Задача о немецких танках: различия между версиями

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В современном виде задача была сформулирована во время [[Вторая мировая война|Второй мировой войны]] в странах [[Антигитлеровская коалиция|антигитлеровской коалиции]] как один из подходов для оценивания промышленного производства противника в условиях недостатка открытой информации. Доступными для анализа оказались серийные номера уничтоженной и захваченной техники противника, в том числе танков, откуда и возникло название задачи. Решение задачи позволило на основании серийных номеров машин и отдельных деталей сделать практические предположения об объёмах военного производства [[Гитлеровская Германия|гитлеровской Германии]]. Многие оценки, выполненные на основе решения задачи, оказались более точными, чем сведения традиционной разведки.
 
==История задачи==
[[Файл:Bundesarchiv Bild 101I-635-3966-27, Panzerfabrik in Deutschland.jpg|thumb|справа|Сборочная линия танка [[Пантера (танк)|Panzer V Пантера]] в Германии, 1944 год]]
На протяжении всей Второй мировой войны воюющие стороны предпринимали значительные усилия в области разведки промышленного потенциала противника. В странах антигитлеровской коалиции наряду с традиционной агентурной разведкой были предприняты усилия для развития прикладных методов [[Статистическая оценка|статистического оценивания]]. Некоторые результаты статистического оценивания позволили значительно улучшить точность сведений традиционной разведки. Важным результатом статистического подхода стала оценка темпов производства танка [[Пантера (танк)|Panzer V Пантера]], позволившая оптимизировать силы союзников для [[Высадка в Нормандии|высадки в Нормандии]]. <!-- в частности значительно In many cases, statistical analysis substantially improved on conventional intelligence. In some cases, conventional intelligence was used in conjunction with statistical methods, as was the case in estimation of [[German tanks in World War II|Panther tank]] production just prior to [[D-Day]].
 
The allied command structure had thought the [[Panzer V]] (Panther) tanks seen in Italy, with their high velocity, long-barreled 75&nbsp;mm/L70 guns, were unusual heavy tanks and would only be seen in northern France in small numbers, much the same way as the [[Tiger I]] was seen in Tunisia. The US Army was confident that the [[Sherman tank]] would continue to perform well, as it had versus the [[Panzer III]] and [[Panzer IV]] tanks in North Africa and Sicily.{{refn|An Armored Ground Forces policy statement of November&nbsp;1943 concluded: "The recommendation of a limited proportion of tanks carrying a 90&nbsp;mm gun is not concurred in for the following reasons: The M4 tank has been hailed widely as the best tank of the battlefield today. ... There appears to be no fear on the part of our forces of the German Mark&nbsp;VI (Tiger) tank. There can be no basis for the T26 tank other than the conception of a tank-vs.-tank duel – which is believed to be unsound and unnecessary."<ref>AGF policy statement. Chief of staff AGF. November 1943. MHI</ref>|group=lower-alpha}} Shortly before D-Day, rumors indicated that large numbers of Panzer V tanks were being used.
 
To determine whether this was true, the Allies attempted to estimate the number of tanks being produced. To do this, they used the serial numbers on captured or destroyed tanks. The principal numbers used were gearbox numbers, as these fell in two unbroken sequences. Chassis and engine numbers were also used, though their use was more complicated. Various other components were used to cross-check the analysis. Similar analyses were done on wheels, which were observed to be sequentially numbered (i.e., 1,&nbsp;2,&nbsp;3,&nbsp;...,&nbsp;''N'').{{sfn|Ruggles|Brodie|1947|p=?}}{{efn|The lower bound was unknown, but to simplify the discussion, this detail is generally omitted, taking the lower bound as known to be 1.}}<ref name=Davies-2006-07-20>
{{cite web
|title=Gavyn Davies does the maths – How a statistical formula won the war
|date=20 July 2006
|url=https://www.theguardian.com/world/2006/jul/20/secondworldwar.tvandradio
|website=[[The Guardian]]
|accessdate=6 July 2014
}}</ref><ref>
{{citation
|title=Data sleuths go to war, sidebar in feature "Hidden truths"
|date=23 May 1998
|journal=[[New Scientist]]
|last=Matthews
|first=Robert
|author-link=Robert Matthews (scientist)
|url=https://www.newscientist.com/article/mg15821355.000-hidden-truths.html
|archiveurl=https://web.archive.org/web/20010418025817/http://www.newscientist.com/ns/980523/features.html#data
|archivedate=18 April 2001
}}</ref>
 
The analysis of tank wheels yielded an estimate for the number of wheel molds that were in use. A discussion with British road wheel makers then estimated the number of wheels that could be produced from this many molds, which yielded the number of tanks that were being produced each month. Analysis of wheels from two tanks (32 road wheels each, 64 road wheels total) yielded an estimate of 270 tanks produced in February 1944, substantially more than had previously been suspected.<ref name="Carruthers">
{{cite book
|author=Bob Carruthers
|title=Panther V in Combat
|url=https://books.google.com/books?id=99JRxKz4Da4C&pg=PT94
|publisher=Coda Books Ltd
|isbn=978-1-908538-15-4
|pages=94–
|date=2012-03-01
}}</ref>
 
German records after the war showed production for the month of February&nbsp;1944 was 276.{{sfn|Ruggles|Brodie|1947|pp=82–83}}{{refn|Ruggles & Brodie is largely a practical analysis and summary, not a mathematical one – the estimation problem is only mentioned in footnote&nbsp;3 on page&nbsp;82, where they estimate the maximum as "sample maximum + average gap".|group=lower-alpha}} The statistical approach proved to be far more accurate than conventional intelligence methods, and the phrase "German tank problem" became accepted as a descriptor for this type of statistical analysis.
 
Estimating production was not the only use of this serial-number analysis. It was also used to understand German production more generally, including number of factories, relative importance of factories, length of supply chain (based on lag between production and use), changes in production, and use of resources such as rubber.
 
===Specific data===
According to conventional Allied intelligence estimates, the Germans were producing around 1,400&nbsp;tanks a month between June&nbsp;1940 and September&nbsp;1942. Applying the formula below to the serial numbers of captured tanks, the number was calculated to be 246 a month. After the war, captured German production figures from the ministry of [[Albert Speer]] showed the actual number to be 245.<ref name=Davies-2006-07-20/>
 
Estimates for some specific months are given as:{{sfn|Ruggles|Brodie|1947|p=89}}
{| class="wikitable"
|- align=center
! Month !! Statistical estimate !! Intelligence estimate !! German records
|- align=center
| June 1940 || 169 || 1,000 || 122
|- align=center
| June 1941 || 244 || 1,550 || 271
|- align=center
| August 1942 || 327 || 1,550 || 342
|}
 
===Similar analyses===
[[File:Fusée V2.jpg|thumb|[[V-2]] rocket production was accurately estimated by statistical methods]]
Similar serial-number analysis was used for other military equipment during World War&nbsp;II, most successfully for the [[V-2]] rocket.{{sfn|Ruggles|Brodie|1947|pp=90–91}}
 
Factory markings on Soviet military equipment were analyzed during the [[Korean War]], and by German intelligence during World War&nbsp;II.{{sfn|Volz|2008}}
 
In the 1980s, some Americans were given access to the production line of Israel's [[Merkava]] tanks. The production numbers were classified, but the tanks had serial numbers, allowing estimation of production.{{sfn|Johnson|1994}}
 
The formula has been used in non-military contexts, for example to estimate the number of [[Commodore 64]] computers built, where the result (12.5&nbsp;million) matches the low-end estimates.<ref name="pagetable.com">
{{cite web
|title=How many Commodore&nbsp;64 computers were really sold?
|date=1 February 2011
|url=http://www.pagetable.com/?p=547
|website=pagetable.com
|accessdate=6 July 2014
|archive-url=https://web.archive.org/web/20160306232450/http://www.pagetable.com/?p=547
|archive-date=6 March 2016
}}</ref>-->
 
{{Statistics-stub}}