Double Sampling X̅ Charts

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Abstract
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.