eldo_user

Statistical Experimental Design and Analysis
Defining the Levels of Factors for the DEX Analysis
Normal Distribution
The normal (or Gaussian) distribution, is a bell shaped continuous distribution. The general
formula for the probability density function of a normal distribution is:
where the parameters , the mean μ, and the standard deviation σ > 0 are known.
Note
The macro GAUSS(NOM_VALUE, REL_VALUE, SIG_COEF) enables negative values
for the standard deviation SIGMA which is computed as NOM_VALUE*REL_VALUE/
SIG_COEF. The .DEX command will only consider the absolute values of these parameters,
even if the nominal value NOM_VALUE is negative.
Figure 12-1 depicts the common statistics relating to the Gaussian distribution.
Figure 12-1. Percentage of Cases in Eight Portions of the Gaussian Distribution
The range [−σ, σ] represents 34.13% + 34.13% = 68.26% of cases obtained after running the
sample process in the Monte Carlo algorithm. The range [−3σ, 3σ] covers 2×(34.13% + 13.59%
+ 2.14%) = 99.72% of cases.
The high and low levels, defined as ±n·σ, are the worst case points of these ranges.
Uniform Distributions
For a continuous distribution, the uniform distribution defines equal probability over a given
range. The general formula for the probability density function of the uniform distribution is:
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Eldo® User's Manual, 15.3