A Comparison of Two Optimal Inspection Procedures in the Presence of Errors
Titel:
A Comparison of Two Optimal Inspection Procedures in the Presence of Errors
Auteur:
Rosenshine, Matthew Soares, Francisco
Verschenen in:
IIE transactions
Paginering:
Jaargang 9 (1977) nr. 1 pagina's 19-24
Jaar:
1977-03-01
Inhoud:
It is well known that the Bayes procedure minimizes the expected loss when the a priori probabilities of the states of nature are known, but it is not clear that the procedure continues to have this property in the presence of unknown errors which occur if these probabilities must be estimated. Furthermore, it is possible that the expected loss for another procedure does not increase as fast as that for the Bayes procedure. A procedure which might behave this way is the procedure for a group of N items, designated the N-procedure, because the expected loss for this procedure does not depend explicitly on the a priori probabilities. It is found, however, that the Bayes procedure consistently yields lower expected costs than the N-procedure. The results obtained suggest that the Bayes procedure will give smaller expected losses than other procedures in the presence of unknown errors in the a priori probabilities. Somewhat surprisingly, the superiority of the Bayes procedure increases with the size of the errors of the estimated a priori probabilities, regardless of whether the estimated probabilities lie above or below the correct values.
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