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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.