Instruction 18-7
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 five 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.
$$\begin{array} { | l | l | l | }
\hline \text { Hour } & \underline { \underline { X } } & \underline { R } \
\hline 1 & 18.4 & 25 \
\hline 2 & 16.9 & 27 \
\hline 3 & 23.0 & 30 \
\hline 4 & 21.2 & 23 \
\hline 5 & 21.0 & 24 \
\hline 6 & 24.0 & 25 \
\hline 7 & 19.3 & 12 \
\hline 8 & 15.8 & 14 \
\hline 9 & 20.0 & 13 \
\hline 10 & 23.0 & 11 \
\hline
\end{array}$$
-Referring to Instruction 18-7,suppose the sample mean and range data were based on six observations per hour instead of five.How would this change affect the lower and upper control limits of an R chart?
A) Both LCL and UCL would remain the same.
B) LCL would remain the same; UCL would decrease.
C) LCL would increase; UCL would decrease.
D) LCL would decrease; UCL would increase.

Question

Instruction 18-7
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 five 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.
 $$\begin{array} { | l | l | l | } 
\hline \text { Hour } & \underline { \underline { X } } & \underline { R } \
\hline 1 & 18.4 & 25 \
\hline 2 & 16.9 & 27 \
\hline 3 & 23.0 & 30 \
\hline 4 & 21.2 & 23 \
\hline 5 & 21.0 & 24 \
\hline 6 & 24.0 & 25 \
\hline 7 & 19.3 & 12 \
\hline 8 & 15.8 & 14 \
\hline 9 & 20.0 & 13 \
\hline 10 & 23.0 & 11 \
\hline
\end{array}$$
-Referring to Instruction 18-7,suppose the sample mean and range data were based on six observations per hour instead of five.How would this change affect the lower and upper control limits of an R chart?
A) Both LCL and UCL would remain the same.
B) LCL would remain the same; UCL would decrease.
C) LCL would increase; UCL would decrease.
D) LCL would decrease; UCL would increase.

Quizplus · Accepted Answer

The formula for calculating the upper control limit (UCL) for an R chart with six observations per hour is D4 times the sample range, where D4 is a constant based on sample size. For five observations per hour, D4 is 2.115. For six observations per hour, D4 is 2.282. Since a larger value of D4 results in a smaller UCL, the UCL for an R chart with six observations per hour would decrease compared to the UCL for a chart with five observations per hour. The lower control limit (LCL) is not affected by the sample size, as it is always zero for an R chart. Therefore, the correct answer is B.

Instruction 18-7 a Factory Supervisor Is Concerned That the Time

Instruction 18-7
a Factory Supervisor Is Concerned That the Time