Research on the economic-statistical model of VSI control chart based on multiple mass variation factors

Statistical control chart is an important tool for statistical process control, which is used to keep the production process under control to ensure product manufacturing quality. The traditional control chart is static, while the recently developed control chart is dynamic. This dynamic design enables the control chart to detect abnormal fluctuations in the process more quickly. The criteria for measuring the quality of control charts are mainly statistical characteristics and implementation costs, that is, statistical and economic. There are many researches on statistical characteristics in China, but few on economic characteristics. In this paper, we first study the design method of variable sampling interval
$(\text{VSI}\overline{X})$
control chart, and construct the model of
$\text{VSI}\overline{X}$
control chart using Markov chain method. On the basis of sorting out the statistical performance indicators to measure the quality of dynamic
$\overline{X}$
control chart, the statistical performance expression is derived. Secondly, the economic model of
$\text{VSI}\overline{X}\text{control}$
chart is established, and the parameters of the proposed economic model are optimized based on genetic algorithm.