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 xp 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 n2(e2- 2e-1)/e2. The quantile proposed is equal or close to the mode of the distribution of the n-th order statistic, for exponential, logistic, Gumbel and uniform distribution.

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

[1] Departamento de Ensino, Escola Preparatória de Cadetes do Ar - EPCAR, CEP 36200-000, Barbacena, MG, Brasil. E-mail: abelha@ufla.br

[2] Departamento de Ciências Exatas, Universidade Federal de Lavras - UFLA, CEP 37200-000, Lavras, MG, Brasil. E-mail: lucas@ufla.br