GENERATION

STATISTICAL

OFSYSTEMMOMENTS/

ERRORPROPAGATION

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Derived from a multivariate Taylor series expansion of P = f(X₁, X₂, . . . . . . X_n)

Retaining the terms up tothird order, and assuming that thecomponent variables (process factors) areuncorrelated:

[!] ² [!] S(X i⁾
[!] ^[!]

[!] [!] [!]

[!] [!] [!]

[!] [!] ^[!]

[!]ⁿ

i = 1

[!]ⁿ

i = 1

[^S(P)]²

m₃(X_i)

=

+

Where:

S(P)=Standard deviation of device parameter P S(X_i)=Standard deviation of process factor X µ₃(X_i)=Third central moment of process factoⁱ
r X_i

Neglecting the last term, the variance of device parameter P can bepartitioned into the variance due to each process factor:

[!] ² S(X i⁾_{[!] [!]}

[!] [!] ^[!]

[^{S(P )}]²
i

[!]

=