Suppose that $\overline { \mathrm { X } }$
And R charts based on subgroups of size 4 are being used to monitor the tire diameter size of a new radial tire.The $\overline { \mathrm { X } }$
And R charts are found to be in statistical control with $\overline { \overline { X } } = 50.25 , \bar { R } = .8$

Inches.A histogram of the tire diameter measurements indicates that these measurements are approximately normally distributed.Calculate the estimate of the percentage of tires that are out of specification.
A)1.93%
B)2.68%
C)1.62%
D)17.36%

Question

Suppose that $\overline { \mathrm { X } }$
And R charts based on subgroups of size 4 are being used to monitor the tire diameter size of a new radial tire.The $\overline { \mathrm { X } }$
And R charts are found to be in statistical control with $\overline { \overline { X } } = 50.25 , \bar { R } = .8$

Inches.A histogram of the tire diameter measurements indicates that these measurements are approximately normally distributed.Calculate the estimate of the percentage of tires that are out of specification.
A)1.93%
B)2.68%
C)1.62%
D)17.36%

Quizplus · Accepted Answer

The process is in control, and the measurements are normally distributed. Using the given $\overline { \overline { X } } = 50.25$ and $\bar { R } = .8$, the standard deviation $\sigma$ can be estimated as $\bar { R } / d_2$, where $d_2$ for subgroup size 4 is approximately 2.059. Thus, $\sigma \approx 0.3885$. Assuming specification limits are not given, the percentage of out-of-specification tires is typically calculated using the standard normal distribution. The closest choice to typical out-of-specification percentages for a normally distributed process is 2.68%.

Suppose That X‾\overline { \mathrm { X } }X And R Charts Based on Subgroups of Size 4 Are

Suppose That $\overline { \mathrm { X } }$ And R Charts Based on Subgroups of Size 4 Are