Z Score & Cpk


Normal Distribution,
P.D.F (Probability Density Function), N (μ, σ2)




Standard Normal Distribution, N (0, 1)

,





C.D.F (Cumulative Distribution Function)







 ,
USL→X, →μ
Cpk=Z/3






Z(=±z)
P(Z+z)
P(Z-z)
P(-zZ+z)
Zσ(=X-μ)
Cpk(=Z/3)
1
0.841344746069
0.158655253931
0.682689492137
0.3333
2
0.977249868052
0.022750131948
0.954499736104
0.6667
3
0.998650101968
0.001349898032
0.997300203937
1.0000
4
0.999968328758
0.000031671242
0.999936657516
1.3333
5
0.999999713348
0.000000286652
0.999999426697
1.6667
6
0.999999999013
0.000000000987
0.999999998027
2.0000
MS Excel Statistical Function:
P(Z+z)=NORMSDIST(z)
P(Z-z)=NORMSDIST(-z)
P(-zZ+z)=P(Z+z)-P(Z-z)

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