The first of these shows how measurement error (meaning “noise” not “mistake”) was initially unstable but was quickly fixed by removing non-applicable cases. The chart’s spike revealed this flaw in the tracking systems and found it also throughout all the data (not just the spike). That stabilized measurement error (i.e. the data all then fell inside tighter tramlines). Calls for measurement perfection were advised against since it would have been uneconomic (i.e. a severe drain on resources) and often impossible. This economic aspect is one of the most valuable features of economic control.
The next pair of charts are a hybrid. On the top chart, the gray areas are measurement error (i.e. noise) and the outer limits are the process (i.e. chronic events). This gray area offers a simple way to always know measurement error will not get in the way. It is clear the gray portion is not obscuring the chronic events month by month. The gray is about a quarter of distance between the outer dotted lines. Since statisticians use squared (not linear) distances, only about a quarter2 = 1/16= 6 ¼% of the process is really obscured. A good rule of thumb here is 25% tops, but 10-15% preferred.
This is surprising, given the visual impression, so the square law clarifies.
The lower chart is also measurement error but looks at precision (i.e. how much measurement error varies). The top chart was measurement accuracy (i.e. how close to the true mark it gets and how well it discriminates process shifts).
This simple hybrid method allows processes to be improved and all questions about measurement error answered (really pre-empted) in real time, in the months ahead.
This case produced about a third improvement (against experimental prediction of a quarter) in a 3-month study plus a couple of months to solve implementation problems. The implementation population was double the size of the random sample used in the study.