Interpreting x bar R Charts
8. What the control chart says about the underlying population.
#34 In A through D, assume we have a process which gives normally distributed measurements.
Choose the letter of the diagram which illustrates the samples you might get when:
_______ The process dispersion has increased.
_______ The process center and dispersion are changing, but in a random way. This process is probably under statistical control.
_______ The process center is trending upward. The product variation is consistent.
_______ The process center has drifted upward, and is now out of previously established control limits.
True or false? Control limits apply to sample averages, not individual measurements. __________
A
B
C
D
Signs that a process is not in statistical control
Assignable causes are likely present-- taking a process out of statistical control-- when the x bar R chart shows:
  • Any point outside the control limits. Only about 3 points in 1,000 are expected to fall outside of 3 standard deviations when the process is in statistical control.
  • A run of 7 points all above or below the grand average. For a process that is in statistical control this condition would be expected to occur with probability at most 0.57= 0.0078. This pattern is expected less than 8 times in 1000.
  • A run of seven intervals consistently up or consistently down. Again, for a process in statistical control we would expect to see this condition less than 8 times in 1000.
  • Sawteeth, cycles, or any other obviously non-random pattern.

Notes
On the chart, record any unusual changes in machinery, methods, materials, or measurements. Write any changes that were made in conjunction with out of control points on the chart.

Recalculate control limits after any planned changes in the process, collecting at least 25 new subgroups. Preliminary calculations may be made after 8 or 10 subgroups.

Keep in mind the whole history of the numbers on the chart. Each number begins with a measurement. A number resulting from an error in measurement carries the same weight as a correct measurement, and may look like a problem in manufacturing or materials. Errors in measurement may be assignable causes themselves. Wear on measuring tools, or in methods of hand measurement, may produce apparent shifts in the process average.

Sample averages, as plotted on control charts, provide a window on the population or "universe" from which our samples are taken.

The control chart is a starting point for the operator, technician or engineer to track down assignable causes. The place in the chart at which at the which the process ceased being in control, together with notes on the chart, can help to identify the causes of the problem.

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