A 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?