Questions: 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 ± 2 σ, and at μ ± 3 σ. Determine if the process shown is in control or out of control. Explain. Liquid Dispenser Is the process in control or out of control? Choose the correct answer below. A. Out of control, because there are nine consecutive points either above or below the mean. B. Out of control, because a point lies more than three standard deviations from the mean. C. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean. D. In control, because none of the three warning signals detected a change.

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 ± 2 σ, and at μ ± 3 σ. Determine if the process shown is in control or out of control. Explain.

Liquid Dispenser

Is the process in control or out of control? Choose the correct answer below.
A. Out of control, because there are nine consecutive points either above or below the mean.
B. Out of control, because a point lies more than three standard deviations from the mean.
C. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean.
D. In control, because none of the three warning signals detected a change.

Transcript text: 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, $\mu$, at $\mu \pm 2 \sigma$, and at $\mu \pm 3 \sigma$. Determine if the process shown is in control or out of control. Explain. Liquid Dispenser Is the process in control or out of control? Choose the correct answer below. A. Out of control, because there are nine consecutive points either above or below the mean. B. Out of control, because a point lies more than three standard deviations from the mean. C. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean. D. In control, because none of the three warning signals detected a change.

Solution

Solution Steps

Step 1: Calculate the control limits

The mean is 1.0 liter and the standard deviation is 0.2 liter. The control limits are:

μ - 3σ = 1.0 - 3 * 0.2 = 0.4
μ - 2σ = 1.0 - 2 * 0.2 = 0.6
μ = 1.0
μ + 2σ = 1.0 + 2 * 0.2 = 1.4
μ + 3σ = 1.0 + 3 * 0.2 = 1.6

Step 2: Analyze the control chart

The process is considered out of control if any of the following occur:

One or more points outside the 3σ control limits
Two out of three consecutive points outside the 2σ control limits on the same side of the center line.
Nine or more consecutive points on the same side of the center line.

From the graph, we see that two out of three consecutive points (observations 5 and 6) lie above the +2σ limit.