Action lines

The elements of gear teeth common to all gears are tooth surface and profile, flank, top and bottom land, crown, root and pitch circle, gear center, line of centers, pitch point, line of action, line of contact, and point of contact. Figure 57.27 labels many of the common gear tooth elements. Figure 57.28 labels the common rack tooth elements. 

FIGURE 11.22 Control charts and outliers, (a) pEC50 values (ordinates) run as a quality control for a drug screen over the days on which the screen is run (abscissae). Dotted lines are the 95% c.l. and the solid lines the 99.7% c.l. Data points that drift beyond the action lines indicate significant concern over the quality of the data obtained from the screen on those days, (b) The effect of significant outliers on the criteria for rejection. For the data set shown, the inclusion of points A and B lead to a c.l. for 95% confidence that includes point B. Removal of point A causes the 95% limits to fall below points B, causing them to be suspect as well. Thus, the presence of the data to be possibly rejected affects the criteria for rejection of other data. 

Wills, G. (1993). Your Enterprise School of Management A Proposition and Action Lines. MCB University Press. 

The analyst might have elected to follow the process more closely and plot the duplicate means twice a day. Now the warning and action lines are at 2 X s/ /2 and 3 x s/ /2, respectively (figure 4.12). Comparing figures 4.11 and 4.12, although the lines are wider apart with fewer repeats, the points are more scattered, too. 

Upper action line - Upper warning line... 

For a Gaussian distribution, 95.5% of all observations are within 2oVV/t from the mean and 99.7% are within a 3o-/V/, where n is the number of tablets (=25) that are averaged each hour. The 2oVVn limits are warning lines and the 3cr/Vn limits are action lines. We expect —4.5% of measurements to be outside the warning lines and —0.3% to be outside the action lines. It is unlikely that we would observe two consecutive measurements at the warning line (probability = 0.045 X 0.045 = 0.002 0). 

There should be no observations outside the action lines—One observation (day 101) lies above the upper action line. 

There are not 2 out of 3 consecutive measurements between warning and action lines—OK. 

Key action line 1 National policy on information security and cross-border co-operation... 

Control charts often have a center line and two control lines with two pairs of limits a warning line at m 2s and an action line at m 3s. Statistics predict that 95.45% and 99.7% of the data will fall within the areas enclosed by the 2s and 3s limits. The center line is either the mean or the true value. In the ideal case, where unbiased methods are being used, the center line would be the true value. This would apply, for example, to precision control charts for standard solutions. 

When the process is under statistical control, the day-to-day results are normally distributed about the center line. A result outside the warning line indicates that something is wrong. Such a result need not be rejected, but documented procedures should be in place for suitable action. Instruments and sampling procedures should be checked for errors. Two successive values of the Quality Control sample falling outside the action line indicate that the process is no longer under statistical control. In this case, the results should be rejected and the process investigated for its unusual behavior. Further analyses should be suspended until the problem is resolved. 

Figure 3.13 Typical control chart showing upper and lower warning and action lines and capability histogram [15]...

Static analysis requires consideration of forces and moments of force acting on the body at rest (static equilibrium). A magnitude of the moment of force at the point of rotation is equal to the product of force and the perpendicular distance from the force action line to that point. The moment (M) equals force (F) times moment arm (d), with unit of measurement (N-m). The static analysis ignores the effects of accelerations, momentum, and friction and is adequate only for analysis of static postures. 

Figure 1 Example of a Shewhart control chart. The warning limit corresponds to +2s, and the action line is set at +3s.

Control chart. The graph in Box 5-1 shows mean values for five replicate quality control samples measured each day. The standard operating procedure calls for stopping work to identify the source of error if the mean daily quality control result is outside the action lines ( 3a/V7i). This condition does not occur in Box 5-1. Are any other rejection conditions from Box 5-1 observed in this data ... 

One observation (day 101) is outside the action line. None of the other criteria are violated. 

It is not always the practice to plot the lower action and warning lines on a control chart for the range, as a reduction in the range is not normally a cause for concern. However, as already noted, the variability of a process is one measure of its quality, and a reduction in R represents an improvement in quality, the causes of which may be well worth investigating. So plotting both sets of warning and action lines is recommended. 

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