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Distributions
Normal distributions are
perhaps the most widely known distribution: the familiar bell-shaped curve.
While some statisticians would have you believe they are also nature's most
widely occurring distribution, others would suggest you take a good look
at one in a textbook, since you're not likely to see one occur in the "real
world."
Some years ago, some statisticians
held the belief that when processes were not Normally distributed, there
was something "wrong" with the process, or even that the process
was "out of control." In their view, the purpose of the control
chart was to determine when processes were non-normal so they could be "corrected,"
and returned to Normality. 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 only due to its simplicity. It is well defined, so it is convenient to
assume Normality when errors associated with that assumption would be minor.
In fact, most of the efforts done in the interest of quality improvement
lead to non-normal processes, since they try to narrow the distribution
using process stops. Similarly, nature itself can impose stops to a process,
such as a service process whose waiting time is physically bounded at the
lower end by zero. The design of a waiting process would move the process
as close as economically possible to zero, causing the process mode, median
and average to move towards zero. This process would tend towards non-normality,
regardless of whether it is stable or non-stable.
Any distribution can be
characterized by four parameters, whose calculations are the same for any
distribution:
- Average: For symmetrical
distributions (see Skewness, below) the average (or Mean) provides a
good description of the central tendency or location, of the process.
For very skewed distributions, the median is a much better indicator
of location (or central tendency).
- Standard Deviation:
Denoted with the Greek symbol Sigma, the standard deviation provides
an estimate of variation. In mathematical terms, it is the second
moment about the mean. In simpler terms, you might say it is how
far the observations vary from the mean.
- Skewness: provides
a measure of the location of the mode (or high point in the distribution)
relative to the average. In mathematical terms, it is the third moment
about the mean. Symmetrical distributions, such as the Normal distribution,
have a skewness of zero. When the mode is to the left of the average,
the skewness is negative; to the right it is positive.
- Kurtosis: provides
a measure of the "peaked-ness" of a distribution. In mathematical
terms, it is the fourth moment about the mean. The Normal distribution
has a kurtosis of one. Distributions that are more peaked have higher
kurtosis.
Distributions can be fit
to data using Curve Fitting techniques.
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