Autopitch devices are made for both major- and minor-league teams to them improve their batting averages. when set at the standard position, autopitch can throw hardballs toward a batter at an average speed of 60 mph. to monitor these devices and to maintain the highest quality, autopitch executives take samples of 10 devices at a time. the average range is 3 mph. using this information, construct control limits for x overbar and r charts.

Control limits for x_bar are between 59.076 and 60.924

Control limits for R are between 0.669 and 5.331

Explanation:

Given data:

x_bar = 60 mph

n = 10

R = 3 mph

Step 1: Factors (see table attached)

At n = 10, factors for computing control charts limits are,

A2 = Mean factor = 0.308

D3 = Lower range = 0.223

D4 = Upper range = 1.777

Step 2: Control limits for x_bar

Lower Control limit:

LCL =  x_bar - A2*R = 60 - (0.308)(3) = 60 - 0.924 = 59.076

Upper Control limit:

UCL =  x-bar + A2*R = 60 + (0.308)(3) = 60 + 0.924 = 60.924

The control limits for x_bar are between 59.076 and 60.924

Step 3: Control limits for R

Lower Control limit:

LCL = D3*R = 0.223(3) = 0.669

Upper Control limit:

UCL = D4*R = 1.777(3) = 5.331

The control limits for R are between 0.669 and 5.331

Hope this helps!

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