Many-objective x-bar control chart using hybrid NSGA-III and DEA

Abstract

The present study aimed to find the optimal design of the x-bar control chart which optimises quadruple objectives. The objectives are the average run length, the detection power, the average time to signal, and the expected cost per hour. In this study, a many-objective mathematical model was developed to find the optimal design and solved it using three different variations of the third version of the non-dominated sorting genetic algorithm, named NSGA-III, θ-NSGA-III, and NSDGA-III. The third one is the contribution of this paper which hybridised the NSGA-III with data envelopment analysis (DEA) and technique for order of preference by similarity to ideal solution (TOPSIS). The performances of the three algorithms were tested using a numerical example. The results revealed that the developed NSDGA-III is well defined to explore the search area and in each generation, it is always the best one in choosing solutions that have higher efficiency. Therefore, it is superior in comparing with other algorithms to find better solutions. Hence, the new hybrid algorithm can outperform NSGA-III and θ-NSGA-III. It can be used in all processes with variation due to an assignable cause.