- 1. Six Sigma Applications in a Renal Transplantation Process Dr. Lee Pollock Kidney Transplant Recipient from the University of Miami/Jackson Memorial Hospital with Analysis fromDr. Mark Kiemele Air Academy Associates
2. Background Statistics
- As of 4 Nov 04 in the US:
- 87,249 Waiting List Candidates (85,595 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)
- Median Waiting Times, Based on Blood Type, are Increasing Each Year:
- Heart Lung: 252-1084 Days
- Kidney Pancreas: 311-650 Days
- New Registrations are Outpacing Transplantation Rates
- Long Term Graft Survival Rates are Excellent and Increasing Each Year
3. Kidney Median Waiting Times 1996-2001 Source: UNOS 4. Kidney New Registrations: 1999-2001 Source: UNOS 5. Graft Survival Rates - Kidney Source: UNOS 6. Kidney Transplant Process End Stage Renal Disease Imminent Patient Advised of Options Option Selected After Consultation Transplant ? Completion of Center Prescribed Pre-Transplant Tests Living Related ? Dialysis Selected ? Additional Medication and Dietary Regimens Commence Alternative Protocols Prescribed and Followed A Patients Health StatusContinually Monitored Potential Kidney Identified Patient Notified Patient Admitted to Transplant Ctr. Continuous Regional Harvesting and Tissue Typing NationalLiaison with UNOS 1 Access Type Identified and Prepared 2 3 4 C B Yes No No No Yes Yes X X Yes 7. Kidney Transplant Process(Continued) X X 1 2 3 4 Dialysis Regimen Commences Medical Assessment Of Test Results Transplant Candidate ? Patient Listed With UNOS A Monthly Tissue Typing Identify and Complete Required Medical Test Final Donor and Patient Tissue Typing Match ? Patient Preparation Graft Transplantation C B Life-Long Patient Care and 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 IPO Post Kidney Transplantation 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 Test 7:00 AM Blood Results Posted 8:00 AM Surgeon Compares Blood ResultsWith Medication Dose Levels; Prescribes Changes 9. Transfer Functions
- Where does the transfer function come from?
- - Historical DataAnalysis
2004 Air Academy Associates LLC Process y (CTC) X 1 X 2 X 3 s y = f 1(x 1 , x 2 , x 3 ) = f 2(x 1 , x 2 , x 3 ) Parameters or Factors that Influence the CTC 10. Exact Transfer Function Dept. 1 Dept. 2 Dept. 3 Dept. 4 Dept. 5 2004 Air Academy Associates LLC
- Many transfer functions are representative of additive components:
- Loan processing involves 5 steps
- Total Processing Time = y = T 1+ T 2+ T 3+ T 4+ T 5
- where T i= Time to Process Step i
B i= Height of Block i B 1 B 2 B 3 B 4 y = Total Height = B 1+ B 2+ B 3+ B 4 11. Exact Transfer Function 2004 Air Academy Associates LLC
- Engineering Relationships
R 2 R 1 The equation for the impedance (Z) through this circuit is defined by: 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 cm H : magnetizing force, in amperes per centimeter r x The equation for magnetic force at a distance X from the center of a solenoid is: 12. What Is a Designed Experiment? Purposeful changes of the inputs (factors) in order to observe corresponding changes in the output (response). 2004 Air Academy Associates LLC Run 1 2 3 . . X 1 X 2 X 3 X 4 Y 1Y 2 . . . . . .Y S Y Inputs X 1 X 2 X 4 X 3 Y 1 Outputs . . . . . . PROCESS Y 2 13. Catapulting Statistics IntoEngineering Curricula Statapult 2004 Air Academy Associates LLC 14. Catapulting Statistics IntoEngineering Curricula (cont.) 2004 Air Academy Associates LLC y B D R d x 0 0 0 x 0 y Mg F mg 0 15. Formulas 2004 Air Academy Associates LLC 16. Statapult Exercise (DOE demonstration) Run 1 2 3 4 AB AB AB Y 1Y 2 Y S Actual Factors Coded Factors Response Values Avg Avg + 2004 Air Academy Associates LLC 17. Value Delivery:Reducing Time to Market for New Technologies Total # of Combinations= 3 5= 243Central 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 2004 Air Academy Associates LLC 18. Aircraft Equations
- C L= .233 + .008(P) 2+ .255(P) + .012(R) - .043(WD1) - .117(WD2) + .185(WD3) + .010(P)(WD3) - .042(R)(WD1) + .035(R)(WD2) + .016(R)(WD3) + .010(P)(R) - .003(WD1)(WD2) - .006(WD1)(WD3)
- C D= .058 + .016(P) 2+ .028(P) - .004(WD1) - .013(WD2) + .013(WD3) + .002(P)(R) - .004(P)(WD1) - .009(P)(WD2) + .016(P)(WD3) - .004(R)(WD1) + .003(R)(WD2) + .020(WD1) 2+ .017(WD2) 2+ .021(WD3) 2
- C Y= -.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) - .029(R)(WD2) + .048(R)(WD3) - .008(WD1) 2
- C M= .023 - .008(P) 2+ .004(P) - .007(R) + .024(WD1) + .066(WD2) - .099(WD3) - .006(P)(R) + .002(P)(WD2) - .005(P)(WD3) + .023(R)(WD1) - .019(R)(WD2) - .007(R)(WD3) + .007(WD1) 2- .008(WD2) 2+ .002(WD1)(WD2) + .002(WD1)(WD3)
- C YM = .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)(WD2) - .013(R)(WD3) + .004(WD1) 2+ .003(WD2) 2- .005(WD3) 2
- C e= .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)(WD1)
2004 Air Academy Associates LLC 19. Fusing Titanium and Cobalt-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 toiterate an approximate transfer function.
21. Renal Transplant Example
- 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 Performancey: Amount of Creatinine Prograf (FK506) Cellcept Methylprednisome Kidney Function Process 22. 38 Days of Medication Dosage and Creatinine Levels The following analysis utilizes Air Academys DOE PRO Software. 23. Removing Insignificant Terms from The Model First Regression Model Second Regression Model 24. Transfer Function for Renal Performance Final Regression Model 25. Surface Plot 26. Contour Plot 27. Interaction Plot 28. Changes in Creatinine Over Time(X-Bar Charts) First 38 Days Post Transplant 6 to 8 Years Post Transplant Xbar Chart UCL=2.00062 LCL=1.53785 CEN=1.76923 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 5 6 7 8 9 10 11 12 13 This analysis utilizes Air Academys SPC XL Software. 29. Changes in Creatinine Over Time(R-Bar Charts) This analysis utilizes Air Academys SPC XL Software. First 38 Days Post Transplant 6 to 8 Years Post Transplant 30. Summary: Six Sigma Tools Used