Excel Report

Champion of Italy ® 2005-2006 SixSigmaIn Team snc
Transfer Function  R= f(A,B,…) ((1/B)+(1/C)-D)*A**2
Data Entry Summary [R] [A] [B] [C] [D]
Variable Name Power V_In Res_1 Res_2 Xi
IV Distribution Type Normal Normal Normal Normal
IVD 1*Par Value (Nominal Mean) 50 5 10 2.5
IVD 2*Par Value (Nominal StDev) 0.53 0.1 0.1 0.03
IVD 3*Par Value (..) 0 0 0 0
Lower Spec Limit (IV*opt) -5800 48 4.5 9.5 2.4
Upper Spec Limit (IV*opt) -5200 52 5.5 10.5 2.6
Use/Priority in Solver (0 to 1) 1 1 1 1
Upper Z-LT Constrains (*opt) 6 6 6 6
Simulation Summary - Step 0 [R] [A] [B] [C] [D]
Variable Name Power V_In Res_1 Res_2 Xi
Mean -5500.45 50.00045 4.999997 9.999862 2.499984
Standard Deviation 138.9376 0.529803 0.099944 0.099914 0.029963
Anderson-Darling 28.93528
P Value 0
Coeff. of Variability -0.02526 0.010596 0.019989 0.009991 0.011985
Mean Std. Error 0.138938 0.00053 0.0001 0.0001 0.00003
Variance 19303.66 0.280691 0.009989 0.009983 0.000898
Skewness -0.0515 -4.8E-05 0.000825 -0.00229 -0.00061
Kurtosis 3.007584 3.00702 3.002638 3.003095 2.99592
Median -5499.24 50.00075 4.999929 9.99997 2.500004
IQ1 -5593.41 49.64346 4.932633 9.93261 2.479753
IQ3 -5406.27 50.35744 5.067286 10.0672 2.520195
Range Minimum -6214.3 47.57431 4.525319 9.460738 2.350488
Range Maximum -4863.18 52.45114 5.484932 10.55048 2.646519
Range Width 1351.118 4.876835 0.959613 1.089743 0.296031
Lower Spec Limit/Test -5800 48 4.5 9.5 2.4
Upper Spec Limit/Test -5200 52 5.5 10.5 2.6
Ppk 0.718672 1.258046 1.667592 1.667649 1.112297
Pp 0.719747 1.25833 1.667601 1.668108 1.112472
PpL 0.718672 1.258613 1.667592 1.667649 1.112297
PpU 0.720823 1.258046 1.66761 1.668567 1.112647
Z-LT Value 2.156015 3.774139 5.002777 5.002947 3.336892
L-PPM 16746 78 0 1 419
U-PPM 14155 94 0 1 387
PPM 30901 172 0 2 806
Prob @<LSL 0.016746 0.000078 0 0.000001 0.000419
Prob @>USL 0.014155 0.000094 0 0.000001 0.000387
Prob @>=LSL And <=@USL 0.969099 0.999828 1 0.999998 0.999194
L-Area Items (1 Million base) 16746 78 0 1 419
R-Area Items(1 Million base) 14155 94 0 1 387
C-Area Items(1 Million base) 969099 999828 1000000 999998 999194
Variable [R] [A] [B] [C] [D]
Contribution to Variance 0 0.703866 5.11E-03 3.40E-04 0.290683
M [..] [R] [A] [B] [C] [D]
Pearson [R].. [Var(N)) 1 -0.83881 -0.07148 -1.84E-02 -0.53905
Pearson [A].. [Var(N)) 1 -2.36E-04 7.63E-04 -1.44E-04
Pearson [B].. [Var(N)) 1 5.52E-04 -6.71E-04
Pearson [C].. [Var(N)) 1 -3.95E-04
Pearson [D].. [Var(N)) 1
5D CubeSpace Analysis © -  14 populated on  243 possible HyperCubes
HyperCube Items
[<R_f(=A,=B,=C,=D)] 16501
[<R_f(=A,=B,=C,>D)] 155
[<R_f(>A,=B,=C,=D)] 90
[=R_f(<A,=B,=C,=D)] 2
[=R_f(=A,=B,<C,=D)] 1
[=R_f(=A,=B,=C,<D)] 261
[=R_f(=A,=B,=C,=D)] 968598
[=R_f(=A,=B,=C,>D)] 232
[=R_f(=A,=B,>C,=D)] 1
[=R_f(>A,=B,=C,<D)] 1
[=R_f(>A,=B,=C,=D)] 3
[>R_f(<A,=B,=C,=D)] 76
[>R_f(=A,=B,=C,<D)] 157
[>R_f(=A,=B,=C,=D)] 13922
Defects Pareto Analysis:  6 HyperCubes found
DF_HyperCube DF_Items Cum_DF
[<R_f(=A,=B,=C,=D)] 16501 16501
[>R_f(=A,=B,=C,=D)] 13922 30423
[>R_f(=A,=B,=C,<D)] 157 30580
[<R_f(=A,=B,=C,>D)] 155 30735
[<R_f(>A,=B,=C,=D)] 90 30825
[>R_f(<A,=B,=C,=D)] 76 30901
Ppm StDev[R] StDev[A] StDev[B] StDev[C] StDev[D]
18242 127.1626 0.479504 0.099083 0.09962 0.028107
15278 123.8096 0.465489 0.09876 0.099464 0.027533
14148 122.3627 0.459552 0.098588 0.099348 0.02727
13378 121.3521 0.455457 0.098451 0.099241 0.02708
12653 120.3956 0.451592 0.098318 0.099134 0.026899
11967 119.4463 0.447758 0.098184 0.099028 0.026718
11320 118.4811 0.44386 0.098048 0.098922 0.026535
10667 117.4553 0.439709 0.097905 0.098813 0.026341
9990 116.4154 0.435501 0.09776 0.098704 0.026144
9334 115.3171 0.431051 0.097607 0.098593 0.025936
8648 114.1621 0.426366 0.097448 0.098481 0.025718
7939 112.952 0.421455 0.097281 0.098366 0.025491
7209 111.6667 0.416233 0.097104 0.098249 0.025249
6537 110.287 0.410622 0.096916 0.098129 0.02499
5858 108.8161 0.404637 0.096714 0.098006 0.024714
5158 107.236 0.398205 0.096498 0.097878 0.024418
4455 105.4885 0.391086 0.096259 0.097745 0.024091
3814 103.5591 0.383225 0.095994 0.097605 0.023729
3105 101.3542 0.374238 0.095689 0.097454 0.023315
2364 98.74455 0.363602 0.095325 0.097287 0.022824
StD[R] 87.1133891541238 +6.18028434940138E-3*Ppm^1 -6.37727208967401E-7*Ppm^2 +4.62282804684211E-11*Ppm^3 -1.76095977784659E-15*Ppm^4 +2.66835124621747E-20*Ppm^5
R2 Eq[R] 0.999982
StD[A] .316250111723311 +2.5148670172917E-5*Ppm^1 -2.58889977917384E-9*Ppm^2 +1.87464146345748E-13*Ppm^3 -7.17928276097469E-18*Ppm^4 +1.10404362848931E-22*Ppm^5
R2 Eq[A] 0.999982
StD[B] 9.36642171855872E-2 +8.94572134852681E-7*Ppm^1 -9.77399290325435E-11*Ppm^2 +7.25727760076364E-15*Ppm^3 -2.70038449806112E-19*Ppm^4 +3.69923120545572E-24*Ppm^5
R2 Eq[B] 0.999982
StD[C] .096583325758565 +3.53941085541408E-7*Ppm^1 -2.91173043033768E-11*Ppm^2 +2.05941148656798E-15*Ppm^3 -5.60867256721987E-20*Ppm^4 -1.11407499567464E-26*Ppm^5
R2 Eq[C] 0.999956
StD[D] 2.06221306266949E-2 +1.17395437840762E-6*Ppm^1 -1.22927961060299E-10*Ppm^2 +8.95432996950513E-15*Ppm^3 -3.36644396386368E-19*Ppm^4 +4.90019002216455E-24*Ppm^5
R2 Eq[D] 0.999983
Equations Validity Range (Ppm) 2364 18242
Simulation Summary - Step 20 [R] [A] [B] [C] [D]
Variable Name Power V_In Res_1 Res_2 Xi
Mean -5500.13 50.00032 4.999998 9.999866 2.499988
Standard Deviation 100.4014 0.370487 0.095512 0.097313 0.02312
Anderson-Darling 15.67652
P Value 0
Coeff. of Variability -0.01825 0.00741 0.019102 0.009731 0.009248
Mean Std. Error 0.100401 0.00037 0.000096 0.000097 0.000023
Variance 10080.45 0.13726 0.009123 0.00947 0.000535
Skewness -0.03749 -4.8E-05 0.000825 -0.00229 -0.00061
Kurtosis 3.005148 3.00702 3.002638 3.003095 2.99592
Median -5499.5 50.00053 4.999932 9.999971 2.500003
IQ1 -5567.53 49.75068 4.93562 9.934364 2.484377
IQ3 -5432.2 50.24996 5.064303 10.06546 2.515582
Range Minimum -6006.56 48.30373 4.546369 9.474775 2.384636
Range Maximum -5031.7 51.71406 5.463427 10.53615 2.613055
Range Width 974.8664 3.410329 0.917057 1.061377 0.228419
Lower Spec Limit/Test -5800 48 4.5 9.5 2.4
Upper Spec Limit/Test -5200 52 5.5 10.5 2.6
Ppk 0.995567 1.799152 1.744977 1.712231 1.44159
Pp 0.996002 1.799436 1.744985 1.71269 1.441765
PpL 0.995567 1.799719 1.744977 1.712231 1.44159
PpU 0.996436 1.799152 1.744994 1.713149 1.44194
Z-LT Value 2.986702 5.397457 5.23493 5.136693 4.324771
L-PPM 1647 0 0 1 13
U-PPM 1181 0 0 1 9
PPM 2828 0 0 2 22
Prob @<LSL 0.001647 0 0 0.000001 0.000013
Prob @>USL 0.001181 0 0 0.000001 0.000009
Prob @>=LSL And <=@USL 0.997172 1 1 0.999998 0.999978
L-Area Items (1 Million base) 1647 0 0 1 13
R-Area Items(1 Million base) 1181 0 0 1 9
C-Area Items(1 Million base) 997172 1000000 1000000 999998 999978
Variable [R] [A] [B] [C] [D]
Contribution to Variance 0 0.659077 8.97E-03 6.09E-04 0.331348
M [..] [R] [A] [B] [C] [D]
Pearson [R].. [Var(N)) 1 -0.8117 -9.47E-02 -2.47E-02 -0.57554
Pearson [A].. [Var(N)) 1 -2.36E-04 7.63E-04 -1.44E-04
Pearson [B].. [Var(N)) 1 5.52E-04 -6.71E-04
Pearson [C].. [Var(N)) 1 -3.95E-04
Pearson [D].. [Var(N)) 1
5D CubeSpace Analysis © -  9 populated on  243 possible HyperCubes
HyperCube Items
[<R_f(=A,=B,=C,=D)] 1645
[<R_f(=A,=B,=C,>D)] 2
[=R_f(=A,=B,<C,=D)] 1
[=R_f(=A,=B,=C,<D)] 10
[=R_f(=A,=B,=C,=D)] 997153
[=R_f(=A,=B,=C,>D)] 7
[=R_f(=A,=B,>C,=D)] 1
[>R_f(=A,=B,=C,<D)] 3
[>R_f(=A,=B,=C,=D)] 1178
Defects Pareto Analysis:  4 HyperCubes found
DF_HyperCube DF_Items Cum_DF
[<R_f(=A,=B,=C,=D)] 1645 1645
[>R_f(=A,=B,=C,=D)] 1178 2823
[>R_f(=A,=B,=C,<D)] 3 2826
[<R_f(=A,=B,=C,>D)] 2 2828
Data Comparison [R] [A] [B] [C] [D]
Variable Name Power V_In Res_1 Res_2 Xi
Nominal Value -5500 50 5 10 2.5
Starting [R] Ppm 30901 30901 30901 30901 30901
Starting Mean -5500.45 50.00045 4.999997 9.999862 2.499984
Starting StDev 138.9376 0.529803 0.099944 0.099914 0.029963
Starting Tolerance (±) 416.8129 1.59 0.3 0.3 0.09
Starting LSL -5800 48 4.5 9.5 2.4
Starting USL -5200 52 5.5 10.5 2.6
Pp 0.719747 1.25833 1.667601 1.668108 1.112472
Target [R] Ppm 2828 2828 2828 2828 2828
Estimated Mean -5500.13 50.00032 4.999998 9.999866 2.499988
Estimated StDev 100.4014 0.370487 0.095512 0.097313 0.02312
Estimated Tolerance (±) 301.2043 1.11146 0.286535 0.291938 0.069359
LSL / Suggested LSL (Pp=1) -5800 48.88886 4.713462 9.707928 2.430628
USL / Suggested USL (Pp=1) -5200 51.11178 5.286533 10.29181 2.569347
Pp [Base Limits] 0.996002 1.799436 1.744985 1.71269 1.441765
Pp [Suggested Limits] 1 1 1 1
Defect Reduction % 90.84819
StDev Reduction % 27.73632 30.07087 4.434667 2.603041 22.83958
 
Minitab Project Report
 
—————   11/04/2006 11:26:12   ———————————————————— 

Welcome to Minitab, press F1 for help.
 
Results for: MTBdgSheet1 - Minitab MC Simulation (8000 Els)

Row   Els      Mean    StDev  C13  C14    Est_Pp  Est_<LSL  Est_>USL  Est_PpmTotal
  1  8000  -5501.22  139.040            0.719218   15822.9   15138.2       30961.2

* NOTE * One or more variables are undefined.

**************************************************************************
Transfer Function: [R] = ((1/B)+(1/C)-D)*A**2
See annexed docs for more info...
Starting Champion of Italy ® MC Simulation - 1. Million Els
... please wait during the elaboration ...
**************************************************************************
 
Results for: MTBdgSheet3 - Champion of Italy MC Simulation (1000000 Els)

                                                                              Mean
                        Standard                               Coeff. of      Std.
Row  Labels      Mean  Deviation  Anderson-Darling  P Value  Variability     Error  Variance   Skewness  Kurtosis    Median
  1  Power   -5500.45    138.938           28.9353        0    -0.025259  0.138938   19303.7  -0.051497   3.00758  -5499.24
  2  V_In       50.00      0.530                 *        *     0.010596  0.000530       0.3  -0.000048   3.00702     50.00
  3  Res_1       5.00      0.100                 *        *     0.019989  0.000100       0.0   0.000825   3.00264      5.00
  4  Res_2      10.00      0.100                 *        *     0.009991  0.000100       0.0  -0.002286   3.00310     10.00
  5  Xi          2.50      0.030                 *        *     0.011985  0.000030       0.0  -0.000611   2.99592      2.50

                            Range     Range               Lower Spec  Upper Spec
Row       IQ1       IQ3   Minimum   Maximum  Range Width  Limit/Test  Limit/Test      Ppk       Pp      PpL      PpU  Z-LT Value
  1  -5593.41  -5406.27  -6214.30  -4863.18      1351.12     -5800.0     -5200.0  0.71867  0.71975  0.71867  0.72082     2.15602
  2     49.64     50.36     47.57     52.45         4.88        48.0        52.0  1.25805  1.25833  1.25861  1.25805     3.77414
  3      4.93      5.07      4.53      5.48         0.96         4.5         5.5  1.66759  1.66760  1.66759  1.66761     5.00278
  4      9.93     10.07      9.46     10.55         1.09         9.5        10.5  1.66765  1.66811  1.66765  1.66857     5.00295
  5      2.48      2.52      2.35      2.65         0.30         2.4         2.6  1.11230  1.11247  1.11230  1.11265     3.33689

                                                            L-Area
                                                     Prob    Items
                                                   @>=LSL       (1
                                                      And  Million
Row  L-PPM  U-PPM    PPM  Prob @<LSL  Prob @>USL   <=@USL    base)
  1  16746  14155  30901    0.016746    0.014155  0.96910    16746
  2     78     94    172    0.000078    0.000094  0.99983       78
  3      0      0      0    0.000000    0.000000  1.00000        0
  4      1      1      2    0.000001    0.000001  1.00000        1
  5    419    387    806    0.000419    0.000387  0.99919      419

 
Results for: MTBdgSheet5 - HyperCubes Report

**************************************************************************
Starting Champion of Italy ® 20 Steps Equations Optimizer
Creating Equations ... please wait ...
**************************************************************************
**************************************************************************
HyperSpace Defects Optimization done - 43.157 sec required. (2.158/Step)
Best Equations: StD(V)= f(Ppm[R]) - Variable(s) StDeviation as function of Response Defects (Ppm)
StD[R] 87.1133891541238 +6.18028434940138E-3*Ppm^1 -6.37727208967401E-7*Ppm^2 +4.62282804684211E-11*Ppm^3 -1.76095977784659E-15
*Ppm^4 +2.66835124621747E-20*Ppm^5
R2 Eq[R] 0.999982
StD[A] .316250111723311 +2.5148670172917E-5*Ppm^1 -2.58889977917384E-9*Ppm^2 +1.87464146345748E-13*Ppm^3 -7.17928276097469E-18*
Ppm^4 +1.10404362848931E-22*Ppm^5
R2 Eq[A] 0.999982
StD[B] 9.36642171855872E-2 +8.94572134852681E-7*Ppm^1 -9.77399290325435E-11*Ppm^2 +7.25727760076364E-15*Ppm^3 -2.70038449806112
E-19*Ppm^4 +3.69923120545572E-24*Ppm^5
R2 Eq[B] 0.999982
StD[C] .096583325758565 +3.53941085541408E-7*Ppm^1 -2.91173043033768E-11*Ppm^2 +2.05941148656798E-15*Ppm^3 -5.60867256721987E-2
0*Ppm^4 -1.11407499567464E-26*Ppm^5
R2 Eq[C] 0.999956
StD[D] 2.06221306266949E-2 +1.17395437840762E-6*Ppm^1 -1.22927961060299E-10*Ppm^2 +8.95432996950513E-15*Ppm^3 -3.36644396386368
E-19*Ppm^4 +4.90019002216455E-24*Ppm^5
R2 Eq[D] 0.999983
Equations Validity Range (Ppm) 2364 18242
**************************************************************************
 
Results for: MTBdgSheet6 - Champion of Italy Optimized Equations

The regression equation is
StDev[A] = 0.3291 + 0.000017 Ppm - 0.000000 Ppm**2 + 0.000000 Ppm**3

S = 0.000649981   R-Sq = 100.0%   R-Sq(adj) = 100.0%

Analysis of Variance

Source      DF         SS         MS         F      P
Regression   3  0.0193412  0.0064471  15260.20  0.000
Error       16  0.0000068  0.0000004
Total       19  0.0193479

Sequential Analysis of Variance

Source     DF         SS       F      P
Linear      1  0.0188051  623.62  0.000
Quadratic   1  0.0004883  152.20  0.000
Cubic       1  0.0000478  113.09  0.000

The regression equation is
StDev[B] = 0.09425 + 0.000001 Ppm - 0.000000 Ppm**2 + 0.000000 Ppm**3

S = 0.0000325325   R-Sq = 99.9%   R-Sq(adj) = 99.9%

Analysis of Variance

Source      DF         SS         MS        F      P
Regression   3  0.0000216  0.0000072  6809.28  0.000
Error       16  0.0000000  0.0000000
Total       19  0.0000216

Sequential Analysis of Variance

Source     DF         SS       F      P
Linear      1  0.0000209  487.27  0.000
Quadratic   1  0.0000007  338.35  0.000
Cubic       1  0.0000000   18.84  0.001

The regression equation is
StDev[C] = 0.09688 + 0.000000 Ppm + 0.000000 Ppm**2 - 0.000000 Ppm**3

S = 0.0000221473   R-Sq = 99.9%   R-Sq(adj) = 99.9%

Analysis of Variance

Source      DF         SS         MS        F      P
Regression   3  0.0000092  0.0000031  6277.44  0.000
Error       16  0.0000000  0.0000000
Total       19  0.0000092

Sequential Analysis of Variance

Source     DF         SS       F      P
Linear      1  0.0000091  885.00  0.000
Quadratic   1  0.0000002  165.33  0.000
Cubic       1  0.0000000   19.03  0.000

The regression equation is
StDev[D] = 0.02128 + 0.000001 Ppm - 0.000000 Ppm**2 + 0.000000 Ppm**3

S = 0.0000353076   R-Sq = 100.0%   R-Sq(adj) = 99.9%

Analysis of Variance

Source      DF         SS         MS         F      P
Regression   3  0.0000411  0.0000137  10989.10  0.000
Error       16  0.0000000  0.0000000
Total       19  0.0000411

Sequential Analysis of Variance

Source     DF         SS       F      P
Linear      1  0.0000399  586.63  0.000
Quadratic   1  0.0000011  211.82  0.000
Cubic       1  0.0000001   56.95  0.000

**************************************************************************
Now a new MC Simulation to test (verify) the target of 2839. Ppm (Response Defects)
using [Ind_Var] values gotten from Optimized Equations.
MonteCarlo Simulation Prediction Interval : MC PI95% From 2765. To 2911.
[Ind_Var] Standard Deviations used in next simulation, will be :
[A] : .370624413686869
[B] : 9.55653331517799E-2
[C] : 9.73969594410939E-2
[D] : .02314812599597
**************************************************************************
 
Results for: MTBdgSheet7 - Minitab MC Simulation (8000 Els)

Row   Els      Mean    StDev  C13  C14    Est_Pp  Est_<LSL  Est_>USL  Est_PpmTotal
  1  8000  -5500.51  100.468            0.995346   1436.87   1389.66       2826.53

* NOTE * One or more variables are undefined.

Results for: MTBdgSheet9 - Champion of Italy MC Simulation (1000000 Els)

                                                                              Mean
                        Standard                               Coeff. of      Std.
Row  Labels      Mean  Deviation  Anderson-Darling  P Value  Variability     Error  Variance   Skewness  Kurtosis    Median
  1  Power   -5500.13    100.401           15.6765        0    -0.018254  0.100401   10080.4  -0.037490   3.00515  -5499.50
  2  V_In       50.00      0.370                 *        *     0.007410  0.000370       0.1  -0.000048   3.00702     50.00
  3  Res_1       5.00      0.096                 *        *     0.019102  0.000096       0.0   0.000825   3.00264      5.00
  4  Res_2      10.00      0.097                 *        *     0.009731  0.000097       0.0  -0.002286   3.00310     10.00
  5  Xi          2.50      0.023                 *        *     0.009248  0.000023       0.0  -0.000611   2.99592      2.50

                            Range     Range               Lower Spec  Upper Spec
Row       IQ1       IQ3   Minimum   Maximum  Range Width  Limit/Test  Limit/Test      Ppk       Pp      PpL      PpU  Z-LT Value
  1  -5567.53  -5432.20  -6006.56  -5031.70      974.866     -5800.0     -5200.0  0.99557  0.99600  0.99557  0.99644     2.98670
  2     49.75     50.25     48.30     51.71        3.410        48.0        52.0  1.79915  1.79944  1.79972  1.79915     5.39746
  3      4.94      5.06      4.55      5.46        0.917         4.5         5.5  1.74498  1.74499  1.74498  1.74499     5.23493
  4      9.93     10.07      9.47     10.54        1.061         9.5        10.5  1.71223  1.71269  1.71223  1.71315     5.13669
  5      2.48      2.52      2.38      2.61        0.228         2.4         2.6  1.44159  1.44177  1.44159  1.44194     4.32477

                                                           L-Area
                                                    Prob    Items
                                                  @>=LSL       (1
                                                     And  Million
Row  L-PPM  U-PPM   PPM  Prob @<LSL  Prob @>USL   <=@USL    base)
  1   1647   1181  2828    0.001647    0.001181  0.99717     1647
  2      0      0     0    0.000000    0.000000  1.00000        0
  3      0      0     0    0.000000    0.000000  1.00000        0
  4      1      1     2    0.000001    0.000001  1.00000        1
  5     13      9    22    0.000013    0.000009  0.99998       13


**************************************************************************
For correct comparison between Minitab and Champion of Italy results...
please remenber that:
- Kurtosis algo is different between Minitab and Champion of Italy ...
- (**) do not compare absolute Ppm values from simulations with DIFFERENT ELS SIZE ...
  but compare only simulations with same els size ...
  (use Save Data to Minitab Worksheet option to do it)
- RNGeneration CANNOT BE NEVER exactly the same between the two softwares ...
- If BoxCox transformation is used, FORCE the same lambda for correct values comparison.
**************************************************************************
**************************************************************************
 

Minitab Graph Report

 

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