Javier Garcia - Verdugo Sanchez Six Sigma Training. Week 3. Solver, a helpful Microsoft Excel application.

1. Solver
> A helpful Microsoft Excel application<
Week 3
Knorr-Bremse Group
About this module
The SOLVER is an Excel application
is an easy and fast tool for :
pp
is an easy and fast tool for :
• Solution of DOE equations
• Optimization of the Mean
• Optimization of the Variation
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 2/14

2. Solver in Excel
Extras
S l>Solver
The Solver function is not
at all installation activatedat all installation activated
automatically. In this case
you have to activate it over
the “Add Ins Manager”.the Add Ins Manager .
Extras
>Add Ins Manager
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 3/14
The Solver in Excel
Extras
>Solver
Mean or Targeting Model:
Term Effect Coef Factor Coef*Factor
Constant 104,563 1,0000 104,563
angle 64,458 32,229 0,5820 18,757
>enter value
>solve
Fix point 55,292 27,646 1,0000 27,646
Tension 49,542 24,771 1,0000 24,771
angle*peg 18,625 9,313 0,5820 5,420
angle*hook 13,208 6,604 0,5820 3,843
185,00 <-- MEAN or TARGET
Varaiblity Model:
Term Effect Coef Factor Coef*Factor
Constant 7,968 1,000 7,968
angle 4,048 2,024 0,582 1,178
Tension -4,081 -2,041 1,000 -2,041
angle*tension -5,301 -2,65 0,582 -1,542
5 563 Sd5,563 <--- Sdev
angle coded value actual value
-1 140
1 180
171,6
Alternative
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 4/14

3. The catapult optimization
Ball type
6Rubber band -
fix point Rubber band -
tension adjustment
4 4
Rubber band5
6
Stop -Position3
4
2
3
4
2
2
345
1
2
Tension angle
6
1
1
26
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 5/14
Use of solver at the catapult example
In the file „Solver exersice.xls you find the results of a DOE
with the catapult and linked to the Solver. In order to get the
d l h t th i t l l i t Mi it bmodel we have to copy the experimental plan into Minitab.
The evaluation can be done for the single mean values and
the standard deviationthe standard deviation.
Angle Factor RT Factor RF Result 1 Result 2 Result 3Angle Factor RT Factor RF Result 1 Result 2 Result 3
1 -1 -1 85 74 58
1 -1 1 128 132 122
1 1 -1 150 145 120,5
1 1 1 215 208 204
-1 -1 -1 32 5 36 38 5-1 -1 -1 32,5 36 38,5
-1 -1 1 69 80 68
-1 1 -1 68 81,5 68,5
Factor RT: Rubber Tension Factor RF: Rubber Fix Point
-1 1 1 114 101,5 110,5
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 6/14
Factor RT: Rubber Tension Factor RF: Rubber Fix Point

4. Solver, further steps
Copy the Matrix in Minitabpy
• Calculate Standard Deviation
• Define Custom Factorial DesignDefine Custom Factorial Design
•DOE Analysis•DOE Analysis
• Define equation for mean value
D fi ti f V i ti• Define equation for Variation
•Create Excel sheet for evaluation with SOLVER
• Model for Mean• Model for Mean
• Model for Variation
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 7/14
Create model in Minitab
Analyze DOE and establish Excel table for Solver (for this example):
1. Copy Excel matrix in Minitab
2. Stack results R1, R2, R3, in column R1
3. Copy factor settings 2 times
4. Insert new column after column R3 and calculate standard deviation
Calc > Row Statistics
5. Define matrix for DOE evaluation
Stat > DOE > Define Custom Factorial Design
6 DOE evaluation for averages and standard Deviation6. DOE evaluation for averages and standard Deviation
Stat > DOE > Analyze Factorial Design
7. Establish equation (model) with significant factors/interactions (P-value!)
8 Transfer model in Excel for averages and standard deviation8. Transfer model in Excel for averages and standard deviation
• Form sum from all Coef x Factors (use excel functions) Target Cell
• Define Changing Cells
• Define Constraints for changing cells
• Enter required value in Target cell field Target Cell
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 8/14

5. The Solver in Excel
Definitions: 1
2
1) Target cell:
3
1) Target cell:
Cell which shows the result of the
equation
(M & StD )
4
(Mean & StDev)
2) Target value:
Defined value for target cell
(Target for Mean & StDev)
3) Changing cells:
Cells which changes
corresponding the Target value
The following operators can be used for
constraints:
Sign Meaningcorresponding the Target value
(Setting of the factors, „Factor
level“)
Sign Meaning
<= smaller equal
>= bigger equal
= equal
4) Constraints:
Conditions for changing cells
= equal
Integer integer (for changing cells only)
bin Binary (for changing cells only)
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 9/14
(Constraints for settings)
Solution of a problem with Solver
1. Click in the Menu Extras on Solver.
(Is the command Solver in menu Extras not shown, activate with “Add-In
M ”)Manager”)
The procedureThe procedure
2 Enter in the field Target Cell a cell relation or a name for the Target cell2. Enter in the field Target Cell a cell relation or a name for the Target cell.
The Target cell has to include an equation.
3. To define the highest value for the Target cell, click on Max.
To define the lowest value for the Target cell, click on Min.
To define a certain value in the Target cell, enter the corresponding
value in this field.
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 10/14

6. Solution of a problem with Solver
4 Enter in the field Changing Cells the name or the cell relation for the4. Enter in the field Changing Cells the name or the cell relation for the
changing cells, separate not adjacent relations with a semicolon. The
changing cells have to have a direct or indirect relation to the Target cell.
You can define up to 200 changing cellsYou can define up to 200 changing cells.
If solver shall calculate automatically the values of depending cellsIf solver shall calculate automatically the values of depending cells
based on the value in the Target cell, click on estimate.
5. Enter in the field Subject to the Constraints the applicable constraints.
6. Click on solve.
7 I d t h th lt i th t bl li k i th di l b lt7. In order to show the results in the table click in the dialog box result
click on use solution.
In order to see the origin values again click on restore start values.
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 11/14
Summary
If you analyze a DOE and calculate the effects of the factors
and the interactions you are able to establish an empirical equationand the interactions you are able to establish an empirical equation
(mathematical Model). With the SOLVER function the equation can
be solved in order to optimize the described process in respect tobe solved in order to optimize the described process in respect to
required response:
Factor adjustment for optimized Mean value
Factor adjustment for optimized Standard deviation
Optimization of Std. dev. In relation to Mean and versus
Attention consider error term in calculation!
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 12/14
Attention, consider error term in calculation!

7. Solver in Excel (English Version)
Extras
S l>Solver
The Solver function is not
at all installation activatedat all installation activated
automatically. In this case
you have to activate it over
the “Add Ins Manager”.the Add Ins Manager .
Extras
>Add Ins Manager
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 13/14
Solver in Excel (Hungary Version)
Extras
S l>Solver
The Solver function is not
at all installation activatedat all installation activated
automatically. In this case
you have to activate it over
the “Add Ins Manager”.the Add Ins Manager .
Extras
>Add Ins Manager
Knorr-Bremse Group 05b BB W3 Solver, 04, D. Szemkus/H. Winkler Page 14/14