Stats tip: A run of 6? or 7?

Matt SavageA CHARTrunner customer in the UK recently contacted me to ask why her control chart was not flagged with an out-of-control condition.

Specifically, note the run down of points in her chart. I replied that the out-of-control test that she defined is looking for seven consecutive samples that are decreasing. I agree that a run of points exists;  however, my assertion is that there are six consecutively decreasing points.

She counts seven consecutively decreasing points. How many consecutively decreasing points do you count on the chart above?

I used an analogy to explain. When one counts steps in a staircase, the initial starting point (the base or landing) is not counted as a step; the first step up is an increasing step if one is going up (and the first step below the top is a decreasing step if descending), but the beginning point is really just a beginning. It is not considered to be increasing or decreasing. The stair could also be an ending step, if one is descending, but it in itself, is neither increasing nor decreasing. Comparatively, I am not aware of a method to identify a point as both increasing and decreasing.

I also pointed to a well respected text by Acheson J. Duncan’s “Quality Control and Industrial Statistics,” Fifth Edition. In this book, he states (page 429) “… Thus in the series 5, 4, 6, 8, 10, 12, 11, there is a run up (increasing) of 4, since there are four increases in a row. Likewise, 7, 10, 8, 6, 5, 4, 3, 2, 4 illustrates a run down of 6.”

I’m interested in your thoughts. When a run up or down exists, where do you begin to count the number of consecutively increasing or decreasing values in the run?

10 thoughts on “Stats tip: A run of 6? or 7?

  1. I agree with Matt – mostly.

    The only point that I would make in the examples given is that the last point, although going the opposite direction of the trend, may still be consideraboly above or below the average or target, and an adjustment of the process may still be required.

  2. There are only six downward trending points. As stated in the example, the point before the downward trend is not part of the downward trend.

  3. We would count them as seven points. A point is a point and thus it is in the grey shaded area, you have 7 points intervals down in order. At our factory we actually train our operators to start watching at 5 points before we have serious problems at the machines.

  4. I was thinking about your question above. I pulled out the TQT manual and looked up what it had to says. pg. 90 of Chart Interpretation. QUOTE From TQT manual– “”ii) Seven or more points in a row going in one direction, up or down. For this test, look for groups of points moving upward or downward in succession. Count consecutive points, including horizontal runs within the run. Circle any groups of seven or more. If multiple groups appear, circle them all. This is probably the result of a trend in one of the system resources. The Xbar-R chart below shows a group of eight medians moving downward”” I wish I could import the picture. There is even a picture of the eights points circled. So the question is this 6 or 7? seven is my final answer.

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