Suppose, after developing the control chart, a subgroup of size 4 yields a sample mean of 12.09 ounces and a range of 0.08. Which of the following statements is true? A) The process is out of control on the x-bar chart but in control on the R chart. B) The process is in control on the x-bar chart and out of control on the R chart. C) Since 12.09 12.074, the process is in control on the x-bar chart. D) Since 0.08 12.03, the process is in control on the x-bar chart.

Question

Suppose, after developing the control chart, a subgroup of size 4 yields a sample mean of 12.09 ounces and a range of 0.08. Which of the following statements is true?
A) The process is out of control on the x-bar chart but in control on the R chart.
B) The process is in control on the x-bar chart and out of control on the R chart.
C) Since 12.09 > 12.074, the process is in control on the x-bar chart.
D) Since 0.08 < 0.137, the process is out of control on the R chart.
E) Since 12.09 > 12.03, the process is in control on the x-bar chart.

Quizplus · Accepted Answer

The control charts for the process have been developed based on the historical data and process capabilities. The x-bar chart monitors the central tendency of the process, and R chart monitors the variability of the process. In this case, the sample mean of 12.09 ounces is not necessarily out of control because the process may have shifted due to assignable causes, and control limits on the chart may not reflect the current process. However, the range of 0.08 is very small compared to the range of historical data used to develop the control limits, suggesting that the process variability has decreased or some special cause is at work. Hence, the process is out of control on the x-bar chart, but in control on the R chart.

Suppose, After Developing the Control Chart, a Subgroup of Size