Page 250 - Six Sigma Demystified

230 Six SigMa DemystifieD

Exponential Distributions

Minitab

Use Calc\Random Data\Exponential to generate random numbers.

Use Stat\Quality Tools\Individual Distribution Identification to test whether
sample data meet the Exponential distribution. Use goodness-of-fit tests
(described below) to determine if an assumed distribution provides a reason-
able approximation.

Excel

To generate a set of randomly distributed exponential data, use Data\Data
Analysis\Random Number Generation.

Set Distribution = Uniform, and then transform the data to an exponential dis-
tribution using the formula M*(–LN(UNIFORM)), where M is the average of
the exponential distribution to be constructed, and UNIFORM refers to a value
in the uniform distribution. For example, if the uniform distributed data are in
cells A2:A1000, to create an exponential distribution whose mean equals 20,
transform the uniform data value in cell A2 to an exponential distribution using
the formula 20*(–LN($A2)).

Normal Distribution

Used for measurement (continuous) data that are theoretically without bound
in both the positive and negative directions and symmetric about an average
(i.e., skewness equals zero) with a defined shape parameter (i.e., kurtosis equals
1), normal distributions are perhaps the most widely known distribution—the
familiar bell-shaped curve. While some statisticians would have you believe
that they are also nature’s most widely occurring distribution, others would
suggest that you take a good look at one in a textbook because you’re not likely
to see one occur in the “real world.” Most statisticians and quality practitioners
today would recognize that there is nothing inherently “normal” (pun intended)
about the normal distribution, and its use in statistics is due only to its simplic-
ity. It is well defined, so it is convenient to assume normality when errors as-
sociated with that assumption are relatively insignificant.