A manufacturer of windows produces one type that has a plastic coating.The specification limits for the plastic coating are 30 and 70.From time to time the plastic coating can become uneven.Therefore,to keep the coating as even as possible,thickness measurements are periodically taken at four different locations on the window.15 subgroups were observed,each consisting of four thickness measurements,with the following results: mean of the means = $\overline { \overline { x } }$

= 50.05,and average range of 8.85.Assuming that the process is in statistical control,calculate the natural tolerance limits for the process.
A)[45.75,54.35]
B)[37.16,62.94]
C)[42.40,57.70]
D)[47.50,52.60]

Question

A manufacturer of windows produces one type that has a plastic coating.The specification limits for the plastic coating are 30 and 70.From time to time the plastic coating can become uneven.Therefore,to keep the coating as even as possible,thickness measurements are periodically taken at four different locations on the window.15 subgroups were observed,each consisting of four thickness measurements,with the following results: mean of the means =

\overline { \overline { x } }

= 50.05,and average range of 8.85.Assuming that the process is in statistical control,calculate the natural tolerance limits for the process.

= 50.05,and average range of 8.85.Assuming that the process is in statistical control,calculate the natural tolerance limits for the process.
A)[45.75,54.35]
B)[37.16,62.94]
C)[42.40,57.70]
D)[47.50,52.60]

Quizplus · Accepted Answer

The natural tolerance limits are calculated using the formula: $\overline { \overline { x } } \pm 3 \times \frac{R}{d_2}$, where $d_2$ is a constant for subgroup size 4, approximately 2.059. Thus, limits are 50.05 ± 3 × (8.85/2.059) = [37.16, 62.94].

A Manufacturer of Windows Produces One Type That Has a Plastic