The target load weight for a ladder is 250 lb. A technician selects 5 ladders at random per day to test load limit and records the mean load for each day. Determine the most accurate mean control chart drawn from the data shown in the table. $\begin{array}{cccccc}
\text { Hour } &1 & 2 & 3 & 4 & 5 & 6 \
\
\text { Mean } &260 & 238 & 275 & 238 & 258 & 260 \
\text { Hour } &7 & 8 & 9 & 10 & 11 & 12 \
\
\text { Mean } &250 & 270 & 261 & 265 & 241 & 248 \
\text { Hour } &13 & 14 & 15 & 16 & 17 & 18 \
\
\text { Mean } &273 & 265 & 260 & 253 & 240 & 245
\end{array}$

Question

Quizplus · Accepted Answer

To determine the most accurate mean control chart, we need to calculate the control limits for each set of means and look for any outliers or patterns. The control limits can be calculated using the formula:

Upper Control Limit (UCL) = Mean + (3 * Standard Deviation)
Lower Control Limit (LCL) = Mean - (3 * Standard Deviation)

Using the given data, we calculate the mean and standard deviation for each set of means:

Hours 1-6:
Mean = (260+238+275+238+258+260)/6 = 252.5
Standard Deviation = 15.4

Hours 7-12:
Mean = (250+270+261+265+241+248)/6 = 255.8
Standard Deviation = 11.4

Hours 13-18:
Mean = (273+265+260+253+240+245)/6 = 257.7
Standard Deviation = 12.3

Using these values, we can calculate the control limits for each set of means:

Hours 1-6:
UCL = 252.5 + (3 * 15.4) = 299.7
LCL = 252.5 - (3 * 15.4) = 205.3

Hours 7-12:
UCL = 255.8 + (3 * 11.4) = 290.0
LCL = 255.8 - (3 * 11.4) = 221.6

Hours 13-18:
UCL = 257.7 + (3 * 12.3) = 294.6
LCL = 257.7 - (3 * 12.3) = 220.8

Looking at the options, we can see that only option B has the correct control limits for Hours 7-12, with the mean line at 255.8 and the UCL and LCL values matching our calculations. Additionally, option B shows that there are no outliers or patterns in the data, indicating that it is the most accurate mean control chart for this scenario.

The Target Load Weight for a Ladder Is 250 Lb