Risk-Based X-bar chart with variable sample size and sampling interval

Flexibility is increasingly important in production management, and adaptive control charts (i.e., control charts with variable sample size and/or variable sampling interval) have significant importance in the field of statistical process control. The value of the variable chart parameters depends on the detected process parameters. The process parameters need to be estimated based on observed values; however, these values are distorted by measurement uncertainty. Therefore, the performance of the method is strongly influenced by the precision of the measurement. This paper proposes a risk-based concept for the design of an X-bar chart with variable sample size and sampling interval. The optimal set of the parameters (control line, sample size and sampling interval) is determined using genetic algorithms and the Nelder-Mead direct search algorithm to minimize the risks arising from measurement uncertainty.