Further Analysis of a Separate Tin of 25 Cal JSB King Pellets Using

Analysis of 25 Caliber JSB King Diabolo
Pellets using the Lead Head
Probability of misclassification of pellets into the wrong sizing bin
Sam Glover
Sam’s Research Bench
Table of Contents
Lorem Ipsum Dolor ..........................................................................................................1
Probability of misclassification of pellets into the wrong sizing bin ..................................1
Abstract ........................................................................................................................1
Introduction ..................................................................................................................1
Method .........................................................................................................................2
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Sam Glover
[Class, Semester]
[Teacher Name]
[Insert Date]
LEAD HEAD Pellet Sizer
Probability of misclassification of pellets into the wrong sizing bin
Abstract
Article discusses the measurement of 30 pellets
(25 caliber JSB Diabolo King 25.43 grain pellets to
be specific) in triplicate using a Lead Head sizing
tool to determine the error rate that was to be
Head Pellet Measurement Tool
expected by binning the pellets into 0.01 mm bins. Lead
(22/25 caliber) with 0.001 mm
indicator
These measurements showed that the pellets are
variable but that the measurements tend to support that reasonable binning of
the pellets into increments of 0.01 mm is supportable based on replicate
measures.
Introduction
Sorting pellets into similarly sized groups or ‘bins’ has been proposed and in some cases
shown to significantly improve the precision of an air rifle by helping to find the best sized
pellet to match with that particular gun. This is a trial and error kind of process! Some guns
may not be affected, some may show marked improvement. But first you have to sort the
pellets!
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Method
The Lead Head Pellet sizing tool was upgraded from a Fowler indicator (capable of 0.01
mm precision), to a Mitutoyo indicator capable of 0.001 mm. Another tin of 25 caliber
pellets was sorted, again a JSB 25 cal Diabo Kings, 25.43 grain pellets with notional head
size of 6.35 mm.
The unit was zeroed with a ‘master’ that has a size of 6.350 mm. The unit was qc’d by remeasuring the master and insuring it read zero. This was done frequently. Any other result
than zero, the unit was zeroed before continuing.
Thirty pellets measured three times each, removing the pellet each time. Afterwards, a total
of 161 pellets were recorded with a single measurement to better show the distribution.
Finally the entire tin of 350 pellets was sorted into the bins shown. Several pellets with
significant damage to the skirt (<10) were discarded and not measured.
The pellets selected at random were measured 3 times each in order to determine the
likelihood of misclassification into sorted bins. Bins were established as follows (deviation
from notional 6.35 mm). Thus a -0.034 reading meant 6.350 – 0.034 mm=6.326 mm. This
would be placed in the bin -0.03 mm (corresponding to 6.32 mm).
Data was analyzed using S-Plus, Excel, and Sigma Plot.
Bin
(deviation from 6.35 mm)
0
-0.01
-0.02
-0.03
Upper range
Lower range
+0.005
-0.006
-0.016
-0.026
-0.005
-0.015
-0.025
-0.035
The ninety measurements were normally distributed as shown in Figure 1.
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Figure 1: Probability plot of 30 pellets measured three times each
Probability Plot of 30 Pellets Measured 3 times each
with the Lead Head Measuring tool (0.001 mm indicator)
0.01
-0.03
-0.02
-0.01
0.00
measure
-0.01
-0.02
-0.03
-0.04
-3
-2
-1
0
1
2
3
Normal Distribution
While the symbols provide some degree of observation if there is substantial
misclassification, the results of a box and whisker plot are more informative. It is clear from
Figure 2 that the trend is that the mean result of the distribution does follow the general
classification, but the range of data does show that there will likely be some misclassification
from a single measurement. This could because of pellets that are slightly out of round.
Figure 2
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Uncertainly in Classification of Pellets
as measured in triplicate
-0.001
-0.006
measure
-0.011
-0.016
-0.021
-0.026
-0.031
-0.03
-0.02
-0.01
bin
A more quantitative expression of this uncertainy is shown the quantile plots of individual
bins (see
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Table 1). Bin -0.01 shows that the median value corresponds well with the bin (-0.011) and
that review of the probabily plot indicates that the range of -0.015 to -0.006 roughly
corresponds to 67% of the data (+/- 1 standard deviation). Since it is close to normally
distributed, this indicates that about 16% of the data may fall to the category below and 16%
of the data to the category above if only a single measurement of the pellet size is made. To
exceed 1 category shift is a small fraction of the set, approximately 5%. Similar results are
obtained for bin -0.02. Not enough results were obtained for bin -0.03 for a proper statistical
treatment. Review of the standard deviations for the bins “-0.01” and “-0.02” are rought
0.005 mm. This indicates that 95% of the pellets would be expect to fall within 2 standards
deviations (and hence bins of 0.02 mm range) based on this initial data for this particular bin
of 25 caliber pellets.
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Table 1
bin
Min
1st Qu.
Mean
Median
3rd Qu.
Max
Total N
NA's
Std Dev.
!0.01
!0.02
!0.03
!0.02
!0.027
!0.031
!0.015
!0.022
!0.026
!0.0114359 !0.0174667
!0.0235
!0.011
!0.018
!0.026
!0.009
!0.014
!0.02225
!0.001
!0.002
!0.011
39
45
6
0
0
0
0.00488173 0.00571919 0.00689202
Figure 3: Probability plot of the bin for pellets with a head size 6.34 mm (bin -0.01)
bin == "-0.01"
0.000
measure
-0.005
-0.010
-0.015
-0.020
-3
-2
-1
0
1
2
Normal Distribution
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Figure 4
bin == "-0.02"
-0.005
measure
-0.010
-0.015
-0.020
-0.025
-0.030
-3
-2
-1
0
1
2
Normal Distribution
Figure 5
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bin == "-0.03"
-0.011
measure
-0.016
-0.021
-0.026
-0.031
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Normal Distribution
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Bibliography
Last Name, F. (Date). Dolor Sit Amet. Lorem Ipsum, 1 - 10.
Last Name, F. (Date). Lorem Ipsum Dolor Sit Amet. City: Publisher.
Last Name, F. (Date). Lorem Ipsum Dolor Sit Amet. Duis sed elit ante, pp. 10-20.
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