A new sampling strategy to reduce the effect of autocorrelation on a control chart

On-line monitoring of quality characteristics is essential to limit scrap and rework costs due to bad quality in a manufacturing process. In several manufacturing environments, during production process data can be massively collected with high sampling rates and tight sampling frequencies. As a consequence, natural autocorrelation may arise among consecutive measures <italic>within</italic> a sample. Autocorrelation significantly inflates the average run length of a control chart and deteriorates its sensitivity to the occurrence of assignable causes. In this paper, we propose a new <italic>mixed</italic> sampling strategy for the Shewhart <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cjas_a_871507_ilm0001.gif"/></inline-formula> chart monitoring the sample mean in a process where temporal autocorrelation between two consecutive observations can be represented by means of a first order autoregressive model AR(1). With this strategy, the sample mean at each inspection time is computed by merging measures of a generic quality characteristic from two consecutive samples taken <italic>h</italic> hours apart. The statistical properties of a Shewhart <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cjas_a_871507_ilm0002.gif"/></inline-formula> control chart implementing the proposed strategy are compared to those implementing a <italic>skipping</italic> strategy recently proposed in literature. A numerical analysis shows that the <italic>mixed</italic> sampling outperforms the <italic>skipping</italic> sampling strategy for high levels of autocorrelation.