Double Sampling Chart Research Articles

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

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.

Design of double- and triple-sampling X-bar control charts using genetic algorithms

As today's manufacturing firms are moving towards agile manufacturing, quick and economic on-line statistical process control solutions are in high demand. Multiple sampling X-bar control charts are such an alternative. They can be designed to allow quick detection of a small shift in process mean and provide a quick response in an agile manufacturing environment. In this paper, the designs of double-sampling (DS) X-bar control charts are formulated and solved with a genetic algorithm. Based on the results in solving the DS chart design problems, triple sampling (TS) X-bar control charts are developed. The efficiency of the TS charts is compared with that of the DS charts. The results of the comparison show that TS charts are more efficient in terms of minimizing the average sample size.

Double Sampling X̅ Charts

The purpose of this paper is to propose a new control chart, the double sampling X̅ chart, which is the counterpart to double sampling plans. This procedure offers better statistical efficiency (in terms of the average run length) than the Shewhart X̅ chart, without increased sampling. Alternatively, the procedure can be used to reduce the sampling without reducing the statistical efficiency. The properties (probability of a signal, average run length, average sample size, etc.) of the double sampling X̅ chart are studied, and it is compared with variable sampling interval Shewhart charts, EWMA charts, and CUSUM charts. The double sampling chart depends on five parameters, and therefore, there is a great deal of flexibility in designing the chart. Tables are provided to aid in the choice of these parameters.