2. Eng Mgt 385 Statistical Process Control Stephen A. Raper Chapter 4 - Continued

3. Control Charts Control charts provide a “visual” tool for quality control Control charts provide “reasonable evidence” of when to hunt for trouble, and when to leave the process alone. Lack of statistical control implies a shift in the universe The universes may differ in average only (Xbar chart) They may differ in dispersion only (R and s charts) They may differ in both average and dispersion (Xbar, R and s charts)

4. Control Charts Lack of statistical control can also be observed based on secondary rules or observations. Some observations can include trends, runs, cycles. Some are more statistical and are cause for concern: –Whenever, in 7 successive points on the control chart, all are on the same side of the line; –Whenever, in 11 successive points on the control chart, at least 10 are on the same side of the line; –Whenever, in 14 successive points on the control chart, at least 112 are on the same side of the line; –Whenever, in 17 successive points on the control chart, at least 14 are on the same side of the line; –Whenever, in 20 successive points on the control chart, at least 16 are on the same side of the central line;

5. Control Charts Type I and Type II Error – Finding the correct balance between these errors is a matter of judgment (3  ) limits and cost (size of subgroup) Type I or  error is “concluding that the universe has changed when it really is unchanged.” … a point falls outside of the control limits –Based on continuous distribution – normal – which goes from minus to plus infinity –From a numerical point of view, is the area outside of the control limits, and is calculated using the Subgroup average characteristic for the Normalized statistic Z.

6. Control Charts Type II or  error is concluding that the universe has not change, when it really has. –Is associated with the Xbar chart and a shift in the mean. –If the shift in mean is small, it may take several plotted subgroups before the shift is detected by an out of control point. –Only defined when there is a shift in the mean, in other words, Type II error is not equal to 1 – Type I error. What is the correct balance between Type I and II errors? –Generally, 3  limits provide the best balance. –Type I error probability can remain the same, but responsiveness (ability to detect Type II error) of the xbar chart can be improved with increasing subgroup sample size. –Type II error probability can be reduced with smaller  limits, but at the increase of Type I errors

7. Program Completed Program Completed University of Missouri-Rolla Copyright 2001 Curators of University of Missouri