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Exam 14: Statistical Process Control

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Question 1

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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.

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Process mean is not within sta...

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Question 2

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

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1) There is a pattern, trend, or cycle t...

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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.

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 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.

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

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.

Which type of chart does not have control limits?

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 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.

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

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. $\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 21.1 & 3.4 & 1.2 \\2 & 23.4 & 4.7 & 1.7 \\3 & 20.9 & 3.1 & 0.9 \\4 & 25.6 & 6.2 & 2.3 \\5 & 21.3 & 4.7 & 1.3 \\6 & 20.5 & 3.7 & 1.7 \\7 & 25.8 & 5.8 & 2.1 \\8 & 23.7 & 6.2 & 2.9 \\9 & 29.8 & 2.1 & 0.8 \\10 & 22.7 & 4.4 & 1.6 \\11 & 20.0 & 2.7 & 0.7 \\12 & 24.6 & 7.8 & 3.0\end{array}$

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

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.

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?

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

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.