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Published: 09/21/2021
There are many control chart rules to detect special causes (i.e., outofcontrol conditions). Although most of these rules are clear, the one that seems to befuddle most people is the rule about trends. Is it six points (including the first point), six points (excluding the first point), or seven points including the first point? Confusing, isn’t it? The goal of this article is to identify the usable answer to this question. But first, it might be interesting to take a look at the various rules proposed over the years.
The original Western Electric rules^{1} did not include a trend rule. These four rules compare a series of points in the data set to zones created by the 1, 2, and 3 sigma lines.

In 1984, Lloyd Nelson added control chart rules, including the trend rule: six consecutive points increasing or decreasing.^{2} I suspect this rule was particularly hard to describe because Nelson included a visual representation of the rule (figure 1). Note that his written description lists “six points in a row steadily increasing or decreasing,” and each of the data sets shown in the illustration contain exactly six points. So, we can infer that Nelson’s definition of the trend rule is six points in a row steadily increasing or decreasing including the first point.
Joseph Juran’s Quality Control Handbook, 4th Edition^{3} uses Nelson’s rules and diagram.

In 2011, Provost and Murray published The Health Care Data Guide (HCDG).^{4} This book defines statistical rules and practices that the healthcare field adopted as standards for data analysis. In this book, Provost and Murry define a trend in a Shewhart (i.e., control) chart as “Six consecutive points increasing (trend up) or decreasing (trend down).” Figure 2 shows six points decreasing (all circled) and eight points increasing (all circled). So again, this rule includes the first point.
In Douglas Montgomery’s Introduction to Statistical Quality Control,^{5} the rule is: “six points in a row steadily increasing or decreasing,” but without a visual, leaving the rule open to ambiguity.
In the Automotive Industry Action Group’s (AIAG) Statistical Process Control, 2nd Edition,^{6} the trend rule is defined as six points in a row, all increasing or all decreasing (Table II.1, p. 75). Again, ambiguous. The first edition used seven points in a row as a trend, but the rule was changed in the second edition.

In Basic QC Practices,^{7} James Westgard introduces “Westgard Rules,” which are a variation on the Nelson rules for Levey Jennings charts used in laboratories. Levey Jennings charts use standard deviation instead of sigma estimator to calculate limits. His 7T rule (figure 3) adds one additional point to the trends in figure 1. Seven points trending in the same direction, including the initial point, violates the rule. So, the rule is seven points including the first point.
Incidentally, it must be noted that not everyone in the statistical community agrees that the “trend” rule adds value, regardless of the number of points involved. In Understanding Statistical Process Control, 2nd Edition^{8} Donald Wheeler says that a “runs up” or “runsdown” (i.e., a trend) does not increase the sensitivity of the control chart and will result in more false alarms. For a more detailed understanding of his point, see his article here.^{9}
People sometimes forget that control chart rules can detect something positive—solutions, not just problems. Working extensively with healthcare, I have found that the trend rule helps confirm the effects of process changes. Because services involve people and processes, not just machines, the improvement often takes place over time.
If we use Western Electric rules on healthcare patient falls data (figure 4), it shows an outofcontrol condition in May and June but misses the process improvement that occurred later in October through March (figure 5). An improvement team discovered that falls were concentrated in an orthopedicrecovery nursing unit and involved men between the ages of 20 to 40.
The trend rule confirms improvement before the process stabilizes and shows a run. Healthcare is chasing a goal of zero harm, popularized by the Joint Commission. Once a hospital approaches zero, it becomes more difficult to detect changes.
As another example, increases in hospitalacquired infections happen slowly but steadily. The trend rule will detect these kinds of problems before they become a hospitalwide epidemic.
As Wheeler and other who work in manufacturing environments have pointed out, trend rules may not be as useful in those situations. However, based on my experience, they are useful in service industries. And if we are going to use them, we need to be clear about the rule.
After reviewing these references, it is clear that the trend rule is either six or seven points in a row increasing or decreasing, including the initial point as shown in figures 1 and 3. Let’s stop arguing about whether the trend rule includes the first point. According to Nelson, it does, and the correct number of points is six. The vast majority of cited sources agree. So, the choice of trend rule is seven points for labs using LeveyJennings charts and six points for everyone else.
Similarly, there’s disagreement about how many points constitute a run above or below the center line. Most sources say seven, eight, or nine points in a row. The most common number of points is eight, so consider that to be a good starting point. I have found Montgomery’s rules to be the best hybrid of Nelson’s and AIAG’s rules.
Concerning the question of whether to use the trend rule or not, I would rather be alerted to a potential unstable condition so that I can investigate rather than be blindsided after the fact. If you are analyzing these runs manually or mechanically, use your customer’s desired rule set. (I use healthcare rules when working with hospitals and AIAG rules when working with automotive.)
When using SPC software, you will need the flexibility to use any of these rules to meet your customer’s requirements. Figure 6 is a summary of the commonly used rules.
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References
1. Western Electric Co. Statistical Quality Control Handbook, 2nd Edition. AT&T Technologies/Western Electric, 1982.
2. Nelson, Lloyd S. “The Shewhart Control Chart—Tests for Special Causes.” Journal of Quality Technology, Feb. 22, 2018.
3. Juran, Joseph M. Juran’s Quality Control Handbook, 4th Edition. McGrawHill, 1988.
4. Provost, Lloyd P. and Murray, Sandra K. The Health Care Data Guide. JoseyBass, 2011.
5. Montgomery, Douglas C. Introduction to Statistical Quality Control, 7th Edition. Wiley, 2013.
6. Automotive Industry Action Group (AIAG). Statistical Process Control—SPC, 2nd edition. AIAG, 2005.
7. Westgard, James O. Basic QC Practices 3rd Edition. Westgard QC, 2010.
8. Wheeler, Donald J. and Chambers, David S. Understanding Statistical Process Control, 2nd Edition. SPC Press, 1992.
9. Wheeler, Donald J. and Stauffer, Rip. “When Should We Use Extra Detection Rules?” Quality Digest, Oct. 9, 2017.
Links:
[1] https://www.qualitydigest.com/inside/statisticscolumn/whenshouldweuseextradetectionrules100917.html
[2] https://www.jointcommission.org/
[3] https://www.amazon.com/StatisticalQualityControlHandbookSecond/dp/B004OVUP24
[4] https://www.tandfonline.com/doi/abs/10.1080/00224065.1984.11978921
[5] https://www.amazon.com/JuransQualityControlHandbookJuran/dp/0070331766
[6] https://www.amazon.com/HealthCareDataGuideImprovement/dp/0470902582
[7] https://www.amazon.com/StatisticalQualityControlDouglasMontgomery/dp/1118146816
[8] https://www.amazon.com/StatisticalProcessControlSPC/dp/B004Z0VWWQ
[9] https://www.amazon.com/BasicQCPracticesJamesWestgard/dp/1886958076
[10] https://www.abebooks.com/servlet/BookDetailsPL?bi=30992816717&searchurl=sortby%3D17%26tn%3Dunderstanding%2Bstatistical%2Bprocess%2Bcontrol&cm_sp=snippet_srp1_title2