Multiple control limits

A long shot, or just a bad slice?

In the world of continuous improvement, it might seem that one does not want to look back. After all, as systems improve, old data is no longer useful, and keeping it around—like keeping old love letters—may someday get you into trouble.

Knowing when to recalculate control limits is important, as quality managers know. The traditional seven-points-above or seven-points-below the mean, for example, are among several clear signals that can identify the need to investigate and perhaps to recalculate control limits. Recalculating control limits represents an opportunity to move forward, recognizing the dynamic nature of systems and the effects of careful improvement strategies.

New control limits, of course, must be applied only to a current process, thus rendering old information obsolete. There are times, however, when it may be fruitful—or at least interesting—to revisit earlier control limit calculations. This exercise may shed light on how a system has changed, or provide insight about historical patterns that recur in a system.

In the case of the game of golf, for example, a control chart can capture an individual's scores over a period of time, and a player can see how his or her scores have changed in that time. Looking at aggregated historical information, one can also see how the game itself has changed.

For example, golf scores in general became dramatically lower when a new ball design was introduced in 1914. Steel shafted clubs were legalized in Britain in the 1930s, representing a major leap in technology that enabled the ball to travel further and improved golf scores substantially. Changes in the game itself, such as limiting the number of clubs in a bag to 14, influenced scores as well.

With respect to data analysis, control limits on individuals charts can be recalculated after the impact of a particular change becomes clear. In the same way, other improvements in the game itself—design of clubs, for example—might result in a system change that necessitates other recalculations. These calculations are based on a collection of data from not one, but many players.

One can look at winning golf scores in the U.S. Open over the period from 1902 to 1995 to see the dramatic changes that came about in those scores (and in the control limits) when specific game improvements were introduced. Historical data is interesting and enlightening, in this case. SPC software programs, like SQCpack, can offer a number of options for applying multiple limits to a chart. The software program itself can determine the limits, either with or without overlap; one can use an "active" set of control limits; or the user can designate a custom arrangement of any number of sets of limits. Special-cause variation can be identified: a new set of clubs; a week at a professional golf camp; a systematic change in strategy with respect to club choice, etc. While these special causes may translate into only "blips" on a chart, the golfer will know when the system has really changed as a result of their impact, by examining the patterns of data. A steady rise in golf scores after beginning to use a new putter provides a different message from a single out-of-control point—provided that nothing else has changed in the system.

An SPC software program should offer the opportunity to calculate and store several sets of control limits for a particular characteristic. SQCpack are examples of SPC software programs that offer this ability. Each set of limits named can be computed by using a different filter and range of subgroups. One set is always defined as "active" limits.

In a production setting, for example, two lines may be producing a product. A user may have included "line number" as one of the customized identifiers in the SPC program. Although the data for both lines is stored in the same database, with the use of a filter one can create a set of limits for each line:

Compute 'Set 1' where line number = 1
Compute 'Set 2' where line number = 2

Data can be compared with both sets of limits displayed on a multi-chart (or a set of multiple charts) and information about variation in the lines can be gleaned from the charts.

The exercise of examining multiple control charts with a variety of re-calculated limits reinforces one's understanding of the system—both "then" and “now”—and at the same time provides an opportunity to continue to learn how the theoretical aspects of statistical process control manifest themselves in consistent ways over time.

And in the meantime, it might improve your golf game.

Originally published in the February 2011 edition of Quality eLine, our free monthly newletter.

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