Question

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

Is the process mean within statistical control? Why or why not?

Short answer

No, the process mean is not within statistical control as the following two features are clearly noticeable in the \(\bar x\) chart:

• At least eightconsecutive points lie below the centerline.
• At least one point lies above the upper control limit.

Step-by-step solution

Given information

The\(\bar x\)chart is plotted for the measurement of errors (in feet) obtained when the aircraft altimetersare tested in a pressure chamber.

The sample size is equal to 100.

Criteria to determine when the statistical process is out of control

If any of the below-mentioned features appear,the process is said to be out of control.

• There is a distinguishably visible pattern, trend, or cycle.
• One or more pointsexceed the upper control limit and fall below the lower control limit.
• At least eight points must lie above or below the centerline in a row. This condition is called the Run of 8 Rule.

Step 3:Analysing process control

Since it is required to assess whether the process mean is within statistical control or not, the

\(\bar x\)chart is observed.

The following two criteria can be distinctly observed, which imply that the process mean is out of control:

• More than eight consecutive points lie below the centerline (CL).
• Some points lie above the upper control limit (UCL).

Thus, it can be concluded that the process mean is not within statistical control.