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Exam 14: Statistical Process Control

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Question 1

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Construct an R chart and determine whether the process variation is within statistical control. A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour.

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The process appears ...

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Question 2

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A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

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Process appears to b...

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Question 3

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A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below. What would be the value of the centerline that would be used in creating an R chart?

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour.

A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.

Sketch a control chart that indicates that a process is not statistically stable due to the run of 8 rule.

Construct an $\bar { x }$ chart and determine whether the process variation is within statistical control. A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes.

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.

A control chart for attributes is to be constructed. Which process would have wider control limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

Which of the following is not one of the criteria for determining if a control chart indicates that a process is not statistically stable?

A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

Which type of chart does not have control limits?

Examine the given run chart or control chart and determine whether the process is within statistical control.

Describe an R chart and give an example. What does it attempt to monitor?

Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at x and control limits at x + A3 s and x - A3 s where A3 is found in the Control Chart Constants table and s is the mean of the sample standard deviations. Construct an x chart based on standard deviations for the data below. A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality control. The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated. The results for 12 consecutive days are shown in the table below. $\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 21.1 & 3.4 & 1.2 \\2 & 23.4 & 4.7 & 1.7 \\3 & 20.9 & 3.1 & 0.9 \\4 & 25.6 & 6.2 & 2.3 \\5 & 21.3 & 4.7 & 1.3 \\6 & 20.5 & 3.7 & 1.7 \\7 & 25.8 & 5.8 & 2.1 \\8 & 23.7 & 6.2 & 2.9 \\9 & 29.8 & 2.1 & 0.8 \\10 & 22.7 & 4.4 & 1.6 \\11 & 20.0 & 2.7 & 0.7 \\12 & 24.6 & 7.8 & 3.0\end{array}$