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In the Introduction of his "Sequential Analysis" Wald writes that

Because of the usefulness of the sequential probability ratio test in development work on military and naval equipment, it was classified Restricted within the meaning of the Espionage Act. The author was requested to submit his findings in a restricted report 7 dated September, 1943.

Beyond the obvious desire by bureaucrats to classify almost anything they can put their hands on was there really any strategic/tactical military reason to classify Wald's work, and if yes what specific idea or method was of national security interest? In what industrial production was SPRT used during war that might have inspired the classification? (That SPRT could be applied to improve and speed up radar detection was already known early on but its actual deployment in a practical system took a much longer time and I do not believe that anybody would have ever attempted to use it with analog computers.)

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    $\begingroup$ This work was done in war time, for a military research organization, and was obviously useful for industrial production of things like munitions and airplane parts and so on, so you might want to cut the bureaucrats some slack here. $\endgroup$ Sep 19, 2022 at 14:42
  • $\begingroup$ @kimchilover I do not think the answer is that simple: if you were to spend time in industrial production you would quickly learn that changing production protocol, such as quality assurance, is among the most difficult practical things to do, especially when you are in a hurry. $\endgroup$
    – hyportnex
    Sep 19, 2022 at 14:53
  • $\begingroup$ Given that Turing used a variant to help with Enigma, it seems pretty clear to me. $\endgroup$
    – Jon Custer
    Sep 20, 2022 at 12:59
  • $\begingroup$ @JonCuster now that is very interesting, I did not know about that; could you elaborate maybe in a full answer? $\endgroup$
    – hyportnex
    Sep 20, 2022 at 14:55
  • $\begingroup$ See en.wikipedia.org/wiki/Banburismus (linked from en.wikipedia.org/wiki/Sequential_analysis). $\endgroup$
    – Jon Custer
    Sep 20, 2022 at 15:01

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From Bruno de Finetti, "L'opera di Abraham Wald e l'assestamento concettuale della statistica matematica moderna", Statistica, 11 (1951), pp. 185-192

L'idea essenziale dei procedimenti sviluppati sotto il nome di «Sequential Analysis» ed esposti nel volume di ugual titolo è altrettanto feconda quanto semplice. Per afferrarne il senso, basta esporla riferendoci all'esempio più elementare. Si tratti di collaudare una partita di oggetti, sottoponendo a date prove un certo campione per concludere, in base alla percentuale di pezzi difettosi riscontrativi, se la percentuale di oggetti difettosi nell'intera partita sembri tale da consigliare di accettarla o di respingerla. Quanti pezzi occorre sottoporre a collaudo prima di poter prendere tale decisione? Non si tratta di entrare nel merito dei criteri in base ai quali tale numero può venir determinato; si tratta di discutere se è opportuno porsi la questione in tali termini, fissare cioè un numero $n$ di prove, in base al risultato delle quali prendere la decisione. L'osservazione, in fondo intuitiva, del Wald, consiste nel notare che se fin dal principio i risultati sono decisamente favorevoli o decisamente sfavorevoli si è in grado di prendere una decisione dopo poche prove, mentre solo se la conclusione si mantiene sul limite dell'incertezza occorre prolungare l'esperimentazione e aumentare il numero delle prove. Analizzando tale concetto sia sotto l'aspetto probabilistico che in nesso a circostanze quali il costo dell'esperimentazione e l'entità del danno derivante da una decisione erronea, il Wald è pervenuto a costruire una dottrina altrettanto elegante e pregevole dal punto di vista matematico quanto appropriata e vantaggiosa per le applicazioni pratiche. Il fatto di sospendere le prove non appena il risultato acquisito appaia sufficiente elemento per la decisione, anziché continuarle in ogni caso fino al numero necessario nel caso più sfavorevole di decisione incerta, costituisce infatti un risparmio così notevole di tempo, lavoro e materiale nell'esecuzione dei collaudi, che il procedimento stesso era stato tenuto segreto durante la guerra perché potessero avvantaggiarsene in modo esclusivo le attività connesse con la preparazione militare alleata.

My translation:

The essential idea of the procedures developed under the name of «Sequential Analysis» and set forth in the volume of the same title is as fruitful as it is simple. To grasp its meaning, we need only expound it by referring to the most basic example. Let it be a matter of testing a batch of objects, subjecting a certain sample to given tests in order to conclude, on the basis of the percentage of defective pieces found, whether the percentage of defective objects in the whole batch seems to be such as to recommend acceptance or rejection. How many pieces need to be tested before such a decision can be made? It is not a question of going into the criteria by which this number can be determined; it is a question of discussing whether it is appropriate to pose the question in such terms, that is, to fix a $n$ number of tests, on the basis of the result of which to make the decision. Wald's basically intuitive observation is that if from the outset the results are decidedly favorable or decidedly unfavorable one is able to make a decision after only a few trials, whereas only if the conclusion remains on the borderline of uncertainty is it necessary to prolong the experiment and increase the number of trials. By analyzing this concept both from a probabilistic point of view and in connection with circumstances such as the cost of experimentation and the extent of damage resulting from an erroneous decision, Wald has come to construct a doctrine that is as elegant and valuable mathematically as it is appropriate and advantageous for practical applications. The fact of suspending the tests as soon as the result acquired appears to be sufficient element for decision, instead of continuing them in any case up to the necessary number in the most unfavorable case of an uncertain decision, constitutes in fact such a considerable saving of time, labor and material in the execution of the tests, that the proceedings themselves had been kept secret during the war so that only activities connected with Allied military production could benefit from them.

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  • $\begingroup$ Thank you. This is a very nice quote and relevant to my question but I do not believe it contradicts anything to which @JonCuster referred above, and I believe that particular application is more of a "classified military type" than capturing defective parts on a production line. In your quote De Finetti says the idea is quite simple and intuitive, so why would the Germans not do the same for a production line? They had excellent mathematicians, knew Neyman-Pearson-Fisher, etc, but they did not have the Colossus... $\endgroup$
    – hyportnex
    Oct 10, 2022 at 2:20

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