A cell phone manufacturer has been experiencing physical quality control problems. The back case of phones does not always fit and snap into place on the phone body. The dimensions of the case have constantly been in statistical process control (SPC). To monitor process control, the company uses -charts. Seven samples, each containing three phone cases, were selected from different batches. The data is presented in Table 1 below.
Table 1: Cell Phone Plastic Case Widths in Centimeters Data*
$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline \text { Observation } & \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } & \text { Sample 4 } & \text { Sample 5 } & \text { Sample 6 } & \text { Sample 7 } \
\hline 1 & 6.02 & 5.92 & 5.88 & 5.99 & 6.05 & 5.94 & 6.00 \
\hline 2 & 5.97 & 5.83 & 5.97 & 6.08 & 6.06 & 5.96 & 5.95 \
\hline 3 & 5.90 & 5.87 & 5.88 & 6.08 & 5.98 & 5.99 & 5.82 \
\hline \text { Average } & 5.963 & 5.873 & 5.912 & 6.051 & 6.035 & 5.963 & 5.923 \
\hline \text { Range } & 0.12 & 0.09 & 0.09 & 0.09 & 0.08 & 0.05 & 0.18 \
\hline
\end{array}$
*The sample averages and ranges help avoid simple math errors and quicken the time to complete the SPC analysis.
If
for the
-chart is 1.023, the lower control limit for the
-chart (LCL) will be:
A) less than or equal to 3.0.
B) greater than 3.0 but less than or equal to 4.0.
C) greater than 4.0 but less than or equal to 5.0.
D) greater than 5.0.

Question

A cell phone manufacturer has been experiencing physical quality control problems. The back case of phones does not always fit and snap into place on the phone body. The dimensions of the case have constantly been in statistical process control (SPC). To monitor process control, the company uses -charts. Seven samples, each containing three phone cases, were selected from different batches. The data is presented in Table 1 below.
Table 1: Cell Phone Plastic Case Widths in Centimeters Data*
$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Observation } & \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } & \text { Sample 4 } & \text { Sample 5 } & \text { Sample 6 } & \text { Sample 7 } \
\hline 1 & 6.02 & 5.92 & 5.88 & 5.99 & 6.05 & 5.94 & 6.00 \
\hline 2 & 5.97 & 5.83 & 5.97 & 6.08 & 6.06 & 5.96 & 5.95 \
\hline 3 & 5.90 & 5.87 & 5.88 & 6.08 & 5.98 & 5.99 & 5.82 \
\hline \text { Average } & 5.963 & 5.873 & 5.912 & 6.051 & 6.035 & 5.963 & 5.923 \
\hline \text { Range } & 0.12 & 0.09 & 0.09 & 0.09 & 0.08 & 0.05 & 0.18 \
\hline
\end{array}$
*The sample averages and ranges help avoid simple math errors and quicken the time to complete the SPC analysis.
If 
for the
-chart is 1.023, the lower control limit for the
-chart (LCL) will be:
A) less than or equal to 3.0.
B) greater than 3.0 but less than or equal to 4.0.
C) greater than 4.0 but less than or equal to 5.0.
D) greater than 5.0.

Quizplus · Accepted Answer

The lower control limit (LCL) for the R-chart can be calculated using the formula LCL = D4 * R̄, where D4 is a constant that depends on the sample size (in this case, 1.023 for the R-chart) and R̄ is the average range of the samples. Given the ranges provided in the table, the average range (R̄) can be calculated, and it will be a positive number. Since D4 is also positive, the product of D4 and R̄ will be a positive number, which, when considering the typical scale of measurements for such manufacturing processes, will likely place the LCL greater than 5.0, especially since the ranges are relatively small and the constant 1.023 would not reduce the value significantly to fall below 5.0.

A Cell Phone Manufacturer Has Been Experiencing Physical Quality Control