Question 1

The p-chart tells us whether there has been a
A) gain or loss in dispersion
B) change in the percent defective in a sample
C) change in the central tendency of the process output
D) change in the number of defects in a sample
E) none of the above

Accepted Answer

The p-chart is a control chart used to monitor the proportion of defective items in a sample. Therefore, it tells us whether there has been a change in the percent defective in a sample.

Question 2

Consumer's risk is the probability of
A) accepting a good lot
B) rejecting a good lot
C) rejecting a bad lot
D) accepting a bad lot
E) none of the above

Accepted Answer

Consumer's risk refers to the risk of accepting a bad lot, i.e. the risk that the consumer will accept a product that is actually defective or of poor quality.

Question 3

If $\overline { \bar { X } }$ = 23 ounces, ? = 0.4 ounces, and n = 16, the ±3? control limits will be
A) 21.8 to 24.2 ounces
B) 23 ounces
C) 22.70 to 23.30 ounces
D) 22.25 to 23.75 ounces
E) none of the above

Accepted Answer

The control limits are calculated as $\overline { \bar { X } } \pm 3 \times \frac{\sigma}{\sqrt{n}}$. Here, $\overline { \bar { X } } = 23$, $\sigma = 0.4$, and $n = 16$. So, the limits are $23 \pm 3 \times \frac{0.4}{\sqrt{16}} = 23 \pm 0.3$, which gives 22.70 to 23.30 ounces.

Question 4

The Central Limit Theorem
A) is the theoretical foundation of the c-chart
B) states that the average of assignable variations is zero
C) allows managers to use the normal distribution as the basis for building some control charts
D) states that the average range can be used as a proxy for the standard deviation
E) controls the steepness of an operating characteristic curve

Accepted Answer

The Central Limit Theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution. This allows managers to use the normal distribution as the basis for building some control charts. Therefore, choice C is the correct answer. The other choices are incorrect because A is referring to the theoretical foundation of the c-chart, B is referring to the concept of assignable variations, D is referring to the use of average range as a tool for estimating standard deviation, and E is referring to the control of the steepness of an operating characteristic curve, none of which are related to the Central Limit Theorem.

Question 5

Statistical process control charts
A) display the measurements on every item being produced
B) display upper and lower limits for process variables or attributes, and signal when a process is no longer in control
C) indicate to the process operator the average outgoing quality of each lot
D) indicate to the operator the true quality of material leaving the process
E) none of the above

Accepted Answer

Statistical process control charts display upper and lower limits for process variables or attributes, and signal when a process is no longer in control. They are used to monitor and control a process to ensure it remains within set parameters and to identify when the process is performing outside of those parameters. The charts do not display measurements on every item being produced, indicate the average outgoing quality, or show the true quality of material leaving the process.

Question 6

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?
A) Since there is no obvious pattern in the measurements, variability is in control.
B) One value outside the control limits is insufficient to warrant any action.
C) Lower than expected dispersion is a desirable condition; there is no reason to investigate.
D) The process is out of control; reject the last units produced.
E) Variation is not in control; investigate what created this condition.

Accepted Answer

When the most recent value is below the lower control limit, it indicates that there is a deviation from the expected level of variability. This suggests that the process is not in control and requires investigation to identify the source of the issue. Therefore, option E, "Variation is not in control; investigate what created this condition," is the best course of action.

Question 7

Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?
A) p-charts
B) c-charts
C) $\overline { \mathrm { X } }$ - and R-charts
D) $\overline { \mathrm { X } }$ -, but not R-charts
E) both p- and c-charts

Accepted Answer

$\overline { \mathrm { X } }$ - and R-charts are used for monitoring the mean and range of a process where the output is a continuous measurement, like the weight of jars of pickles, making them suitable for this scenario.

Question 8

The usual purpose of an R-chart is to signal whether there has been a
A) gain or loss in dispersion
B) change in the percent defective in a sample
C) change in the central tendency of the process output
D) change in the number of defects in a sample
E) none of the above

Accepted Answer

The R-chart is used to monitor the variability or dispersion of a process over time. It plots the range of the sample data over time and signals whether there has been a significant gain or loss in dispersion. Choices B, C, and D are not the usual purpose of an R-chart.

Question 9

The mean and standard deviation for a process for which we have a substantial history are ? µ = 120 and σ = 2. For the x-bar chart, a sample size of 16 will be used. What is the mean of the sampling distribution?
A) 1/8 (0.125)
B) 7.5
C) 2
D) 40
E) 120

Accepted Answer

The mean of the sampling distribution (also known as the central limit theorem) is equal to the mean of the population, which in this case is given as 120. Therefore, the answer is E. Choices A, B, C, and D are all incorrect as they do not accurately reflect the central limit theorem.

Question 10

The type of inspection that classifies items as being either good or defective is
A) variable inspection
B) attribute inspection
C) fixed inspection
D) all of the above
E) none of the above

Accepted Answer

Attribute inspection is used to classify items as being either good or defective based on a particular attribute, while variable inspection is used to measure a characteristic with a numerical value. Fixed inspection refers to a set inspection schedule, and thus does not relate to the type of inspection being performed. Therefore, only option B, attribute inspection, is the correct answer.

Question 11

Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for
A) Type I errors
B) about 95.5% variation
C) natural variation
D) all types of variation
E) assignable variation

Accepted Answer

The amount of variation allowed by statistical process control is referred to as natural variation, which refers to variation that is inherent to the process itself rather than caused by assignable factors. This variation typically falls within three standard deviations above or below the centerline of the control chart, representing approximately 99.7% of all data points. Therefore, the correct answer is C, natural variation.

Question 12

To set $\bar { X }$ -chart upper and lower control limits, one must know the process central line, which is the
A) average of the sample means
B) total number of defects in the population
C) percent defects in the population
D) size of the population
E) average range

Accepted Answer

The process central line on an $\bar { X }$ -chart, which is used in statistical process control to monitor the mean of a process, is determined by the average of the sample means. This provides a baseline from which to measure process variation.

Question 13

A manager wants to build 3-sigma control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, the UCL and LCL will be
A) -8 and 28
B) 16 and 4
C) 12 and 8
D) 4 and 16
E) 8 and 12

Accepted Answer

The 3-sigma control limits are calculated using the formula: mean ± 3*(standard deviation/sqrt(sample size)). Here, mean = 10, standard deviation = 6, and sample size = 9. So, the control limits are 10 ± 3*(6/sqrt(9)) = 10 ± 6 = 16 (UCL) and 4 (LCL).

Question 14

Which of the following is true of a p-chart?
A) The lower control limit is found by subtracting a fraction from the average number of defects.
B) The lower control limit indicates the minimum acceptable number of defects.
C) The lower control limit equals D₃ times p-bar.
D) The lower control limit may be at zero.
E) The lower control limit is the same as the lot tolerance percent defective.

Accepted Answer

The lower control limit (LCL) of a p-chart can be at zero if the calculated LCL is negative, as the number of defects cannot be negative.

Question 15

For an x-bar chart where the standard deviation is known, the Upper Control Limit
A) is 3 . ? below the mean of sample means for a 3? control chart
B) is 3 . ? above the mean of sample means for a 3? control chart
C) is 3 . ?/ $\sqrt { n }$ below the mean of sample means for a 3? control chart
D) is 3 . ?/ $\sqrt { n }$ above the mean of sample means for a 3? control chart
E) Cannot be calculated unless the average range is known.

Accepted Answer

The Upper Control Limit (UCL) for an x-bar chart, when the population standard deviation (σ) is known, is calculated as the mean of sample means plus 3 times the standard deviation of the sampling distribution of the mean, which is σ divided by the square root of the sample size (n). This is represented as UCL = mean + 3(σ/√n).

Question 16

According to the text, the most common choice of limits for control charts is usually
A) ± 1 standard deviation
B) ± 2 standard deviations
C) ± 3 standard deviations
D) ± 3 standard deviations for means and ± 2 standard deviations for ranges
E) none of the above

Accepted Answer

The most common choice of limits for control charts is ± 3 standard deviations. This is because it provides a good balance between detecting potential problems and avoiding false alarms. It allows for some natural variation in the process, while still flagging any points outside of the limits as potential issues to be investigated.

Question 17

A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1, the appropriate value of D₃ is 0, and D₄ is 2.115. The UCL and LCL for this range chart are
A) 33.9 and 11.2
B) 33.9 and 0
C) 11.2 and 0
D) 6.3 and 0
E) 31.91 and 0.11

Accepted Answer

The answer of A manager wishes to build a 3-sigma...

Question 18

Which of the following was Unisys Corp.'s failed quality measure in its management of Florida Health Care Services?
A) percentage of claims processed with errors
B) percentage of claims processed within 30 days
C) number of claims processed per month
D) number of claims denied
E) both A and B

Accepted Answer

Unisys Corp.'s failed quality measure in its management of Florida Health Care Services was both the percentage of claims processed with errors and the percentage of claims processed within 30 days.

Question 19

An x-bar control chart was examined and no data points fell outside of the limits. Can this process be considered in control?
A) No, there could be a pattern to the points.
B) No, the R-chart must be checked.
C) No, the number of samples must be known.
D) Yes
E) Both A and B

Accepted Answer

An x-bar control chart not having any data points outside the limits does not guarantee the process is in control. Patterns within the control limits, such as cycles or trends, can indicate a lack of control. Additionally, the R-chart, which monitors the process variability, must also be in control for the process to be considered in control.

Question 20

Ten samples of a process measuring the number of returns per 100 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of the sampling distribution. (Hint- Use p-bar formula)
A) There is not enough information.
B) .081
C) 8.1
D) .0273
E) .0863

Accepted Answer

The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size. In this case, the population standard deviation is not known, so we cannot calculate the standard deviation of the sampling distribution.

Quiz 7: Statistical Process Control

The p-chart tells us whether there has been a

Consumer's risk is the probability of

If Xˉ‾\overline { \bar { X } }Xˉ = 23 ounces, ? = 0.4 ounces, and n = 16, the ±3? control limits will be

The Central Limit Theorem

Statistical process control charts

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?

Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?

The usual purpose of an R-chart is to signal whether there has been a

The mean and standard deviation for a process for which we have a substantial history are ? µ = 120 and σ = 2. For the x-bar chart, a sample size of 16 will be used. What is the mean of the sampling distribution?

The type of inspection that classifies items as being either good or defective is

Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for

To set Xˉ\bar { X }Xˉ -chart upper and lower control limits, one must know the process central line, which is the

A manager wants to build 3-sigma control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, the UCL and LCL will be

Which of the following is true of a p-chart?

For an x-bar chart where the standard deviation is known, the Upper Control Limit

According to the text, the most common choice of limits for control charts is usually

A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1, the appropriate value of D₃ is 0, and D₄ is 2.115. The UCL and LCL for this range chart are

Which of the following was Unisys Corp.'s failed quality measure in its management of Florida Health Care Services?

An x-bar control chart was examined and no data points fell outside of the limits. Can this process be considered in control?

Ten samples of a process measuring the number of returns per 100 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of the sampling distribution. (Hint- Use p-bar formula)

If $\overline { \bar { X } }$ = 23 ounces, ? = 0.4 ounces, and n = 16, the ±3? control limits will be

To set $\bar { X }$ -chart upper and lower control limits, one must know the process central line, which is the