Question 1

You want to determine the control lines for a p-chart for quality control purposes. If the total number of defects from all samples is 560, the number of samples is 70, and the sample size is 80, which of the following would be the standard deviation used in developing the control lines?
A) 0.9000
B) 0.4556
C) 0.0335
D) 0.0011
E) 0.0112

Accepted Answer

The formula for calculating the standard deviation for a p-chart is sqrt(p*(1-p)/n), where p is the proportion of defects and n is the sample size.

First, we need to calculate the overall proportion of defects:
p = total defects / (total samples * sample size) 
p = 560 / (70 * 80) 
p = 0.1

Then, we can plug in p and n into the formula for standard deviation:
sqrt(0.1 * 0.9 / 80) = 0.0335

Therefore, the standard deviation used in developing the control lines is 0.0335, which is answer choice C.

Question 2

You want to determine the control lines for a p-chart for quality control purposes. If the total number of defects from all samples is 2,500, the number of samples is 100, and the sample size is 500, which of the following would be the standard deviation used in developing the control lines?
A) 0.4900
B) 0.2499
C) 0.0707
D) 0.000315
E) 0.000975

Accepted Answer

The answer of You want to determine the control lines...

Question 3

If there are 12 total defects from 10 samples, each sample consisting of 100 individual items in a production process, which of the following is the fraction defective that can be used in a p-chart for quality control purposes?
A) 12
B) 1.2
C) 0.12
D) 0.012
E) 0.0012

Accepted Answer

The fraction defective is calculated by dividing the total number of defects by the total number of items inspected. Here, 12 defects from 1000 items (10 samples of 100 each) results in a fraction defective of 12/1000 = 0.012.

Question 4

You want to develop a three-sigma R-chart. You know the average range is 5 based on several samples of size 10. Which of the following is the resulting UCL?
A) 20.9
B) 8.9
C) 7.02
D) 5
E) 3.1

Accepted Answer

For a three-sigma R-chart, the Upper Control Limit (UCL) is calculated using the formula UCL = D4 * R-bar, where R-bar is the average range (5 in this case) and D4 is a factor that depends on the sample size. For a sample size of 10, D4 is approximately 2.114. Therefore, UCL = 2.114 * 5 = 10.57, which rounds to approximately 10.6, but since this option is not available, the closest provided option is B) 8.9, indicating a possible mistake in the calculation or in the provided options.

Question 5

You are going to develop an R-chart based on range statistics, and you are using a sample size of 9 for your charting purposes. Which of the following is the lower control limit D₃ factor for the chart? A) 0.08 B) 0.14 C) 0.18 D) 0.22 E) 0.29

Accepted Answer

The D3 factor for a sample size of 9 is 0.18.

Question 6

You are going to develop an X-bar chart based on range statistics, and you are using a sample size of 12 for your charting purposes. Which of the following is the A₂ factor for the X-bar chart? A) 0.37 B) 0.31 C) 0.27 D) 0.22 E) 0.18

Accepted Answer

The answer of You are going to develop an X-bar...

Question 7

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is a reason that the process being monitored with the chart should be investigated?
A) A single point falls above or below the control limits.
B) Behavior is normal.
C) A large number of plots are on or near the central line.
D) There is no real trend in any direction.
E) There is a change in raw materials or operators.

Accepted Answer

A single point falling above or below the control limits indicates an abnormality in the process and should be investigated. The other options do not necessarily require investigation.

Question 8

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?
A) A large number of plots are close to the upper or lower control lines.
B) The behavior of the plots is erratic.
C) A single point falls above or below the control limits.
D) There is a change in raw materials or operators.
E) There is a run of five above the central line.

Accepted Answer

The need for investigation in the context of quality control charts is typically triggered by statistical signals indicating potential out-of-control conditions, such as points outside the control limits or unusual patterns within the control limits. A change in raw materials or operators, while important to note, does not inherently signal a process issue on the chart itself without corresponding statistical evidence.

Question 9

For which of the following should we use an R-chart to monitor process quality?
A) Grades in a freshman "pass/fail" course
B) Tire pressures in an auto assembly plant
C) Vehicles passing emissions inspection
D) Computer software errors
E) Number of units with missing operations

Accepted Answer

An R-chart is used to monitor the variability in a process over time. Tire pressures in an auto assembly plant can vary from one tire to another and from one vehicle to another, so an R-chart would be an appropriate tool to monitor the process and detect any patterns of variation.

Question 10

For which of the following should we use an R-chart to monitor process quality?
A) Weighing trucks at a highway inspection station to determine if they are overloaded
B) Deciding whether an airliner has sufficient fuel for its trip
C) Student grades measured from 1 to 100
D) Determining whether vehicles from a motor pool will run
E) Determining the accuracy of a forecast of "snow"

Accepted Answer

An R-chart is used to monitor the variability of a process, specifically the range of measurements. Since student grades can vary over a specific period, an R-chart can help identify any significant changes in grading variability.

Question 11

You are developing an X-bar chart based on sample means. You know the standard deviation of the sample means is 4, the desired confidence level is 99 percent, and the average of the sample means is 20. Which of the following is your LCL?
A) 36
B) 24
C) 9.68
D) 16.79
E) 30.32

Accepted Answer

To find the lower control limit (LCL) for an X-bar chart, we use the formula: 
LCL = X-double-bar - A2 * (sigma / sqrt(n)), where 
X-double-bar = average of the sample means (given as 20) 
A2 = a constant based on the sample size and desired confidence level (looked up from a table or calculated) 
sigma = standard deviation of the sample means (given as 4) 
n = sample size (not given, but assumed to be sufficient)

For a 99 percent confidence level and sample size of 25 or more, the A2 value is 2.78. Plugging in the values: 
LCL = 20 - 2.78 * (4 / sqrt(n))

Since sqrt(n) is not given, we cannot solve for the exact value of LCL. However, we can compare the answer choices to the equation and eliminate any that are clearly incorrect.

Eliminating A and E: 
A) LCL = 20 - 2.78 * (4 / sqrt(1)) = negative value, not possible 
E) LCL = 20 - 2.78 * (4 / sqrt(100)) = 17.68, too high

Eliminating B and D: 
B) LCL = 20 - 2.78 * (4 / sqrt(9)) = 15.12, too low 
D) LCL = 20 - 2.78 * (4 / sqrt(16)) = 18.84, too high

Therefore, the only answer choice that remains is C) LCL = 20 - 2.78 * (4 / sqrt(n)), which is the best choice for the lower control limit.

Question 12

You want to determine the upper control line for a p-chart for quality control purposes. You take several samples of a size of 100 items in your production process. From the samples, you determine the fraction defective is 0.05 and the standard deviation is 0.01. If the desired confidence level is 99.7 percent, which of the following is the resulting UCL value for the line?
A) 0.39
B) 0.08
C) 0.06
D) 0.05
E) None of these choices are correct.

Accepted Answer

The answer of You want to determine the upper control...

Question 13

You want to develop a three-sigma R-chart. You know the average range is 12 based on several samples of size 6. Which of the following is the resulting LCL?
A) 20.0
B) 18.3
C) 7.02
D) 5.6
E) 0.0

Accepted Answer

The LCL (Lower Control Limit) for an R-chart is calculated using the formula LCL = D3 * R-bar. For a sample size of 6, D3 is 0. Therefore, LCL = 0 * 12 = 0.0.

Question 14

For which of the following should we use a p-chart to monitor process quality?
A) The dimensions of brick entering a kiln
B) Lengths of boards cut in a mill
C) The weight of fluid in a container
D) Grades in a freshman "pass/fail" course
E) Temperatures in a classroom

Accepted Answer

A p-chart is used for monitoring the proportion of defective items in a process where the output is classified into two categories: "pass" or "fail", "defective" or "non-defective". Among the options, only the grades in a freshman "pass/fail" course fit this description, as they are explicitly categorized into two groups: pass or fail.

Question 15

For which of the following should we use a p-chart to monitor process quality?
A) Defective electrical switches
B) Errors in the length of a pencil
C) Weight errors in cans of soup
D) Temperature of entrees in a restaurant
E) Letter grades on a final examination

Accepted Answer

A p-chart is used to monitor the proportion of defective items in a process, which applies to defective electrical switches.

Question 16

You are developing an X-bar chart based on sample means. You know the standard deviation of the sample means is 4, the desired confidence level is 99.7 percent, and the average of the sample means is 24. Which of the following is your UCL?
A) 36
B) 24
C) 12
D) 4
E) None of these choices are correct.

Accepted Answer

The UCL (Upper Control Limit) for an X-bar chart is calculated as the average of the sample means plus the product of the standard deviation of the sample means and the Z-score for the desired confidence level. For 99.7% confidence, the Z-score is 3. Therefore, UCL = 24 + (3 * 4) = 36.

Question 17

If there are 40 total defects from 8 samples, each sample consisting of 200 individual items in a production process, which of the following is the fraction defective that can be used in a p-chart for quality control purposes?
A) 2.5
B) 0.25
C) 0.025
D) 0.0025
E) 0.00025

Accepted Answer

To find the fraction defective, we need to divide the total number of defects (40) by the total number of items produced (8 samples x 200 items per sample = 1600 items). This gives us 40/1600 = 0.025, which is equivalent to choice C.

Question 18

You want to determine the control lines for a p-chart for quality control purposes. If the desired confidence level is 99 percent, which of the following values for "z" would you use in computing the UCL and LCL?
A) 0.99
B) 2
C) 2.58
D) 3
E) None of these choices are correct.

Accepted Answer

To determine the control lines for a p-chart with a 99% confidence level, we need to use a z-value that corresponds to the 99.5th percentile of the standard normal distribution (since we need to divide the alpha level of 0.01 equally between the two tails of the distribution). This value is 2.58. Therefore, we would use a value of 2.58 in computing the UCL and LCL.

Question 19

You want to determine the lower control line for a p-chart for quality control purposes. You take several samples of a size of 50 items in your production process. From the samples, you determine the fraction defective is 0.006 and the standard deviation is 0.001. If the desired confidence level is 99.7 percent, which of the following is the resulting LCL value for the line?
A) 0.0
B) 0.002
C) 0.003
D) 0.004
E) None of these choices are correct.

Accepted Answer

The formula to calculate the lower control limit (LCL) for a p-chart is:

LCL = p̂ - 3√((p̂(1-p̂))/n)

where p̂ is the proportion defective in the sample, n is the sample size, and 3 represents the number of standard deviations from the mean for a 99.7% confidence level (which corresponds to a z-score of 3).

Substituting the given values into the formula, we get:

LCL = 0.006 - 3√((0.006(1-0.006))/50)
LCL = 0.006 - 3(0.0356)
LCL = 0.006 - 0.107
LCL = 0.003

Therefore, the resulting LCL value for the line is 0.003, which is choice C.

Question 20

For which of the following should we use an X-bar chart based on sample means to monitor process quality?
A) Grades in a freshman "pass/fail" course
B) Tire pressures in an auto assembly plant
C) Vehicles passing emissions inspection
D) Computer software errors
E) Number of units with missing operations

Accepted Answer

An X-bar chart based on sample means is appropriate for continuously measured variables, such as tire pressures in an auto assembly plant. It is not appropriate for discrete data, such as pass/fail grades, or count data, such as number of units with missing operations. It is also not appropriate for categorical data, such as vehicles passing emissions inspection. Computer software errors can be counted, but an individuals chart may be more appropriate for monitoring the process.

Quiz 13: Statistical Quality Control

You want to determine the control lines for a p-chart for quality control purposes. If the total number of defects from all samples is 560, the number of samples is 70, and the sample size is 80, which of the following would be the standard deviation used in developing the control lines?

You want to determine the control lines for a p-chart for quality control purposes. If the total number of defects from all samples is 2,500, the number of samples is 100, and the sample size is 500, which of the following would be the standard deviation used in developing the control lines?

If there are 12 total defects from 10 samples, each sample consisting of 100 individual items in a production process, which of the following is the fraction defective that can be used in a p-chart for quality control purposes?

You want to develop a three-sigma R-chart. You know the average range is 5 based on several samples of size 10. Which of the following is the resulting UCL?

You are going to develop an R-chart based on range statistics, and you are using a sample size of 9 for your charting purposes. Which of the following is the lower control limit D3 factor for the chart?

You are going to develop an X-bar chart based on range statistics, and you are using a sample size of 12 for your charting purposes. Which of the following is the A2 factor for the X-bar chart?

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is a reason that the process being monitored with the chart should be investigated?

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?

For which of the following should we use an R-chart to monitor process quality?

For which of the following should we use an R-chart to monitor process quality?

You are developing an X-bar chart based on sample means. You know the standard deviation of the sample means is 4, the desired confidence level is 99 percent, and the average of the sample means is 20. Which of the following is your LCL?

You want to develop a three-sigma R-chart. You know the average range is 12 based on several samples of size 6. Which of the following is the resulting LCL?

For which of the following should we use a p-chart to monitor process quality?

For which of the following should we use a p-chart to monitor process quality?

You are developing an X-bar chart based on sample means. You know the standard deviation of the sample means is 4, the desired confidence level is 99.7 percent, and the average of the sample means is 24. Which of the following is your UCL?

If there are 40 total defects from 8 samples, each sample consisting of 200 individual items in a production process, which of the following is the fraction defective that can be used in a p-chart for quality control purposes?

You want to determine the control lines for a p-chart for quality control purposes. If the desired confidence level is 99 percent, which of the following values for "z" would you use in computing the UCL and LCL?

For which of the following should we use an X-bar chart based on sample means to monitor process quality?

You are going to develop an R-chart based on range statistics, and you are using a sample size of 9 for your charting purposes. Which of the following is the lower control limit D₃ factor for the chart?

You are going to develop an X-bar chart based on range statistics, and you are using a sample size of 12 for your charting purposes. Which of the following is the A₂ factor for the X-bar chart?