Question

a liquid - dispensing machine has been designed to fill bottles with 1.0 liter of liquid. the standard deviation of the process is 0.2 liter. a control chart is shown. the chart has horizontal lines drawn at the mean, μ, at 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? choose the correct answer below. a. out of control, because two out of three consecutive points lie more than two standard deviations from the mean. b. out of control, because a point lies more than three standard deviations from the mean. c. out of control, because there are nine consecutive points either above or below the mean. d. in control, because none of the three warning signals detected a change.

Explanation:

Step1: Analyze control - chart rules

In control - chart analysis, common out - of - control signals include: two out of three consecutive points lie more than two standard deviations from the mean, a point lies more than three standard deviations from the mean, and nine consecutive points either above or below the mean.

Step2: Examine the given control chart

Upon observing the given control chart, we can see that none of the above - mentioned out - of - control signals are present. All points are within the $\mu\pm3\sigma$ limits and there are no patterns like two out of three consecutive points beyond $\mu\pm2\sigma$ or nine consecutive points on one side of the mean.

Answer:

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