nte Carlo simulation has more intuitive appeal thandoes the generation of syste

ments and consequentlyis easier tounderstand.

Thedesiredprecision can be

ained by conductingsufficient trials.

Also, theMonte Carlomethod isvery flexible

can be applied to many highly complex situations for which the methodof generation

tem moments becomes too difficult.

This is especially true whenthere are

rrelationships betweenthecomponent variables.

ajor drawbackof the Monte Carlomethod isthat there isfrequentlynoway of

terminingwhether any of the variables aredominant or more important than

ers.

Furthermore, if a change is made inone variable, theentire simulation must be

one.

Also,the method generally requiresdevelopinga complex computer

gram; and if a large number of trials are required, agreat deal of computer timema

neededto obtain thenecessary answers.

nsequently, the generation of system moments, inconjunction with a Pearson or

nson distribution approximation, issometimesthe most economical approach.

hough theprecision of theanswers usually cannot beeasily assessed for this method,

results of the study

suggest that this approach oftendoes provideanadequate

roximation.

In addition, thegeneration of system momentsallows us to analyze th

ative importanceof each component variableby examining the magnitude of its

rtial derivative.

Derived from a multivariate Taylor series expansion of P = f(X
1, X2, . . . . . . Xn)

Retaining theterms up to thirdorder, and assuming that the component variables
(process factors) are uncorrelated:

S(P)

2

=

i = 1

n∑

∂P
∂Xi

⋅S(Xi)?
?

?
? ?

?

2

+

i = 1

n∑

∂P
∂Xi

?
?
?

?
? ? ∂2P?

2
i? ∂ X

?

?
?

?

μ3(Xi)

ere:

S(P)=Standard deviation of device parameter P
S(Xi)=Standard deviationof process factor Xi
µ3(Xi)=Third central moment of process factor Xi

glectingthe last term, the variance of deviceparameter P can bepartitionedinto the
iance dueto each process factor:

S(Pi)

2

=

∂P
∂Xi

⋅S(Xi)?
?

?
? ?

?

2