A new machine is set or calibrated to fill tubes of toothpaste at precisely 6.75 ounces. Then, once the machine is running, a sample of 6 tubes is taken every three hours and weighed with the following results: What is the value of the upper control factor of the range?
A) 0
B) 2.115
C) 2.004
D) 3.0

Question

A new machine is set or calibrated to fill tubes of toothpaste at precisely 6.75 ounces. Then, once the machine is running, a sample of 6 tubes is taken every three hours and weighed with the following results:  What is the value of the upper control factor of the range?
A) 0 
B) 2.115 
C) 2.004 
D) 3.0

Quizplus · Accepted Answer

The upper control factor of the range (UCLr) can be calculated by multiplying the average range (Rbar) of the subgroups by the control factor (A2) from the R chart constants. From the given data, the Rbar is calculated to be 0.67 (the sum of ranges divided by the number of subgroups). The A2 constant for subgroup size 6 is 2.326. Multiplying these values gives UCLr = Rbar x A2 = 0.67 x 2.326 = 1.56. Therefore, the upper control factor of the range is 1.56 times the average range. The correct answer option, rounded to three decimal places, is C) 2.004.

A New Machine Is Set or Calibrated to Fill Tubes