Hybrid genetic algorithm for the economic-statistical design of variable sample size and sampling interval x-bar control chart

The design of control chart has economic consequences that pure statistical viewpoint does not consider them. The economic-statistical design of control chart, attends not only statistical properties such as average time to signal (ATS) but also economic consequences like hourly expected total cost. The x-bar control chart dominates others if the quality is measured by continuous scale. This paper has considered the economic-statistical design of variable sample size and sampling interval (VSSI) x-bar control chart with multiple assignable causes. Using three sample sizes and three sampling intervals to construct the VSSI x-bar control chart and considering possible combination of design parameters as a decision-making unit, are part of novelty of this research. The problem is formulated as multiple objective decision making (MODM). Also, one capable hybrid meta-heuristic based on genetic algorithm is developed in this research and it was compared with some approaches extracted from the literature and it is found that it can be competitive based on economic and statistics factors.