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"MULTIVARIATE SPC FOR GROUPED AND INDIVIDUAL OBSERVATIONS," Quality Engineering, Vol. 10(1)

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  • Published Date:
    6/12/2015 11:06:54 PM
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  1. 199810QE Multivariate SPC.pdf 6/12/2015 11:59:51 PM

Description

Quality control and process control are based on data that are sequentially collected. The collection is displayed and analyzed, either in "real time", which means that a very fast program works on the data as soon as they are generated, or later after perhaps some cleaning up. It is a fact of life that most data are naturally multivariate. The classical Shewhart approach, dating back to 1924, tracked one variable by detecting shifts in the mean or variance with the assistance of control limits. Later the Western Electric Company (WECO) introduced a set of rules to interpret the manner by which out of control situations occurred. Over time a variety of additional charts have been developed and used as auxiliary tools in the arena of the SPC, SQC and TQM efforts in industry. These include Moving Range, CUSUM, EWMA, median, runsum, etc. A detailed description of these univariate control charts is found in Montgomery(1991) Hotelling in 1947 introduced a statistic which uniquely lends itself to plotting of multiple observations. This statistic, appropriately named "Hotelling T^2" is a scalar, that combines information from the dispersion and mean of several variables. Due to the fact that computations are plentiful and slightly complex and require some knowledge of matrix algebra, acceptance of multivariate control charts by industry was slow and hesitant. However, modern computers in general and the PC in particular changed all that and during the last decade, multivariate control charts started to arrive.

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