero-

Characteristics

Value Delivery: Reducing Value Delivery: Reducing Time to Market for New Time to Market for New

TechnologiesTechnologies

© 2004 Air Academy Associates LLC

18

CCLL = = .233 + .008(P).233 + .008(P)22 + .255(P) + .012(R) - .043(WD1) - .117(WD2) + .255(P) + .012(R) - .043(WD1) - .117(WD2)

+ .185(WD3) + .010(P)(WD3) - .042(R)(WD1) + .035(R)(WD2) + .016(R)+ .185(WD3) + .010(P)(WD3) - .042(R)(WD1) + .035(R)(WD2) + .016(R)(WD3) + .010(P)(R) - .003(WD1)(WD2) - .006(WD1)(WD3)(WD3) + .010(P)(R) - .003(WD1)(WD2) - .006(WD1)(WD3)

CCDD = = .058 + .016(P).058 + .016(P)22 + .028(P) - .004(WD1) - .013(WD2) + .013(WD3) + .028(P) - .004(WD1) - .013(WD2) + .013(WD3)

+ .002(P)(R) - .004(P)(WD1) - .009(P)(WD2) + .016(P)(WD3) - .004(R)+ .002(P)(R) - .004(P)(WD1) - .009(P)(WD2) + .016(P)(WD3) - .004(R)(WD1) + .003(R)(WD2) + .020(WD1)(WD1) + .003(R)(WD2) + .020(WD1)22 + .017(WD2) + .017(WD2)22 + .021(WD3) + .021(WD3)22

CCYY = = -.006(P) - .006(R) + .169(WD1) - .121(WD2) - .063(WD3) - .004(P)(R) -.006(P) - .006(R) + .169(WD1) - .121(WD2) - .063(WD3) - .004(P)(R)

+ .008(P)(WD1) - .006(P)(WD2) - .008(P)(WD3) - .012(R)(WD1) + .008(P)(WD1) - .006(P)(WD2) - .008(P)(WD3) - .012(R)(WD1) - .029(R)(WD2) + .048(R)(WD3) - .008(WD1)- .029(R)(WD2) + .048(R)(WD3) - .008(WD1)22

CCMM = = .023 - .008(P).023 - .008(P)22 + .004(P) - .007(R) + .024(WD1) + .066(WD2) + .004(P) - .007(R) + .024(WD1) + .066(WD2)

- .099(WD3) - .006(P)(R) + .002(P)(WD2) - .005(P)(WD3) + .023(R)- .099(WD3) - .006(P)(R) + .002(P)(WD2) - .005(P)(WD3) + .023(R)(WD1) - .019(R)(WD2) - .007(R)(WD3) + .007(WD1)(WD1) - .019(R)(WD2) - .007(R)(WD3) + .007(WD1)22 - .008(WD2) - .008(WD2)22 + .002(WD1)(WD2) + .002(WD1)(WD3)+ .002(WD1)(WD2) + .002(WD1)(WD3)

CCYMYM== .001(P) + .001(R) - .050(WD1) + .029(WD2) + .012(WD3) + .001(P)(R) - .001(P) + .001(R) - .050(WD1) + .029(WD2) + .012(WD3) + .001(P)(R) -

.005(P)(WD1) - .004(P)(WD2) - .004(P)(WD3) + .003(R)(WD1) + .008(R).005(P)(WD1) - .004(P)(WD2) - .004(P)(WD3) + .003(R)(WD1) + .008(R)(WD2) - .013(R)(WD3) + .004(WD1)(WD2) - .013(R)(WD3) + .004(WD1)22 + .003(WD2) + .003(WD2)22 - .005(WD3) - .005(WD3)22

CCee = = .003(P) + .035(WD1) + .048(WD2) + .051(WD3) - .003(R)(WD3) .003(P) + .035(WD1) + .048(WD2) + .051(WD3) - .003(R)(WD3)

+ .003(P)(R) - .005(P)(WD1) + .005(P)(WD2) + .006(P)(WD3) + .002(R)+ .003(P)(R) - .005(P)(WD1) + .005(P)(WD2) + .006(P)(WD3) + .002(R)(WD1)(WD1)

Aircraft EquationsAircraft Equations

© 2004 Air Academy Associates LLC

19

Fusing Titanium and Fusing Titanium and Cobalt-ChromeCobalt-Chrome

© 2004 Air Academy Associates LLC

20

Historical Data Analysis

• Can be used to develop a mathematical model of a process without conducting a designed experiment.

• Using historical data is a very efficient way to use data that may already be available.

• Can be used with manufacturing or transactional data.

• The drawback to historical data is that there is more noise in it than is typically found in data obtained from a designed experiment.

─ More difficult to analyze.─ Lacks the orthogonality that characterizes DOE─ Requires an analysis of tolerances and a dose of luck to

iterate an approximate transfer function.

21

Renal Transplant Renal Transplant ExampleExample

• Analyze the data on the following page, which represents 38 consecutive days of post-operative treatment. Build a model or transfer function that will predict y as a function of the input variables A, B, and C. Examine what effect each medication has on the response or output variable. Medication A was an experimental drug at the time. What can you say about its effect on y?

• The input variables are dosages of three different medications given to a patient who has just received a kidney transplant. The output (y) variable is the Amount of Creatinine which should be minimized to avoid rejection. There are other important output variables as well, but we will look only at Creatinine in this exercise.

Effect of Medication Dosage on Renal Performance

y: Amount of Creatinine

Prograf (FK506)

Cellcept

Methylprednisome

KidneyFunctionProcess

22

38 Days of Medication 38 Days of Medication Dosage and Creatinine Dosage and Creatinine

LevelsLevelsFactor A B CRow # A B C Y1 Y bar

1 4 2 36 2 22 4 2 20 2 23 5 2 20 1.8 1.84 5 2 20 2.9 2.95 6 2 20 3.5 3.56 9 2 80 3.8 3.87 9 2 50 3.9 3.98 11 2 20 4.3 4.39 12 2 20 3.9 3.9

10 13 2 20 3.5 3.511 15 2 20 3.1 3.112 16 2 20 2.5 2.513 17 2 20 2.2 2.214 19 2 20 2.2 2.215 20 2 20 1.9 1.916 20 2 20 1.8 1.817 18 2 20 2.9 2.918 16 2 20 2.8 2.819 13 2 20 2.9 2.9

Factor A B CRow # A B C Y1 Y bar

20 14 2 0 2.9 2.921 13 2 0 2.8 2.822 12 2 0 2.6 2.623 13 2 0 2.7 2.724 15 2 0 2.8 2.825 16 2 0 2.8 2.826 17 2 0 2.4 2.427 18 2 0 2.4 2.428 9 2 0 2.1 2.129 17 2 0 2 230 16 2 20 2 231 16 2 20 1.9 1.932 14 2 16 1.7 1.733 14 2 16 1.8 1.834 14 2 14 1.9 1.935 13 1.5 12 1.9 1.936 13 0.5 12 2 237 11 1 10 1.9 1.938 11 1 8 2.2 2.2

S S S

The following analysis utilizes Air Academy’s DOE PRO Software.

23

Removing Insignificant Removing Insignificant Terms from The ModelTerms from The Model

Factor Name Coeff P(2 Tail) Tol Act

ive

Const 2.65461 0.0000A A -0.25577 0.0422 0.662 XB B 0.80414 0.1341 0.035 XC C 0.21045 0.1669 0.435 X

AA -0.31408 0.0042 0.566 X

ABC -0.76559 0.4948 0.081

AC 0.12309 0.7522 0.076

BB 0.15555 0.2700 0.048

CC -0.01983 0.7761 0.241 X

Rsq 0.4219

Adj Rsq 0.2624

Std Error 0.5956

F 2.6457

Sig F 0.0260

Source SS df MSRegression 7.5 8 0.9

Error 10.3 29 0.4Total 17.8 37

Factor Name Coeff P(2 Tail) Tol Act

ive

Const 2.80827 0.0000A A -0.25956 0.0303 0.700 XB B 0.24520 0.0217 0.889 XC C 0.20856 0.1593 0.438 X

AA -0.28237 0.0048 0.637 X

CC 0.01172 0.8117 0.462

Rsq 0.3895

Adj Rsq 0.2942

Std Error 0.5826

F 4.0838 99% Prediction IntervalSig F 0.0056

Source SS df MS

Regression 6.9 5 1.4

Error 10.9 32 0.3Total 17.8 37

First Regression Model Second Regression Model

24

Transfer Function for Renal Transfer Function for Renal PerformancePerformance

Factor Name Coeff P(2 Tail) Tol Act

ive

Const 2.82678 0.0000A A -0.26350 0.0244 0.714 XB B 0.24774 0.0181 0.899 XC C 0.23312 0.0273 0.874 X

AA -0.28967 0.0021 0.713 X

PredictionRsq 0.3884

Adj Rsq 0.3143

Std Error 0.5742

F 5.2400

Sig F 0.0022 99% Prediction Interval

Source SS df MS

Regression 6.9 4 1.7

Error 10.9 33 0.3

Total 17.8 37

Final Regression Model

25

Surface PlotSurface Plot

4 5.6 7.2 8.8 10.4 12 13.6 15.2 16.8 18.4 20

0

16

32

48

64

80

0

0.5

1

1.5

2

2.5

3

3.5

4

Res

po

nse

Val

ue

A

C

Surface Plot of A vs. C Constants: B = 2

3.5-4

3-3.5

2.5-3

2-2.5

1.5-2

1-1.5

0.5-1

0-0.5

26

Contour PlotContour Plot

4 5.6 7.2 8.8 10.4 12 13.6 15.2 16.8 18.4 20

0

8

16

24

32

40

48

56

64

72

80

A

C

Contour Plot of A vs. C Constants: B = 2

3.6-4

3.2-3.6

2.8-3.2

2.4-2.8

2-2.4

1.6-2

1.2-1.6

0.8-1.2

0.4-0.8

0-0.4

27

Interaction PlotInteraction PlotInteraction Plot of A vs. C

Constants: B = 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

4 5.6 7.2 8.8 10.4 12 13.6 15.2 16.8 18.4 20A

Res

po

nse

Val

ue

0

80

28

Changes in Creatinine Over Changes in Creatinine Over Time Time

(X-Bar Charts)(X-Bar Charts)Xbar Chart

UCL=3.1088

LCL=2.0017

CEN=2.5553

00.5

11.5

22.5

33.5

44.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

First 38 Days Post Transplant

6 to 8 Years Post Transplant

Xbar Chart

UCL=2.00062

LCL=1.53785

CEN=1.76923

00.5

11.5

22.5

33.5

44.5

1 2 3 4 5 6 7 8 9 10 11 12 13

This analysis utilizes Air Academy’s SPC XL Software.

29

R Chart

UCL=0.96195

LCL=0.0

CEN=0.29444

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

R Chart

UCL=0.40209

LCL=0.0

CEN=0.12308

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12 13

Changes in Creatinine Over Changes in Creatinine Over Time Time

(R-Bar Charts)(R-Bar Charts)

This analysis utilizes Air Academy’s SPC XL Software.

First 38 Days Post Transplant

6 to 8 Years Post Transplant

30

Summary: Six Sigma Tools Summary: Six Sigma Tools UsedUsed

• IPO DiagramIPO Diagram

•Process Flow ChartProcess Flow Chart

•Run ChartRun Chart

•Control ChartsControl Charts

•Historical Data AnalysisHistorical Data Analysis

31

ConclusionsConclusions• Post transplant organ rejections are expected.Post transplant organ rejections are expected.• The duration of the episode:The duration of the episode:

– Requires the administration of toxic medications.Requires the administration of toxic medications.– Reduces the expected life of the graft.Reduces the expected life of the graft.– Causes emotional and physical stress to the recipient and Causes emotional and physical stress to the recipient and

family.family.– Results in significant and adverse financial effects for the Results in significant and adverse financial effects for the

family and society.family and society.

• Six Sigma tools, such as historical data analysis, can Six Sigma tools, such as historical data analysis, can assist the transplant team:assist the transplant team:– Optimization of the medication regimen faster.Optimization of the medication regimen faster.– Earlier release of transplant recipient.Earlier release of transplant recipient.– Longer life of transplanted graft.Longer life of transplanted graft.– Longer and better quality of life for the transplant recipient.Longer and better quality of life for the transplant recipient.– Reduced financial impact to the provider, family and society.Reduced financial impact to the provider, family and society.

• Six Sigma tools can also assist the recipient and family Six Sigma tools can also assist the recipient and family through enhanced awareness and education.through enhanced awareness and education.