An Economic Design of Combined Double Sampling and Variable Sample Size X ̅ Control Chart

Abstract

<strong>Abstract. </strong>In recent years several studies have shown that control charts with adaptive schemes or double sampling plans detect both small and moderate shifts in the process mean more quickly than the traditional Shewhart chart. In the classical double sampling chart, the difference between two points were placed in the central region of first stage was not considered. In this study, a new control chart is proposed by combination of double sampling chart and variable sample size chart (called DSVSS chart), that can successfully reduce the detection time of small mean shift. Before a DSVSS chart is used, its design parameters should be determined, hence economic design model of DSVSS chart is constructed. Markov chain approach is used to compute the statistical properties of the chart that are essential to our cost function. Then, the Genetic Algorithms (GA) are used to solve the optimal designs of DSVSS chart. Finally, a numerical example is provided to illustrate the use of this model.