Multivariable X-Bar and R Charting Techniques


Blank, Ronald E.   (1988, ASQC)   Raymond Engineering, Inc., Middletown, CT

Annual Quality Congress, Dallas TX    Vol. 42    No. 0
QICID: 3467    May 1988    pp. 488-491
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Article Abstract

Quality is well recognized as an element in staying competitive in a world of complex products with markets and competition being world wide. In meeting this challenge, Quality Control has to be preventing defects rather than responding to them. Statistical process control is a useful tool in defect prevention.

Shewhart type X-bar and R charts are conventionally used allow for the control of only one variable at a time, per chart. However, manufacturing may need more then one measurement per piece controlled at the same time.

P charts and C charts are valuable statistical tools for dealing with more than one defect type per piece, but they control the piece quality as a whole, rather than individual characteristics. They also do not give the same level and type of process information that X-bar and R charts give you.

Accurate and reliable multivariable X-bar and R chart techniques have been developed by statisticians, but they involve complex statistical calculations often beyond the scope of those who have to use them. The challenge presented by high technology and global competition does not leave Quality Control in the hands of selected professionals, but requires that it be controlled in a timely manner at the point of manufacture. This means that statistical process control must be performed at the operator/assembler level.

This paper describes methods for controlling two or more characteristics at the same time by the same operator and the methods do not require formal training beyond what is necessary for ordinary one variable X-bar and R charts.

Two methods have been developed. They both initially involve some vector averaging to set the X-bar value, but they differ on how the control limits are determined. One method considers the correlation (if any) between the variables and/or whether or not deviations from the nominal will act synergistically. The other method, for unrelated variables, uses the standard deviation to set the control limits. Once the chart is set up, little or no operator training is needed for use.



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