Question

# A random sample of nine cast aluminum pots is taken from a production line once every...

A random sample of nine cast aluminum pots is taken from a production line once every hour. The interior diameter of the pots is measured and the sample mean is calculated. The target for the diameter is 12 inches and the standard deviation for the pot diameter is 0.05 inches.

Assume the pot diameter is normally distributed.

Construct the centerline and the upper and lower control limits for the x¯x¯ chart.

1. The means of the samples for a given eight-hour day are 12.01 12.06 11.97 12.08 11.92 11.95 11.97 12.04. Plot these values on the x¯x¯ chart.
2. Does it appear that the process is under control?

Solution:

here first we have to find the control limits for this data i.e. upper control limit and lower control limit using the given information

where xbar bar = 12 and sd = 0.05

now Upper limit = UCL = xbar bar + ( 3 * standard deviation)

and Lower limit = LCL = xbar bar - ( 3 * standard deviation)

 xbar UCL LCL 12.01 12.15 11.85 12.06 12.15 11.85 11.97 12.15 11.85 12.08 12.15 11.85 11.92 12.15 11.85 11.95 12.15 11.85 11.97 12.15 11.85 12.04 12.15 11.85

now plot the control chart i.e x bar chart

Comment :

Using this above control chart we say that the given process is in the control because all the sample data points are lies within control limit.

Thank You..!!

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