Question

a gear has been designed to have a diameter of 3 inches. the standard deviation of the process is 0.4 inch. a control chart is shown. each chart has horizontal lines drawn at the mean, μ, μ±2σ, and at μ±3σ. determine if the process shown is in control or out of control. explain.
is the process in control or out of control? select all that apply.
a. out of control, because there are nine consecutive points either above or below the mean.
b. out of control, because two out of three consecutive points lie more than two standard deviations from the mean.
c. out of control, because a point lies more than three standard deviations beyond the mean.
d. in control, because none of the three warning signals detected a change.

Explanation:

Step1: Check for nine - consecutive points

Inspect the control - chart for nine consecutive points either above or below the mean. There are no such runs of nine consecutive points.

Step2: Check for two - out - of - three rule

Check for two out of three consecutive points that lie more than two standard deviations from the mean. There are no such groups of three points.

Step3: Check for points beyond three standard deviations

Check for any points that lie more than three standard deviations beyond the mean. There are no such points.

Answer:

D. In control, because none of the three warning signals detected a change.