Q5CQQ In Exercises 5鈥�8, use the foll... [FREE SOLUTION]

Chapter 12: Q5CQQ (page 566)

In Exercises 5鈥�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 variation within statistical control? Why or why not?

Short Answer

Expert verified

No, the process variation is not within statistical control because there are a few features in the R chartthat imply that the process mean is not under statistical control:

At least eightconsecutive points lie below the CL.
At least eightconsecutive points lie above the CL.
At least one point lies beyond the UCL and LCL.
The sample points seem to follow a nonrandompattern.

Step by step solution

Given information

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

The sample size for each subgroup is equal to 100.

Criteria to determine when the statistical process is not in control

A process is said to be out of control when the statistical process hasshownone of the listed features:

There is a distinguishably visible pattern, trend, or cycle.
One or more pointsexceed the upper control limit and fall below the lower control limit.
There must be at least eight points above or below the centerline in a row,also known as the Run of 8 Rule.

To check whether the process variation is in control or not

It is required to determine whether the process variability is under control or not.

The R control chart is used to monitor the process variability.

The following criteria can be observed in the provided R chart:

At least eightconsecutive points lie below the central line (CL).
At least eightconsecutive points lie below the central line (CL).
Some points are lying above the upper control limit (UCL) and below the lower control limit (LCL).
The points seem to follow a patternthatis not random.

Since the above criteria indicate a violation of stability in a statistical process,it can be said that the process variability is not under statistical control.