A genetic algorithm approach to determine the sample size for attribute control charts

Determining the sample size for control charts (CCs) is generally an important problem in the literature. In this paper, Kaya and Engin’s [İ. Kaya, O. Engin, A new approach to define sample size at attributes control chart in multistage processes: an application in engine piston manufacturing process, Journal of Materials Processing Technology 183 (2007) 38–48] model based on minimum cost and maximum acceptance probability to determine the sample size for attribute control charts (ACCs), and solved by genetic algorithms (GAs) with linear binary representation structure, is handled to solve it by a linear real-valued representation. A new chromosome structure is also suggested to increase the efficiency of GAs. The performance of GAs depends on mutation and crossover operators, and their ratios. To determine the most appropriate operators, five different mutation and crossover operators are used and they are compared with each other. An application in a motor engine factory is illustrated. u-Control charts are constructed with respect to the sample size determined by GA in the model. The piston production stages in this factory are monitorized using the obtained control charts.