Note on ‘Design of double- and triple-sampling X-bar control charts using genetic algorithms’

Abstract

He et al. formulated the designs of double-sampling (DS) X-bar control charts as optimization problems and solved these problems with a genetic algorithm. Based on the results in solving the DS chart design problems, triple-sampling (TS) X-bar control charts were developed. The efficiency of the TS charts was compared with that of the DS charts. They concluded that the TS charts are more efficient in terms of minimizing the average sample size. We explain that, since they only considered the average sample size when the process is in control, their conclusion is questionable. In fact, the question of which control chart (i.e. the standard Shewart X-bar control chart, DS chart or TS chart) is more efficient depends on both the probability of the process shifting from an in-control to an out-of-control state and the time the control chart will need to detect such a shift.