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

Bruno Chaves Franco, Philippe Castagliola, Giovanni Celano and Antonio Fernando Branco Costa

Journal of Applied Statistics, 2014, vol. 41, issue 7, 1408-1421

Abstract: 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 within 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 mixed sampling strategy for the Shewhart 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 h hours apart. The statistical properties of a Shewhart control chart implementing the proposed strategy are compared to those implementing a skipping strategy recently proposed in literature. A numerical analysis shows that the mixed sampling outperforms the skipping sampling strategy for high levels of autocorrelation.

Date: 2014
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DOI: 10.1080/02664763.2013.871507

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