New indices for the evaluation of the statistical properties of Bayesian x¯ control charts for short runs

In this paper we evaluate the statistical performance of various adaptive control schemes, which are implemented for monitoring the process mean in finite production runs. We develop formulas for the computation of a variety of indices, which reflect the statistical properties of the quality control mechanism of a production process, which is conducted through several one-sided, Bayesian x¯ control charts. Moreover, through our numerical study we evaluate the statistical performance of the economically designed adaptive x¯ control charts, in comparison with their static counterpart. Surprisingly, we find out that very often Bayes-nx¯ chart - with adaptive sample sizes but constant sampling intervals - performs better than the other Bayesian control charts, from a statistical point of view.