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,in order 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 = 8.85.Calculate the control limits for the X-bar chart.
A)[41.2,58.9]
B)[48.1,52.0]
C)[43.6,56.5]
D)[29.9,70.2]

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,in order 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 = 8.85.Calculate the control limits for the X-bar chart.

= 50.05,and average range = 8.85.Calculate the control limits for the X-bar chart.
A)[41.2,58.9]
B)[48.1,52.0]
C)[43.6,56.5]
D)[29.9,70.2]

Quizplus · Accepted Answer

To calculate the control limits for the X-bar chart, we will use the formula:

Upper Control Limit (UCL) =  $\overline {\overline{ x } }$+ A2*Average Range
Lower Control Limit (LCL) =  $\overline {\overline{ x } }$- A2*Average Range

where A2 is a constant factor that depends on the subgroup size. Since each subgroup contains 4 measurements, the value of A2 can be found in the control chart constants table to be 0.729.

Plugging in the values of $\overline {\overline{ x } }$ = 50.05 and Average Range = 8.85, we get:

UCL = 50.05 + 0.729*8.85 = 56.56
LCL = 50.05 - 0.729*8.85 = 43.54

Therefore, the control limits for the X-bar chart are [43.54, 56.56].

The correct choice is (C) [43.6, 56.5], which is the closest option to our calculated limits.

A Manufacturer of Windows Produces One Type That Has a Plastic