Serial number: Difference between revisions

Revision as of 02:12, 31 August 2005

Revision as of 10:42, 31 August 2005

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numbers are defined in the following section.

== Estimating the population size using serial numbers ==

If there are items whose serial numbers is part of a sequence of consecutive numbers and you take n number of random samples of the items. You can determine the population of items "in the wild".

== Operations on serial numbers (sequence space arithmetic)==

To do so, calculate the difference between the largest serial number and the smallest serial number in your sample. The expected population size of the item is that difference divided by the expected proportion.

For example:

You take 4 random samples. The serial numbers are 2,7,34,13. Thus the difference is 34-2=32. The expected proportion is 0.6 The expected population size is 32 / 0.6 = 53 and the standard deviation of the expected proportion is 0.2

<pre>numofsamples = 2 proportion = 0.333 std_dev = 0.236

numofsamples = 3 proportion = 0.500 std_dev = 0.224

numofsamples = 4 proportion = 0.600 std_dev = 0.200

numofsamples = 5 proportion = 0.667 std_dev = 0.178

numofsamples = 6 proportion = 0.714 std_dev = 0.160

numofsamples = 7 proportion = 0.750 std_dev = 0.144

numofsamples = 8 proportion = 0.778 std_dev = 0.132

numofsamples = 9 proportion = 0.800 std_dev = 0.121

numofsamples = 10 proportion = 0.818 std_dev = 0.111

numofsamples = 11 proportion = 0.833 std_dev = 0.103

numofsamples = 12 proportion = 0.846 std_dev = 0.097

numofsamples = 13 proportion = 0.857 std_dev = 0.090

numofsamples = 14 proportion = 0.867 std_dev = 0.085

numofsamples = 15 proportion = 0.875 std_dev = 0.080

</pre>

== Operations on serial numbers (sequence space arithmetic)==

Only two operations are defined upon serial numbers, [[addition]] of a

positive integer of limited range, and [[comparison]] with another serial

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Ref: Serial Number Arithmetic from RFC1982.

== ApplicationsEstimating ofthe population size using serial numberingnumbers ==

If there are items whose serial numbers is part of a sequence of consecutive numbers and you take n number of random samples of the items. You can determine the population of items "in the wild".

To do so, calculate the difference between the largest serial number and the smallest serial number in your sample. The expected population size of the item is that difference divided by the expected proportion.

For example:

You take 4 random samples. The serial numbers are 2,7,34,13. Thus the difference is 34-2=32. The expected proportion is 0.6 The expected population size is 32 / 0.6 = 53 and the standard deviation of the expected proportion is 0.2

<pre>numofsamples = 2 proportion = 0.333 std_dev = 0.236

numofsamples = 3 proportion = 0.500 std_dev = 0.224

numofsamples = 4 proportion = 0.600 std_dev = 0.200

numofsamples = 5 proportion = 0.667 std_dev = 0.178

numofsamples = 6 proportion = 0.714 std_dev = 0.160

numofsamples = 7 proportion = 0.750 std_dev = 0.144

numofsamples = 8 proportion = 0.778 std_dev = 0.132

numofsamples = 9 proportion = 0.800 std_dev = 0.121

numofsamples = 10 proportion = 0.818 std_dev = 0.111

numofsamples = 11 proportion = 0.833 std_dev = 0.103

numofsamples = 12 proportion = 0.846 std_dev = 0.097

numofsamples = 13 proportion = 0.857 std_dev = 0.090

numofsamples = 14 proportion = 0.867 std_dev = 0.085

numofsamples = 15 proportion = 0.875 std_dev = 0.080

</pre>

== Applications of serial numbering ==

Serial numbers are valuable in [[quality control]], as once a defect is found in the production of a particular batch of product, the serial number will quickly identify which units are affected. Serial numbers are also used as a deterrent against theft and counterfeit products in that serial numbers can be recorded, and stolen or otherwise irregular goods can be identified.