Economic Design of X-bar Control Chart by Ant Colony Optimization

Abstract

Control charts are widely employed to monitor and maintain the statistical control of a process. Designing a control chart involves selecting a sample size, sample frequency and control limits for the control chart. The costs of sampling and testing, cost of detecting the out-of-control signal and possibly correcting it, and the cost of non-conforming items reaching the consumer give the control chart an economic aspect. In 1956, Duncan developed a Loss Cost Function for X-bar control chart with single assignable cause. The function has to be optimized using a non-conventional optimization technique. In this project, Ant Colony Optimization (ACO) has been employed to optimize Duncan’s Loss Cost Function. Ants while searching for food deposit a chemical pheromone on their way back. The amount of pheromone deposited will be dependent on the quality and quantity of food. As the time progresses the ants become selective in choosing the path depending upon the pheromone deposited. Eventually, this leads the ants to choose the best possible path. An algorithm based on the traditional Ant Colony Optimisation technique developed by Niaki and Ershadi has been applied to the economic model of Duncan. The results were found to be on par with the results obtained by employing other non-conventional optimization techniques such as Genetic Algorithm.