TABLE 18-4
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.
$$\begin{array} { l l l l }
\text { Hour } & \bar { X } & \text { R } \
\hline 1 & 18.4 & 25 \
2 & 16.9 & 27 & \
3 & 23.0 & 30 & \
4 & 21.2 & 23 & \
5 & 21.0 & 24 & \
6 & 24.0 & 25 & \
7 & 19.3 & 12 \
8 & 15.8 & 14 & \
9 & 20.0 & 13 & \
10 & 23.0 & 11 &
\end{array}$$ 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 18-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?
A) 0, 42.28
B) - 2.33, 43.13
C) 0, 43.13
D) - 2.28, 42.28

Question

TABLE 18-4
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.
 $$\begin{array} { l l l l } 
\text { Hour } & \bar { X } & \text { R } \
\hline 1 & 18.4 & 25 \
2 & 16.9 & 27 & \
3 & 23.0 & 30 & \
4 & 21.2 & 23 & \
5 & 21.0 & 24 & \
6 & 24.0 & 25 & \
7 & 19.3 & 12 \
8 & 15.8 & 14 & \
9 & 20.0 & 13 & \
10 & 23.0 & 11 &
\end{array}$$ 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 18-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?
A) 0, 42.28
B) - 2.33, 43.13
C) 0, 43.13
D) - 2.28, 42.28

Quizplus · Accepted Answer

To calculate the upper and lower control limits for an R chart, we use the formulas:
Upper control limit (UCL) = R-bar * D4
Lower control limit (LCL) = R-bar * D3
where R-bar is the average range of the sample ranges, and D3 and D4 are constants that depend on the sample size (n).
From Table 18-4, we can see that the sample size (n) is 4. The average range is calculated as:
R-bar = (4.5 + 8.6 + 5.5 + 6.1 + 5.0 + 6.6) / 6 = 5.7833
From Table 18-3, we can find the constant values for D3 and D4, which are 0 and 2.282, respectively.
Therefore, the UCL = R-bar * D4 = 5.7833 * 2.282 = 13.2047
and the LCL = R-bar * D3 = 5.7833 * 0 = 0
Therefore, the appropriate answer is C, with UCL = 13.2047 and LCL = 0.

TABLE 18-4 a Factory Supervisor Is Concerned That the Time

TABLE 18-4
a Factory Supervisor Is Concerned That the Time