Multivariate multiple sampling charts

Abstract

A new multivariate statistical process control scheme, the Multivariate Multiple Sampling (MMS) control chart scheme, is proposed in this paper. A MMS chart is a multivariate extension of a double sampling X-bar control chart with at least two sampling stages. In the paper, a statistical design optimization procedure to design the MMS chart is presented and the performance of the MMS chart is investigated. The statistical efficiency in terms of average run length of the MMS chart is compared with that of the Hotelling chart both with and without variable sampling schemes, a multivariate CUMulative SUM (CUSUM) chart, and a multivariate Exponentially Weighted Moving Average (EWMA) chart. The ability of the MMS chart to handle the worst-case scenario is also investigated and compared with that of the multivariate EWMA and CUSUM charts. The results of the investigation show that even with only two sampling stages, the MMS chart provides an improvement in efficiency in detecting small shifts over the Hotelling chart without variable sampling schemes. When the number of sampling stages is equal to two, the MMS chart is better in detecting large shifts and the multivariate EWMA and CUSUM charts are better in detecting relatively small shifts. As the number of sampling stages is increased beyond two, the improvement in sensitivity of the MMS chart in detecting the small shifts increases. When the number of sampling stages ≥3, the MMS chart begins to give a better performance than a Hotelling chart with a variable sampling scheme for small shifts and is also better than a multivariate EWMA chart for both small and large shifts. As the number of sampling stages ≥4, the MMS chart begins to give a better performance than a multivariate CUSUM chart for both small and large shifts. The results of the investigation also show that the MMS chart outperforms the multivariate EWMA and CUSUM charts in the worst-case scenario situation.