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Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling

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Abstract:

Traditional control charts for process monitoring are based on taking samples of fixed size at equally spaced sampling points. As an alternative to these traditional fixed sampling rate (FSR) control charts, variable sampling rate (VSR) control charts change the sampling rate as a function of the data from the process. With VSR control charts the sampling rate is increased whenever there is some indication of a problem with the process, and decreased when there is no indication of a problem. This paper investigates a type of VSR control chart based on sequential sampling in which the sample size used at a sampling point is a function of the data from the current and past sampling points. Sequential sampling is investigated in the context of simultaneously monitoring both the mean and variability of a multivariate normal process. Multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from the target are considered. When sequential sampling is used in a combination of the MEWMA charts based on sample means and on squared deviations from the target, the average performance is much better than that of the standard FSR multivariate control charts that have traditionally been used.

Keywords: Average time to signal; Exponentially weighted moving average control chart; Multivariate exponentially weighted moving average control chart; Regression adjustment of variables; Squared deviations from target; Statistical process control; Steady state average time to signal; Variable sampling rate

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/07474940701404898

Affiliations: 1: Departments of Statistics and Forestry, Virginia Tech, Blacksburg, Virginia, USA 2: MedImmune, Inc., Gaithersburg, Maryland, USA

Publication date: July 1, 2007

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