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Yield Power ( Semiconductor data test analysis software ) displays the
semiconductor data test analysis results using histograms. Histograms
are the best way to present the statistical analysis graphically. Test
engineers can easily understand the test data reports by viewing the histograms.
The histogram graphically
shows the following:
1. center
( i.e., the location ) of the semiconductor test data;
2. spread ( i.e., the scale ) of the semiconductor test data;
3. skewness of the semiconductor test data;
4. presence of outliers; and
5. presence of multiple modes in the semiconductor test data.
These features provide
strong indications of the proper distributional model for the semiconductor
test data.
The cumulative histogram
is a variation of the histogram in which the vertical axis gives not just
the counts for a single bin, but rather gives the counts for that bin
plus all bins for smaller values of the response variable.
Both the histogram and cumulative histogram have an additional variant
whereby the counts are replaced by the normalized counts. The names for
these variants are the relative histogram and the relative cumulative
histogram.
There are two common ways to normalize the counts.
1. The normalized count is the count in a class divided by the total number
of observations. In this case the relative counts are normalized to sum
to one ( or 100 if a percentage scale is used ). This is the intuitive
case where the height of the histogram bar represents the proportion of
the data in each class.
2. The normalized count is the count in the class divided by the number
of observations times the class width. For this normalization, the area
( or integral ) under the histogram is equal to one. From a probabilistic
point of view, this normalization results in a relative histogram that
is most akin to the probability density function and a relative cumulative
histogram that is most akin to the cumulative distribution function. If
you want to overlay a probability density or cumulative distribution function
on top of the histogram, use this normalization. Although this normalization
is less intuitive ( relative frequencies greater than 1 are quite permissible
), it is the appropriate normalization if you are using the histogram
to model a probability density function.
The histogram can be used to answer the following questions:
1. What kind of population distribution do the semiconductor test data
come from?
2. Where are the semiconductor test data located?
3. How spread out are the semiconductor test data?
4. Are the semiconductor test data symmetric or skewed?
5. Are there outliers in the semiconductor
test data?
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