A major customer for a vendor of plastic containers requires that its containers
Have a volume of 10,000 cubic inches with a tolerance of 50 cubic inches. To ensure that
Its process is under control and meeting its major customer's specifications, the vendor
Uses control charting. Forty subgroups of five containers each were selected periodically
From the production process. The average of the means across all subgroups was found
To be 10,012 cubic inches and the average range was 48 cubic inches. The estimated
Process standard deviation ( $( \hat { \sigma } )$
) is
A) 48 cubic inches
B) 22.69 cubic inches
C) 20.64 cubic inches
D) 50 inches
E) 32.99 cubic inches

Question

Quizplus · Accepted Answer

The estimated process standard deviation ($ \hat{\sigma} $) is calculated using the formula $\hat{\sigma} = \frac{\bar{R}}{d_2}$, where $\bar{R}$ is the average range and $d_2$ is a constant that depends on the sample size. For a sample size of 5, $d_2$ is approximately 2.326. Thus, $\hat{\sigma} = \frac{48}{2.326} \approx 20.64$ cubic inches.

A Major Customer for a Vendor of Plastic Containers Requires (σ^)( \hat { \sigma } )(σ^)

A Major Customer for a Vendor of Plastic Containers Requires $( \hat { \sigma } )$