Excel Report

Champion of Italy ® 2005-2006 SixSigmaIn Team snc
Transfer Function  R= f(A,B,…) (A*COS(D)+B*SQRT(1-((A/B)*SIN(D))**2))+C
Data Entry Summary [R] [A] [B] [C] [D]
Variable Name Piston_Displ Crank_Length Con_Rod_Length Piston_Height Crank_Angle
IV Distribution Type Normal Normal Normal Normal
IVD 1*Par Value (Nominal Mean) 2.6 7.9 5.25 1.570796
IVD 2*Par Value (Nominal StDev) 0.15 0.15 0.09 0.008727
IVD 3*Par Value (..) 0 0 0 0
Lower Spec Limit (IV*opt) 12.21 2.38 7.54 5.1
Upper Spec Limit (IV*opt) 13.21 2.82 8.26 5.4
Use/Priority in Solver (0 to 1) 1 1 1 0
Upper Z-LT Constrains (*opt) 6 6 6
Simulation Summary - Step 0 [R] [A] [B] [C] [D]
Variable Name Piston_Displ Crank_Length Con_Rod_Length Piston_Height Crank_Angle
Mean 12.70789 2.600127 7.899996 5.249876 1.570792
Standard Deviation 0.191279 0.149944 0.149916 0.089922 0.008716
Anderson-Darling 3.416687
P Value 0
Coeff. of Variability 0.015052 0.057668 0.018977 0.017128 0.005549
Mean Std. Error 0.000191 0.00015 0.00015 0.00009 0.000009
Variance 0.036588 0.022483 0.022475 0.008086 0.000076
Skewness -0.01644 -4.8E-05 0.000825 -0.00229 -0.00061
Kurtosis 3.002447 3.00702 3.002638 3.003095 2.99592
Median 12.70852 2.600213 7.899893 5.249973 1.570798
IQ1 12.57932 2.499093 7.798949 5.189349 1.564907
IQ3 12.8372 2.701162 8.00093 5.310484 1.576671
Range Minimum 11.80888 1.913483 7.187978 4.764664 1.527305
Range Maximum 13.61209 3.293719 8.627398 5.745433 1.613417
Range Width 1.803213 1.380236 1.439419 0.980769 0.086112
Lower Spec Limit/Test 12.21 2.38 7.54 5.1 1.544616
Upper Spec Limit/Test 13.21 2.82 8.26 5.4 1.596976
Ppk 0.867654 0.488787 0.80044 0.555577 1.00105
Pp 0.871328 0.489071 0.800448 0.556036 1.001225
PpL 0.867654 0.489354 0.80044 0.555577 1.00105
PpU 0.875003 0.488787 0.800457 0.556495 1.0014
Z-LT Value 2.602962 1.466362 2.401319 1.666731 3.00315
L-PPM 4820 71014 8118 48045 1316
U-PPM 4168 71346 8350 47678 1306
PPM 8988 142360 16468 95723 2622
Prob @<LSL 0.00482 0.071014 0.008118 0.048045 0.001316
Prob @>USL 0.004168 0.071346 0.00835 0.047678 0.001306
Prob @>=LSL And <=@USL 0.991012 0.85764 0.983532 0.904277 0.997378
L-Area Items (1 Million base) 4820 71014 8118 48045 1316
R-Area Items(1 Million base) 4168 71346 8350 47678 1306
C-Area Items(1 Million base) 991012 857640 983532 904277 997378
Variable [R] [A] [B] [C] [D]
Contribution to Variance 0 7.47E-02 0.689854 0.221242 1.42E-02
M [..] [R] [A] [B] [C] [D]
Pearson [R].. [Var(N)) 1 -0.27335 0.830686 0.470427 -0.11919
Pearson [A].. [Var(N)) 1 -0.00024 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 © -  93 populated on  243 possible HyperCubes
HyperCube Items
[<R_f(<A,<B,<C,=D)] 15
[<R_f(<A,<B,=C,=D)] 33
[<R_f(<A,=B,<C,=D)] 2
[<R_f(=A,<B,<C,=D)] 339
[<R_f(=A,<B,<C,>D)] 1
[<R_f(=A,<B,=C,<D)] 2
[<R_f(=A,<B,=C,=D)] 1642
[<R_f(=A,<B,=C,>D)] 2
[<R_f(=A,<B,>C,=D)] 1
[<R_f(=A,=B,<C,=D)] 1054
[<R_f(=A,=B,<C,>D)] 5
[<R_f(=A,=B,=C,=D)] 473
[<R_f(=A,=B,=C,>D)] 6
[<R_f(>A,<B,<C,=D)] 18
[<R_f(>A,<B,=C,<D)] 1
[<R_f(>A,<B,=C,=D)] 333
[<R_f(>A,=B,<C,=D)] 310
[<R_f(>A,=B,<C,>D)] 1
[<R_f(>A,=B,=C,=D)] 581
[<R_f(>A,=B,=C,>D)] 1
[=R_f(<A,<B,<C,=D)] 14
[=R_f(<A,<B,=C,<D)] 1
[=R_f(<A,<B,=C,=D)] 490
[=R_f(<A,<B,=C,>D)] 1
[=R_f(<A,<B,>C,=D)] 25
[=R_f(<A,=B,<C,<D)] 4
[=R_f(<A,=B,<C,=D)] 3359
[=R_f(<A,=B,<C,>D)] 4
[=R_f(<A,=B,=C,<D)] 76
[=R_f(<A,=B,=C,=D)] 62608
[=R_f(<A,=B,=C,>D)] 90
[=R_f(<A,=B,>C,<D)] 7
[=R_f(<A,=B,>C,=D)] 3062
[=R_f(<A,=B,>C,>D)] 3
[=R_f(<A,>B,<C,=D)] 34
[=R_f(<A,>B,=C,=D)] 257
[=R_f(<A,>B,=C,>D)] 3
[=R_f(=A,<B,<C,<D)] 1
[=R_f(=A,<B,<C,=D)] 6
[=R_f(=A,<B,=C,<D)] 7
[=R_f(=A,<B,=C,=D)] 4669
[=R_f(=A,<B,=C,>D)] 2
[=R_f(=A,<B,>C,=D)] 310
[=R_f(=A,<B,>C,>D)] 2
[=R_f(=A,=B,<C,<D)] 57
[=R_f(=A,=B,<C,=D)] 39360
[=R_f(=A,=B,<C,>D)] 46
[=R_f(=A,=B,=C,<D)] 999
[=R_f(=A,=B,=C,=D)] 759724
[=R_f(=A,=B,=C,>D)] 1016
[=R_f(=A,=B,>C,<D)] 38
[=R_f(=A,=B,>C,=D)] 39333
[=R_f(=A,=B,>C,>D)] 47
[=R_f(=A,>B,<C,<D)] 1
[=R_f(=A,>B,<C,=D)] 372
[=R_f(=A,>B,=C,<D)] 2
[=R_f(=A,>B,=C,=D)] 4909
[=R_f(=A,>B,=C,>D)] 3
[=R_f(=A,>B,>C,=D)] 14
[=R_f(>A,<B,=C,=D)] 179
[=R_f(>A,<B,>C,=D)] 24
[=R_f(>A,=B,<C,<D)] 4
[=R_f(>A,=B,<C,=D)] 2994
[=R_f(>A,=B,<C,>D)] 4
[=R_f(>A,=B,=C,<D)] 95
[=R_f(>A,=B,=C,=D)] 62912
[=R_f(>A,=B,=C,>D)] 61
[=R_f(>A,=B,>C,<D)] 3
[=R_f(>A,=B,>C,=D)] 3237
[=R_f(>A,=B,>C,>D)] 6
[=R_f(>A,>B,<C,=D)] 37
[=R_f(>A,>B,=C,=D)] 490
[=R_f(>A,>B,=C,>D)] 2
[=R_f(>A,>B,>C,=D)] 8
[>R_f(<A,=B,=C,<D)] 4
[>R_f(<A,=B,=C,=D)] 319
[>R_f(<A,=B,>C,=D)] 271
[>R_f(<A,>B,<C,=D)] 1
[>R_f(<A,>B,=C,<D)] 1
[>R_f(<A,>B,=C,=D)] 298
[>R_f(<A,>B,>C,=D)] 32
[>R_f(=A,=B,=C,<D)] 2
[>R_f(=A,=B,=C,=D)] 427
[>R_f(=A,=B,>C,<D)] 5
[>R_f(=A,=B,>C,=D)] 919
[>R_f(=A,>B,<C,=D)] 2
[>R_f(=A,>B,=C,<D)] 5
[>R_f(=A,>B,=C,=D)] 1528
[>R_f(=A,>B,>C,<D)] 1
[>R_f(=A,>B,>C,=D)] 308
[>R_f(>A,=B,>C,=D)] 3
[>R_f(>A,>B,=C,=D)] 23
[>R_f(>A,>B,>C,=D)] 19
Defects Pareto Analysis:  39 HyperCubes found
DF_HyperCube DF_Items Cum_DF
[<R_f(=A,<B,=C,=D)] 1642 1642
[>R_f(=A,>B,=C,=D)] 1528 3170
[<R_f(=A,=B,<C,=D)] 1054 4224
[>R_f(=A,=B,>C,=D)] 919 5143
[<R_f(>A,=B,=C,=D)] 581 5724
[<R_f(=A,=B,=C,=D)] 473 6197
[>R_f(=A,=B,=C,=D)] 427 6624
[<R_f(=A,<B,<C,=D)] 339 6963
[<R_f(>A,<B,=C,=D)] 333 7296
[>R_f(<A,=B,=C,=D)] 319 7615
[<R_f(>A,=B,<C,=D)] 310 7925
[>R_f(=A,>B,>C,=D)] 308 8233
[>R_f(<A,>B,=C,=D)] 298 8531
[>R_f(<A,=B,>C,=D)] 271 8802
[<R_f(<A,<B,=C,=D)] 33 8835
[>R_f(<A,>B,>C,=D)] 32 8867
[>R_f(>A,>B,=C,=D)] 23 8890
[>R_f(>A,>B,>C,=D)] 19 8909
[<R_f(>A,<B,<C,=D)] 18 8927
[<R_f(<A,<B,<C,=D)] 15 8942
[<R_f(=A,=B,=C,>D)] 6 8948
[>R_f(=A,=B,>C,<D)] 5 8953
[>R_f(=A,>B,=C,<D)] 5 8958
[<R_f(=A,=B,<C,>D)] 5 8963
[>R_f(<A,=B,=C,<D)] 4 8967
[>R_f(>A,=B,>C,=D)] 3 8970
[<R_f(=A,<B,=C,>D)] 2 8972
[<R_f(=A,<B,=C,<D)] 2 8974
[>R_f(=A,>B,<C,=D)] 2 8976
[>R_f(=A,=B,=C,<D)] 2 8978
[<R_f(<A,=B,<C,=D)] 2 8980
[>R_f(<A,>B,=C,<D)] 1 8981
[>R_f(<A,>B,<C,=D)] 1 8982
[>R_f(=A,>B,>C,<D)] 1 8983
[<R_f(>A,<B,=C,<D)] 1 8984
[<R_f(>A,=B,<C,>D)] 1 8985
[<R_f(>A,=B,=C,>D)] 1 8986
[<R_f(=A,<B,<C,>D)] 1 8987
[<R_f(=A,<B,>C,=D)] 1 8988
Ppm StDev[R] StDev[A] StDev[B] StDev[C] StDev[D]
5056 0.178527 0.145995 0.138004 0.085828 0.008716
4260 0.175171 0.144833 0.13492 0.084656 0.008716
3978 0.173729 0.144312 0.13361 0.084125 0.008716
3770 0.172672 0.143921 0.132658 0.083723 0.008716
3562 0.171655 0.143541 0.131742 0.083335 0.008716
3391 0.170626 0.143155 0.130816 0.082941 0.008716
3196 0.169552 0.14275 0.129849 0.08253 0.008716
2990 0.168451 0.142332 0.128857 0.082109 0.008716
2792 0.16729 0.141888 0.127811 0.081664 0.008716
2585 0.166069 0.141418 0.126711 0.081198 0.008716
2388 0.16479 0.140922 0.125558 0.080708 0.008716
2189 0.163421 0.140387 0.124323 0.080184 0.008716
1988 0.161964 0.139812 0.123008 0.079626 0.008716
1783 0.160419 0.139197 0.121615 0.079034 0.008716
1605 0.158757 0.138528 0.120115 0.078395 0.008716
1421 0.156916 0.137779 0.118454 0.077686 0.008716
1233 0.154867 0.136935 0.116605 0.076895 0.008716
1064 0.152583 0.135979 0.114545 0.07601 0.008716
873 0.149942 0.134854 0.112164 0.074982 0.008716
688 0.146791 0.133484 0.109324 0.073746 0.008716
StD[R] .130599227133953 +3.02239701754649E-5*Ppm^1 -1.13368431253397E-8*Ppm^2 +2.56154509856762E-12*Ppm^3 -2.78252336369583E-16*Ppm^4 +1.07987605334549E-20*Ppm^5
R2 Eq[R] 0.99998
StD[A] .126210373319781 +1.39079500127421E-5*Ppm^1 -5.71306591415538E-9*Ppm^2 +1.39059092676944E-12*Ppm^3 -1.67701426232665E-16*Ppm^4 +7.67822632397886E-21*Ppm^5
R2 Eq[A] 0.99998
StD[B] 9.47457517260106E-2 +2.71964618115778E-5*Ppm^1 -1.01796245908604E-8*Ppm^2 +2.29934874223317E-12*Ppm^3 -2.50819740709545E-16*Ppm^4 +9.89603714725347E-21*Ppm^5
R2 Eq[B] 0.99998
StD[C] 6.73412119961947E-2 +1.20386051830275E-5*Ppm^1 -4.63674879562475E-9*Ppm^2 +1.06669722794275E-12*Ppm^3 -1.17335026801532E-16*Ppm^4 +4.52704861352539E-21*Ppm^5
R2 Eq[C] 0.99998
StD[D] 0.008727
R2 Eq[D] ***
Equations Validity Range (Ppm) 688 5056
Simulation Summary - Step 20 [R] [A] [B] [C] [D]
Variable Name Piston_Displ Crank_Length Con_Rod_Length Piston_Height Crank_Angle
Mean 12.70833 2.600114 7.899997 5.249897 1.570792
Standard Deviation 0.148928 0.134403 0.111269 0.074555 0.008716
Anderson-Darling 3.782236
P Value 0
Coeff. of Variability 0.011719 0.051691 0.014085 0.014201 0.005549
Mean Std. Error 0.000149 0.000134 0.000111 0.000075 0.000009
Variance 0.022179 0.018064 0.012381 0.005558 0.000076
Skewness -0.01693 -4.8E-05 0.000825 -0.00229 -0.00061
Kurtosis 3.001881 3.00702 3.002638 3.003095 2.99592
Median 12.70889 2.600191 7.899921 5.249978 1.570798
IQ1 12.60828 2.509551 7.824999 5.199714 1.564907
IQ3 12.80892 2.690677 7.974911 5.300147 1.576671
Range Minimum 12.0068 1.984637 7.371533 4.847607 1.527305
Range Maximum 13.4263 3.221818 8.439879 5.660764 1.613417
Range Width 1.419496 1.237181 1.068345 0.813158 0.086112
Lower Spec Limit/Test 12.21 2.38 7.54 5.1 1.544616
Upper Spec Limit/Test 13.21 2.82 8.26 5.4 1.596976
Ppk 1.115384 0.545339 1.078464 0.670189 1.00105
Pp 1.119113 0.545622 1.078472 0.670648 1.001225
PpL 1.115384 0.545905 1.078464 0.670189 1.00105
PpU 1.122842 0.545339 1.078481 0.671107 1.0014
Z-LT Value 3.346151 1.636016 3.235391 2.010568 3.00315
L-PPM 458 50879 646 22316 1316
U-PPM 350 51002 583 22101 1306
PPM 808 101881 1229 44417 2622
Prob @<LSL 0.000458 0.050879 0.000646 0.022316 0.001316
Prob @>USL 0.00035 0.051002 0.000583 0.022101 0.001306
Prob @>=LSL And <=@USL 0.999192 0.898119 0.998771 0.955583 0.997378
L-Area Items (1 Million base) 458 50879 646 22316 1316
R-Area Items(1 Million base) 350 51002 583 22101 1306
C-Area Items(1 Million base) 999192 898119 998771 955583 997378
Variable [R] [A] [B] [C] [D]
Contribution to Variance 0 9.89E-02 0.626887 0.250821 2.34E-02
M [..] [R] [A] [B] [C] [D]
Pearson [R].. [Var(N)) 1 -0.31458 0.791868 0.500887 -0.15286
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 © -  58 populated on  243 possible HyperCubes
HyperCube Items
[<R_f(<A,=B,<C,=D)] 1
[<R_f(=A,<B,<C,=D)] 10
[<R_f(=A,<B,=C,=D)] 104
[<R_f(=A,=B,<C,=D)] 123
[<R_f(=A,=B,<C,>D)] 1
[<R_f(=A,=B,=C,=D)] 82
[<R_f(>A,<B,=C,=D)] 24
[<R_f(>A,=B,<C,=D)] 32
[<R_f(>A,=B,=C,=D)] 80
[<R_f(>A,=B,=C,>D)] 1
[=R_f(<A,<B,<C,=D)] 1
[=R_f(<A,<B,=C,=D)] 42
[=R_f(<A,=B,<C,=D)] 1175
[=R_f(<A,=B,<C,>D)] 1
[=R_f(<A,=B,=C,<D)] 64
[=R_f(<A,=B,=C,=D)] 48368
[=R_f(<A,=B,=C,>D)] 68
[=R_f(<A,=B,>C,<D)] 1
[=R_f(<A,=B,>C,=D)] 1046
[=R_f(<A,>B,<C,=D)] 1
[=R_f(<A,>B,=C,=D)] 22
[=R_f(<A,>B,=C,>D)] 1
[=R_f(=A,<B,=C,<D)] 1
[=R_f(=A,<B,=C,=D)] 445
[=R_f(=A,<B,>C,=D)] 8
[=R_f(=A,=B,<C,<D)] 31
[=R_f(=A,=B,<C,=D)] 19756
[=R_f(=A,=B,<C,>D)] 26
[=R_f(=A,=B,=C,<D)] 1121
[=R_f(=A,=B,=C,=D)] 854773
[=R_f(=A,=B,=C,>D)] 1129
[=R_f(=A,=B,>C,<D)] 25
[=R_f(=A,=B,>C,=D)] 19763
[=R_f(=A,=B,>C,>D)] 26
[=R_f(=A,>B,<C,=D)] 10
[=R_f(=A,>B,=C,=D)] 424
[=R_f(>A,<B,=C,=D)] 11
[=R_f(>A,=B,<C,=D)] 1145
[=R_f(>A,=B,<C,>D)] 1
[=R_f(>A,=B,=C,<D)] 68
[=R_f(>A,=B,=C,=D)] 48482
[=R_f(>A,=B,=C,>D)] 51
[=R_f(>A,=B,>C,<D)] 3
[=R_f(>A,=B,>C,=D)] 1078
[=R_f(>A,=B,>C,>D)] 1
[=R_f(>A,>B,<C,=D)] 2
[=R_f(>A,>B,=C,=D)] 22
[>R_f(<A,=B,=C,=D)] 45
[>R_f(<A,=B,>C,=D)] 35
[>R_f(<A,>B,=C,=D)] 7
[>R_f(<A,>B,>C,=D)] 1
[>R_f(=A,=B,=C,<D)] 1
[>R_f(=A,=B,=C,=D)] 66
[>R_f(=A,=B,>C,=D)] 102
[>R_f(=A,>B,=C,<D)] 1
[>R_f(=A,>B,=C,=D)] 80
[>R_f(=A,>B,>C,=D)] 11
[>R_f(>A,>B,>C,=D)] 1
Defects Pareto Analysis:  21 HyperCubes found
DF_HyperCube DF_Items Cum_DF
[<R_f(=A,=B,<C,=D)] 123 123
[<R_f(=A,<B,=C,=D)] 104 227
[>R_f(=A,=B,>C,=D)] 102 329
[<R_f(=A,=B,=C,=D)] 82 411
[<R_f(>A,=B,=C,=D)] 80 491
[>R_f(=A,>B,=C,=D)] 80 571
[>R_f(=A,=B,=C,=D)] 66 637
[>R_f(<A,=B,=C,=D)] 45 682
[>R_f(<A,=B,>C,=D)] 35 717
[<R_f(>A,=B,<C,=D)] 32 749
[<R_f(>A,<B,=C,=D)] 24 773
[>R_f(=A,>B,>C,=D)] 11 784
[<R_f(=A,<B,<C,=D)] 10 794
[>R_f(<A,>B,=C,=D)] 7 801
[>R_f(=A,>B,=C,<D)] 1 802
[>R_f(<A,>B,>C,=D)] 1 803
[<R_f(>A,=B,=C,>D)] 1 804
[<R_f(<A,=B,<C,=D)] 1 805
[>R_f(=A,=B,=C,<D)] 1 806
[>R_f(>A,>B,>C,=D)] 1 807
[<R_f(=A,=B,<C,>D)] 1 808
Data Comparison [R] [A] [B] [C] [D]
Variable Name Piston_Displ Crank_Length Con_Rod_Length Piston_Height Crank_Angle
Nominal Value 12.70989 2.6 7.9 5.25 1.570796
Starting [R] Ppm 8988 8988 8988 8988 8988
Starting Mean 12.70789 2.600127 7.899996 5.249876 1.570792
Starting StDev 0.191279 0.149944 0.149916 0.089922 0.008716
Starting Tolerance (±) 0.573836 0.45 0.45 0.27 0.02618
Starting LSL 12.21 2.38 7.54 5.1 1.544616
Starting USL 13.21 2.82 8.26 5.4 1.596976