QUANTILE
SELECTION METHOD IN

SEQUENTIAL INSPECTION PROBLEMS

Carla Regina Guimarães BRIGHENTI[1]

Lucas Monteiro CHAVES[2]

§ ABSTRACT: A strategy of sequential
inspection in which the characteristic of an object follows a known
distribution is presented. From the *n-*th
and *(n-1)-*th order statistics, a
quantile x_{p} was defined, where *p = (n-1)/n*. The strategy is to sequentially inspect the
objects of an *n* size sample and
interrupt the process at the first object with a characteristic value higher
than the quantile *(n-1)/n. *If this
does not occur the *n*-th object will
be accepted automatically. Quantile *(n-1)/n*
is obtained from order statistics. The probability of winning, of really taking
the best object, is greater than that obtained by the strategy based upon
relative ranks and smaller than the optimum strategy based on only one decision
number. The expectation of the whole inspection time is asymptotically *n(e-1)/e* and the variance is *n ^{2}(e^{2}- 2e-1)/e^{2}.*
The quantile proposed is equal or close to the mode of the distribution of the

§
Keywords: Order statistics; secretary problem; optimal strategy.