A plastic cell phone case has been experiencing physical quality control problems. That is, the clear screen does not always fit (and snap into place) on the case. The dimensions of the screen have consistently been in statistical process control (SPC) . A root cause quality initiative collected the following data about the plastic cell phone case. Analyze the width of the cell phone case using control charts and make a recommendation.
Table 1 Cell Phone Plastic Case Widths in Centimeters Data*
$\begin{array} { | c | c | c | c | c | c | c | c | } \hline & \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } & \text { Sample 4 } & \text { Sample 5 } & \text { Sample 6 } & \text { Sample 7 } \\\hline \text { Observation } & & & & & & & \\\hline \# 1 & 6.02 & 5.92 & 5.88 & 5.99 & 6.05 & 5.94 & 6.00 \\\hline \# 2 & 5.97 & 5.83 & 5.97 & 6.08 & 6.06 & 5.96 & 5.95 \\\hline \# 3 & 5.90 & 5.87 & 5.88 & 6.08 & 5.98 & 5.99 & 5.82 \\\hline \text { Average } & 5.963 & 5.873 & 5.91 & 6.05 & 6.03 & 5.963 & 5.923 \\\hline \text { Range } & 0.12 & 0.09 & 0.09 & 0.09 & 0.08 & 0.05 & 0.18 \\\hline\end{array}$ *The sample averages and ranges helps in avoiding simple math errors and quickens the time to complete the SPC analysis.
-Using Table 1, for the X-chart, what is the value of UCL_X?

Question

A plastic cell phone case has been experiencing physical quality control problems. That is, the clear screen does not always fit (and snap into place) on the case. The dimensions of the screen have consistently been in statistical process control (SPC) . A root cause quality initiative collected the following data about the plastic cell phone case. Analyze the width of the cell phone case using control charts and make a recommendation.
Table 1 Cell Phone Plastic Case Widths in Centimeters Data*

\begin{array} { | c | c | c | c | c | c | c | c | } \hline & \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } & \text { Sample 4 } & \text { Sample 5 } & \text { Sample 6 } & \text { Sample 7 } \\\hline \text { Observation } & & & & & & & \\\hline \# 1 & 6.02 & 5.92 & 5.88 & 5.99 & 6.05 & 5.94 & 6.00 \\\hline \# 2 & 5.97 & 5.83 & 5.97 & 6.08 & 6.06 & 5.96 & 5.95 \\\hline \# 3 & 5.90 & 5.87 & 5.88 & 6.08 & 5.98 & 5.99 & 5.82 \\\hline \text { Average } & 5.963 & 5.873 & 5.91 & 6.05 & 6.03 & 5.963 & 5.923 \\\hline \text { Range } & 0.12 & 0.09 & 0.09 & 0.09 & 0.08 & 0.05 & 0.18 \\\hline\end{array}

*The sample averages and ranges helps in avoiding simple math errors and quickens the time to complete the SPC analysis.
-Using Table 1, for the X-chart, what is the value of UCL_X?

Quizplus · Accepted Answer

The Upper Control Limit (UCL) for an X-bar chart is calculated using the formula UCL = $ \bar{X} + A_2 \times R $, where $ \bar{X} $ is the average of sample averages and R is the average range. The question does not provide the value of $ A_2 $, which is needed for exact calculation, but given the context that we're analyzing quality control for a manufacturing process, and considering the provided data, the UCL is expected to be significantly higher than the range of the sample averages (which are around 5.9 to 6.05). Since all options are significantly lower than the typical values of $ \bar{X} $ in the dataset, and without the exact value of $ A_2 $ or the average range, we infer that the UCL must be greater than the highest value provided in the options, which leads to the selection of option D by elimination and understanding of typical control chart parameters.

A Plastic Cell Phone Case Has Been Experiencing Physical Quality