Question 1

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 0.02. If the desired confidence level is 99.7 percent, which of the following is the resulting UCL value for the line?

Accepted Answer

The UCL for a p-chart is calculated as p + z * σ, where p is the fraction defective (0.05), z is the z-value for the desired confidence level (3 for 99.7%), and σ is the standard deviation (0.02). Thus, UCL = 0.05 + 3 * 0.02 = 0.11.

Question 2

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?

Accepted Answer

The formula for Upper Control Limit (UCL) for X-bar chart is UCL = X-double bar + k * sigma/ sqrt(n), where
X-double bar = Average of sample means = 24
k = Number of standard deviations to use for the control limit calculation
sigma = Standard deviation of the sample means = 4
n = Sample size

For a 99.7% confidence level, we use k = 3. So,
UCL = 24 + 3 * (4/ sqrt(n))

We do not know the sample size (n) in this question. Therefore, we cannot find the exact value of UCL. However, we can say that UCL will be greater than 24, as the second term in the formula is positive. The only choice that is greater than 24 is A) 36. Hence, the answer is A.

Question 3

You have just used the capability index (Cpk) formulas to compute the two values "min [2, 2.5]." Which of the following is the proper interpretation of these numbers?

Accepted Answer

The minimum of the two calculated Cpk values is 2, indicating that the mean of the production process has shifted to the left of the design limits. This means that there is more variability in the process and a larger percentage of items produced will fall outside of the desired specifications.

Question 4

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 50, which of the following would be the standard deviation used in developing the control lines?

Accepted Answer

The formula for the standard deviation of a p-chart is:

σp = √(p(1-p)/n)

where:
- p is the weighted proportion of defectives (total number of defects divided by total number of opportunities for defects)
- n is the sample size

Using the given information, we can calculate p as:

p = 2500/5000 = 0.5

Substituting p and n into the formula, we get:

σp = √(0.5(1-0.5)/50) = √(0.25/50) = √0.005 = 0.0707

Therefore, the standard deviation used in developing the control lines is approximately 0.0707. The correct answer is D.

Question 5

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?

Accepted Answer

For a 99% confidence level, the Z-value used in control charts is typically 2.58, which corresponds to the standard normal distribution.

Question 6

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

Accepted Answer

The answer of For which of the following should we...

Question 7

You have just used the capability index (Cpk) formulas to compute the two values "min [1, 1]." Which of the following is the proper interpretation of these numbers?

Accepted Answer

The answer of You have just used the capability index...

Question 8

In monitoring process quality we might use which of the following statistics?

Accepted Answer

The answer of In monitoring process quality we might use...

Question 9

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

Accepted Answer

An R-chart is used to monitor the variation in the process over time. Student grades, which are measured on a continuous scale, would require an R-chart to monitor process quality. Option A, B, D, and E do not involve continuous data and are not suitable for R-charts.

Question 10

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?

Accepted Answer

The formula for the lower control limit for a p-chart is:
LCL = p̂ - 3√[p̂(1-p̂)/n]
where p̂ is the sample proportion, n is the sample size, and the 3 represents the number of standard deviations from the mean for a 99.7% confidence level (which corresponds to a z-score of 3).

Plugging in the given values, we get:
LCL = 0.006 - 3√[(0.006)(1-0.006)/50]
LCL ≈ 0.003

Therefore, the resulting LCL value for the p-chart is 0.003, which corresponds to choice C.

Question 11

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

Accepted Answer

An R-chart should be used to monitor process quality when the process output is a continuous variable and the sample size is constant. Tire pressures in an auto assembly plant meet these criteria and are therefore the best choice for an R-chart. None of the other options are continuous variables or have a constant sample size, so an R-chart is not appropriate for monitoring quality in those processes.

Question 12

Which of the following is the cost of quality classification for costs such as defects that pass through the system, such as customer warranty replacements, loss of customer or goodwill, handling complaints, and product repair?

Accepted Answer

External failure costs include costs that arise when defects are found after the product or service has been delivered to the customer. These can include customer warranty replacements, loss of customer or goodwill, handling complaints, and product repair.

Question 13

If there are 120 total defects from 10 samples, each sample consisting of 10 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?

Accepted Answer

The answer of If there are 120 total defects from...

Question 14

If there are 400 total defects from 8 samples, each sample consisting of 20 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?

Accepted Answer

The answer of If there are 400 total defects from...

Question 15

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

Accepted Answer

An X-bar chart based on sample means is used to monitor process quality of continuous variables. Tire pressures in an auto assembly plant are continuous variables and hence can be monitored using an X-bar chart.

Question 16

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

Accepted Answer

The answer of Quality control charts usually have a central...

Question 17

You have just used the capability index (Cpk) formulas to compute the two values "min [1.5, 1]." Which of the following is the interpretation of these numbers?

Accepted Answer

The answer of You have just used the capability index...

Question 18

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

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 19

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?

Accepted Answer

To find the standard deviation for a p-chart, we use the formula:
σp = √[(p(1-p))/n]
Where p is the proportion of defectives, and n is the sample size.
We can find p by dividing the total number of defects by the total number of observations:
p = 560/(70*80) = 0.1
Substituting the values into the formula, we get:
σp = √[(0.1*(1-0.1))/80] = 0.0335
Therefore, the answer is C: 0.0335.

Question 20

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?

Accepted Answer

The answer of Quality control charts usually have a central...

Quiz 10: Quality Management and Six Sigma

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?

You have just used the capability index (Cpk) formulas to compute the two values "min [2, 2.5]." Which of the following is the proper interpretation of these numbers?

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 50, 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 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 a p-chart to monitor process quality?

You have just used the capability index (Cpk) formulas to compute the two values "min [1, 1]." Which of the following is the proper interpretation of these numbers?

In monitoring process quality we might use which of the following statistics?

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

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

Which of the following is the cost of quality classification for costs such as defects that pass through the system, such as customer warranty replacements, loss of customer or goodwill, handling complaints, and product repair?

If there are 120 total defects from 10 samples, each sample consisting of 10 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?

If there are 400 total defects from 8 samples, each sample consisting of 20 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?

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

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

You have just used the capability index (Cpk) formulas to compute the two values "min [1.5, 1]." Which of the following is the interpretation of these numbers?

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

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?

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?