Question 1

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 allows managers to use the normal distribution as the basis for building some control charts. The c-chart (A) is based on counts or frequencies and does not rely on the Central Limit Theorem. Statement (B) is incorrect because the Central Limit Theorem does not address assignable variations. Statement (D) is incorrect because the average range is only used as a proxy for the standard deviation in certain situations, and the Central Limit Theorem is not necessary for this calculation. Statement (E) is incorrect because the Central Limit Theorem does not control the steepness of an operating characteristic curve.

Question 2

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 the type of inspection that classifies items as being either good or defective. Variable inspection involves measuring some characteristic of the item on a continuous scale. Fixed inspection involves inspecting a set number of items or a specific portion of a production run. Therefore, the correct answer is B, attribute inspection.

Question 3

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)± 1 standard deviations for means and ± 2 standard deviations for ranges.

Accepted Answer

The most common choice of limits for control charts is ± 3 standard deviations. This is known as the three sigma limits and includes approximately 99.7% of the data within the limits. It is a good balance between detecting variability in the process and avoiding false alarms. Limit choices of ± 1 standard deviation or ± 2 standard deviations are too strict and may not detect important process shifts, while limits of ± 3 standard deviations for means and ± 2 standard deviations for ranges are too complex and not necessary for most applications.

Question 4

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 used to monitor the proportion of defective items in a sample. It helps in detecting if there is any change in the percentage of defective items from the expected value, indicating a change in the process. It does not provide information about dispersion or central tendency of the process output or the number of defects in a sample.

Question 5

Which of the following is true about cutting costs at Canada Bankers Life Assurance Company?
A)They outsourced their call centre.
B)Customer satisfaction increased.
C)Customer service improved.
D)Quality metrics showed improvements.
E)Wastage decreased.

Accepted Answer

The passage mentions that one way Canada Bankers Life Assurance Company cut costs was by outsourcing their call centre. No other choices are mentioned in the passage.

Question 6

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)shipping a bad lot.

Accepted Answer

Consumer's risk refers to the probability of accepting a bad lot or faulty product. This means that the consumer takes the risk of accepting a product that may not meet their expectations or may have defects or other issues.

Question 7

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 8

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 of x-bar is equal to the population mean. Therefore, the mean of the sampling distribution in this case is 120.

Question 9

To set  -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, also known as the process mean, is determined by calculating the average of the sample means. The upper and lower control limits are then set based on the variability of the process data around this central line. The other options, such as total number of defects, percent defects, size of population, and average range, are not directly relevant to setting control limits.

Question 10

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

This is known as the "3-sigma rule" and pertains to natural variation in a process. It means that about 99.7% of all data should fall within three standard deviations of the centerline. Type I errors, assignable variation, and all types of variation are not applicable to this concept. The 95.5% variation is incorrect as it does not accurately describe the 3-sigma rule.

Question 11

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)display the measurements on every item being purchased.

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 improve process quality, by indicating when a process is falling out of control and needs attention to prevent defects or errors. The other choices, such as displaying measurements on every item being produced, indicating the average outgoing quality of each lot, or displaying the measurements on every item being purchased, are not accurate descriptions of the purpose or function of statistical process control charts.

Question 12

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

Accepted Answer

The answer of For an x-bar chart where the standard...

Question 13

If  = 23 ounces,σ = 0.4 ounces,and n = 16,the ±3σ 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)23.3 to 25.7 ounces.

Accepted Answer

The ±3σ control limits can be calculated as follows:
Upper control limit = 23 + (3 x 0.4) = 23.2
Lower control limit = 23 - (3 x 0.4) = 22.8
Therefore, the ±3σ control limits will be 22.8 to 23.2 ounces, which is closest to option C) 22.70 to 23.30 ounces.

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 answer of Which of the following is true of...

Question 15

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)change in sample size.

Accepted Answer

An R-chart, or Range chart, is used to monitor the variability or dispersion of a process over time. It plots the range of the subgroup data and if there is a significant increase or decrease in range, it signals a change in dispersion. Therefore, the correct answer is A) gain or loss in dispersion.

Question 16

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,the R-chart must be checked.
B)Yes,it is unlikely that there is a pattern in these points.
C)No,the number of samples must be known.
D)Yes.
E)Yes,there is not enough data to determine otherwise.

Accepted Answer

An x-bar control chart showing no data points outside the limits does not guarantee the process is in control. Patterns within the control limits or issues in the range (R-chart) could indicate a lack of control.

Question 17

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)  - and R-charts
D)  -,but not R-charts
E)both p- and c-charts

Accepted Answer

The answer of Jars of pickles are sampled and weighed.Sample...

Question 18

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 in the text,the appropriate value of  is 0,and  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 19

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 answer of Ten samples of a process measuring the...

Question 20

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

A value falling below the lower control limit indicates that the process is out of control and there is variation that needs to be investigated. Therefore, option E is the best choice. The other options suggest that the process is in control or that there is no need to investigate further, which is not the case when a point falls outside the control limits.

Quiz 18: Statistical Process Control

The Central Limit Theorem

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

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

The p-chart tells us whether there has been a

Which of the following is true about cutting costs at Canada Bankers Life Assurance Company?

Consumer's risk is the probability of

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

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?

To set -chart upper and lower control limits,one must know the process central line,which is the

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

Statistical process control charts

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

If = 23 ounces,σ = 0.4 ounces,and n = 16,the ±3σ control limits will be

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

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

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

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 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 in the text,the appropriate value of is 0,and is 2.115.The UCL and LCL for this range chart are

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)

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