Is Your Process Too Good for its Control Limits?


Janis, Stuart J.   (1990, ASQC)   IS&DP Statistical Consulting, St. Paul, MN

Annual Quality Congress, San Francisco, CA    Vol. 44    No. 0
QICID: 9583    May 1990    pp. 1006-1011
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Article Abstract

Attempts to use control charts in injection molding and moving web processes can lead to extremely wide control limits. This occurs when consistent differences exist between cavities of a mold, or a consistent profile exists across the width of a roll in a moving web. The broad control limits lead to a false sense of security since the existence of special causes are covered up by non-random variability between cavities or crossweb positions in a roll. This paper presents an alternative method of control limit calculation, requiring three control charts instead of the usual two, which incorporates the special aspects of these processes.

While the ideal solution is to eliminate crossweb profiles or fixed differences between cavities this is not always practical. One alternative is to plot separate charts for each cavity, or for different crossweb positions of a roll. This approach, however, can present problems if the number of cavities is large. In addition there will be the logistical difficulties of interpreting and keeping track of all the charts.

Variability in these processes can be thought of as having components of space (cavity to cavity or across a roll) and time (cycle to cycle or down a roll). The "space" portion of the variability will often have both fixed and random components. The fixed portion can be due to cavities not machined identically or a coater with consistently uneven flow; the random portion can be due to a variety of causes.

The standard deviation used to determine control limits should be based on the random portion of the variability. It should not include biases such as fixed differences between cavities. The fixed biases only come in to play in determining the central line of a chart to control variability across cavities or across a roll.

Because of these components, plots of three control charts are recommended:

  1. Xbar Chart -- to monitor the process average with limits based on the variability from cycle to cycle or downweb variability.
  2. . R-Between Chart -- to monitor the variability over time between cycles or rolls. The control limits are again based on cycle to cycle or downweb variability.
  3. R-Within Chart -- to monitor the variability across space between cavities or across the width of a roll. Its purpose is to ensure this variability is consistent over time. The limits are based on the random portion of the cavity to cavity or crossweb variability.
An example from an injection molder is used to demonstrate the problems with traditional control limit calculations. The data is plotted using traditional methods and the three control charts listed above.



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