Online control by attributes in the presence of classification errors with variable inspection interval

ABSTRACT

The procedure for online control by attribute consists of inspecting a single item at every m items produced (m ≥ 2). On each inspection, it is determined whether the fraction of the produced conforming items decreased. If the inspected item is classified as non conforming, the productive process is adjusted so that the conforming fraction returns to its original status. A generalization observed in the literature is to consider inspection errors and vary the inspection interval. This study presents an extension of this model by considering that the inspected item can be rated independently r (r ≥ 1) times. The process is adjusted every time the number of conforming classifications is less than a, 1 ≤ a ≤ r. This method uses the properties of an ergodic Markov chain to obtain the expression for the average cost of this control system. The genetic algorithm methodology is used to search for the optimal parameters that minimize the expected cost. The procedure is illustrated by a numerical example.

KEYWORDS:

• Classification errors
• Economic planning
• Genetic algorithms
• Online control by attributes
• Repeated classifications
• Variable inspection interval.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62P30, 60J10

Acknowledgments

The authors acknowledge the referees for their valuable comments and suggestions. This research is partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico; Grant #308914/2013-9) and by FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais; Grant CEX - APQ-01953-12).