Outliers are random points in data sets that
adversely affect the shape and accuracy of computer generated Almen
Saturation curves. These points, unless obviously outside the norm, cannot be
identified and eliminated. This being the case, generated curves and calculated
saturation points are unreliable - unless multiple runs are made and averaged. (*This
of course takes more time and offers no assurance that the problem with outliers
has been dealt with.)*

A major revision in Almen Saturation Curve Calculator 4.0 is the incorporation of a trap that filters outliers in a manner similar to a screen that filters particles of different sizes. This trap has a screen with holes ranging from .01 to 1.00. The smaller holes filter data points very close to the Almen Saturation Curve while the larger ones trap only those that are obvious outliers. Practically all outliers can be filtered in this manner particularly if progressively smaller trap numbers are used.

Use of the outliers trap is illustrated below
with the Wieland^{(1)} data.

**Fig. 1 **Plot
of Wieland data. The average of 25 data sets
- all arc heights are in inchesx1000. Correlation of 99.9% is excellent with a
Standard Deviation of +/-.042
(+/-.000042 inch).

**Fir 2. **Data from Fig. 1 with obvious
outliers introduced at exposure times 100 and 160.
Correlation drops to 86.4% with a Standard Deviation of +/-1.031
(+/-.001031 inch).

**Fig. 3 **The outliers filter is enabled with
the trap at the largest setting of "1". The
outliers were filtered - plotted points are marked with black dots and data is
flagged with asterisks. Calculated results are comparable to those of figure
one.

**Fig. 4 **Multiple outliers were introduced
above. Visual examination of the plot does
not disclose any obvious outliers. Calculated results show very low correlation
and large Standard Deviation.

**Fig. 5 **The
outliers filter is enabled with the trap at the largest setting of
"1". Five points are disclosed and
correlation increases to 98.2% with an error of +/-.000394 inch.

**Fig. 6 **The outliers filter was reset to
".5". Two additional outliers are
eliminated - previously identified outliers are shown as smaller dots. A further
improvement in correlation and error is realized.

**Fig. 7 **A smaller outliers filter of
".25" is used. One more outlier is
identified and the drawn curve is almost a perfect fit. Calculated results are
comparable to those of Fig. 1. Further traps are not needed. **All relevant
outliers have been identified and eliminated.**

The outliers filter works equally well with small data sets as shown below:

**Fig. 8
**Five point data set^{(2)} with apparently multiple outliers. Correlation
is good at 98.7% and error of +/-.000197 inch is low. Visual inspection of the
plot does not disclose any obvious outliers.

**Fig. 9
**The outliers filter is enabled with a setting of ".185". One
outlier is identified and flagged. Correlation improves to 99.8% with and error
of +/-.000067 inch - an excellent fit.

One question must be answered.

*How
reliable is the filter?*

The
filter is a tool developed to trap outliers in Almen data sets. It is
particularly useful in situations where data points are equidistant from the
curve as in Fig. 8 above. The final filtered curves fit the expected shape - **rapid
initial propagation, followed by a sharp knee, then, a gradual almost linear
increase with a slope approaching zero.**

The Wieland data was filtered with verifiable excellent results. The filtered plot of the Peenforming data generated a curve with the characteristic shape.

The
outliers filter is an excellent tool. However, like all tools, results are
dependent on the experience and skill of the user. Using a setting that is too
large will miss relevant outliers. On the other hand, a setting that is too
small will eliminate valid data points. Progressive filtering must be undertaken
in small incremental steps and terminated when results are satisfactory. *The
filter is reliable but results are entirely dependent on the judgment of the
user! *

^{(1)}
Wieland
R. C. "A statistical Analysis of Shot Peening Intensity Measurement",
pp 27-38, Proceedings I.C.S.P.5, Oxford, 1993

^{(2)}Peenforming.squarespace.com