Questions: A liquid-dispensing machine has been designed to fill bottles with 1.0 liter of liquid. The standard deviation of the process is 0.1 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. Liquid Dispenser 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.

A liquid-dispensing machine has been designed to fill bottles with 1.0 liter of liquid. The standard deviation of the process is 0.1 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. Liquid Dispenser 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.
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 0.1 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 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.
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Solution

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Solution Steps

Step 1: Understanding the Control Chart
  • The control chart shows the liquid dispensed by a machine over 11 observations.
  • The mean (μ) is 1 liter, with control limits at μ ± 2σ and μ ± 3σ, where σ is the standard deviation (0.1 liter).
Step 2: Analyzing the Data Points
  • The data points are plotted on the chart.
  • We need to check if any points lie outside the control limits or if there are patterns indicating the process is out of control.
Step 3: Checking for Control Rules
  • Rule 1: A point outside the μ ± 3σ limits.
  • Rule 2: Two out of three consecutive points outside the μ ± 2σ limits.
  • Rule 3: Nine consecutive points on one side of the mean.

Final Answer

  • The process is in control because none of the three warning signals detected a change. Therefore, the correct answer is:
    • D. In control, because none of the three warning signals detected a change.
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