Question

Autopitch devices are made for both​ major- and​ minor-league teams to help 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.

Answer 1

Control limits for x_bar are between 59.076 and 60.924

Control limits for R are between 0.669 and 5.331

Step-by-step 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!