TABLE 14-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.
-Referring to Table 14-4, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart?
A) LCL would increase; UCL would decrease.
B) LCL would remain the same; UCL would decrease.
C) Both LCL and UCL would remain the same.
D) LCL would decrease; UCL would increase.

Question

TABLE 14-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
  
She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.
-Referring to Table 14-4, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart?
A) LCL would increase; UCL would decrease. 
B) LCL would remain the same; UCL would decrease. 
C) Both LCL and UCL would remain the same. 
D) LCL would decrease; UCL would increase.

Quizplus · Accepted Answer

The upper control limit (UCL) for an R chart is calculated by multiplying the average range by a constant factor (typically 2.5 or 3, depending on the number of samples taken per subgroup). As the number of observations per hour increases from 5 to 6, the average range will decrease (since the range is based on the difference between the largest and smallest observation, and more observations will generally lead to a smaller range). Because the average range is a key component in calculating the UCL, a decrease in the average range will result in a lower UCL. However, the lower control limit (LCL) for an R chart is always 0, regardless of the number of observations per subgroup. Therefore, the LCL would remain the same while the UCL would decrease. This corresponds to answer choice B, which is the best choice for this question.

TABLE 14-4 A Factory Supervisor Is Concerned That the Time It Takes