On the robustness of x-charts

In process control the simple x-charts are widely used. In determining an optimum economic design for such a control procedure the time of satisfactory production is usually assumed to be exponentially distributed. In this paper deviations from this optimistic approach are investigated by comparing E-optimal x-charts (using the assumption of an exponentially distributed lifetime) and M-optimal x-charts which are obtained by tfie pessimistic muumax principle applied to all possible lifetime distributions with the same mean value. The comparison shows that the differences between E- and M-optimal x-charts are only minor with respect to a suitable loss function and therefore, the model under consideration is verv robust against deviations from the assumption about the distribution of the time of satisfactory production.