Question 1

The process capability index (Cpk) may mislead if:
(I) the process is not stable.
(II) the process output is not normally distributed.
(III) the process is not centered.
A) I and II
B) I and III
C) II and III
D) II only
E) I, II, and III

Accepted Answer

Cpk can be misleading if the process is not stable, not normally distributed, or not centered, as it assumes a stable, normal distribution and centered process for accurate capability assessment.

Question 2

A control chart used to monitor the number of defects per unit is the:
A) p-chart.
B) R-chart.
C) x-bar chart.
D) c-chart.
E) Gantt chart.

Accepted Answer

A c-chart, which stands for count chart, is the appropriate control chart for monitoring the number of defects per unit. The p-chart is used for proportion of defects, the R-chart is used for range or variation, the x-bar chart is used for monitoring the mean of continuous data, and the Gantt chart is used for project scheduling.

Question 3

Which of the following relationships must always be incorrect? A) Tolerances > process variability > control limits B) Process variability > tolerances > control limits C) Tolerances > control limits > process variability D) Process variability > control limits > tolerances E) Process variability < tolerances < control limits

Accepted Answer

Tolerances are the specifications given by the customer or design team which the product must fall within, while control limits are the statistical limits set by the process for acceptance of the product. Process variability is the amount of variation that occurs in the process. Tolerances should always be narrower than control limits, as meeting the tolerances also ensures that the product falls within the control limits. Therefore, the relationship in option C, where tolerances are greater than control limits, is always incorrect.

Question 4

A shift in the process mean for a measured characteristic would most likely be detected by a:
A) p-chart.
B) x-bar chart.
C) c-chart.
D) R-chart.
E) s-chart.

Accepted Answer

An x-bar chart is used to monitor the process mean of a measured characteristic, so a shift in the process mean would most likely be detected by an x-bar chart. The other charts listed are used for monitoring other aspects of a process such as the proportion of nonconforming items (p-chart), number of nonconformities per unit (c-chart), range of values in a sample (R-chart), or standard deviation of values in a sample (s-chart).

Question 5

Which of the following is not a step in the control process?
A) Define what is to be controlled.
B) Compare measurements to a standard.
C) 100 percent inspection.
D) Take corrective action if necessary.
E) Evaluate corrective action.

Accepted Answer

100 percent inspection is not always necessary or feasible in the control process. It is a technique used for certain types of processes or situations, but it is not always a step in the control process. The other four steps listed are essential for effective control.

Question 6

The purpose of control charts is to:
A) estimate the proportion of output that is acceptable.
B) weed out defective items.
C) determine if the output is within tolerances/specifications.
D) distinguish between random variation and assignable variation in the process.
E) provide meaningful work for quality inspectors.

Accepted Answer

The answer of The purpose of control charts is to:
A)...

Question 7

A plot below the lower control limit on the range chart:
(I) should be ignored since lower variation is desirable.
(II) may be an indication that process variation has decreased.
(III) should be investigated for assignable cause.
A) I and II
B) I and III
C) II and III
D) II only
E) I, II, and III

Accepted Answer

A plot below the lower control limit on the range chart indicates a decrease in process variation, which could be due to an assignable cause. It's not something to be ignored as it might signify an improvement or an issue that needs to be understood and possibly standardized.

Question 8

A time-ordered plot of sample statistics is called a(n) ______ chart.
A) statistical
B) inspection
C) control
D) simo
E) limit

Accepted Answer

A time-ordered plot of sample statistics is called a control chart. Control charts are used to monitor a process and ensure that it remains within certain quality control limits. They plot the sample statistics against time, and include control limits to help identify when a process is experiencing special cause variation.

Question 9

Consider the following information: $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Observations } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Num. of defects } & 10 & 18 & 13 & 15 & 9 & 12 \
\hline
\end{array}$$
The number of runs above and below the sample median is:
A) 3.
B) 4.
C) 5.
D) 6.
E) none of these.

Accepted Answer

The sample median is 12. The runs above the median are 18, 13, 15, and 12. The runs below the median are 10 and 9. So, the total number of runs is 4.

Question 10

If a process is performing as it should, it is still possible to obtain observations which are outside of which limits?
(I) tolerances
(II) control limits
(III) process variability
A) I
B) II
C) I and II
D) II and III
E) I, II, and III

Accepted Answer

The answer of If a process is performing as it...

Question 11

The range chart (R-chart) is most likely to detect a change in:
A) proportion.
B) mean.
C) number defective.
D) variability.
E) sample size.

Accepted Answer

The R-chart is used to monitor the variability of a process. It plots the range (difference between the highest and lowest values) of each subgroup of data. Therefore, it is most likely to detect a change in variability rather than other parameters such as proportion, mean, number defective, or sample size.

Question 12

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { c c c c c } 
\text { Sample } & { \text { Service Life (hours) } } \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}$$
What is the sample mean service life for sample 2?
A) 460 hours
B) 495 hours
C) 500 hours
D) 515 hours
E) 525 hours

Accepted Answer

In order to find the sample mean service life for sample 2, we need to calculate the mean of the sample.

Sample 2: (525 + 515 + 505 + 515)/4 = 515

Therefore, the sample mean service life for sample 2 is 515 hours.

The best choice is D.

Question 13

The traditional view is that the optimum level of inspection is where the:
A) cost of inspection is minimum.
B) cost of passing defectives is minimum.
C) total cost of inspection and defectives is maximum.
D) total cost of inspection and defectives is minimum.
E) difference between inspection and defectives costs is minimum.

Accepted Answer

The traditional view is that the optimum level of inspection is where the total cost of inspection and defectives is minimum. This means finding the level of inspection where the cost of inspecting (including the opportunity cost of lost production during inspection) and the cost of defectives (including the cost of scrap, rework, and customer returns) are balanced to minimize the total cost.

Question 14

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { c c c c c } 
\text { Sample } & & { \text { Service Life (hours) } } \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}$$
What is the mean of the sampling distribution of sample means when the service life is in control?
A) 250 hours
B) 470 hours
C) 495 hours
D) 500 hours
E) 515 hours

Accepted Answer

The mean of the sampling distribution of sample means can be calculated using the formula:

$\mu_{\bar{x}} = \mu = 500$

where $\mu_{\bar{x}}$ is the mean of the sampling distribution of sample means and $\mu$ is the population mean.

Therefore, the mean of the sampling distribution of sample means when the service life is in control is 500 hours. The correct choice is (D).

Question 15

The probability of concluding that assignable variation exists when only random variation is present is:
(I) the probability of a Type I error.
(II) known as the alpha risk.
(III) highly unlikely.
(IV) the sum of probabilities in the two tails of the normal distribution.
A) I and II
B) I and IV
C) II and III
D) I, II, and IV
E) I, III, and IV

Accepted Answer

The probability of concluding that assignable variation exists when only random variation is present is the probability of a Type I error (I) and is known as the alpha risk (II). It is also represented by the sum of probabilities in the two tails of the normal distribution (IV), which are the critical regions for rejecting the null hypothesis when it is actually true.

Question 16

The following data occurs chronologically from left to right: $$\begin{array} { | l | l | l | l | l | l | } 
\hline 15.2 & 19.7 & 16.0 & 11.1 & 14.8 & 14.5 \
\hline
\end{array}$$
The number of runs above and below the sample median is:
A) 2.
B) 3.
C) 4.
D) 5.
E) none of these.

Accepted Answer

To find the median, we must first put the numbers in order: $$11.1,14.5,14.8,15.2,16.0,19.7$$ Then, we find the middle number(s) (or the average of the two middle numbers), which in this case is 15.6. 
There are two numbers (11.1 and 14.5) below the median, and two numbers (19.7 and 16.0) above the median, so the answer is A) 2.

Question 17

A point which is outside of the lower control limit on an R-chart:
A) is an indication that no cause of variation is present.
B) should be ignored because it signifies better-than-average quality.
C) should be investigated because an assignable cause of variation might be present.
D) should be ignored unless another point is outside that limit.
E) is impossible since the lower limit is always zero.

Accepted Answer

A point which is outside of the lower control limit on an R-chart should be investigated because it suggests that an assignable cause of variation might be present, indicating a potential issue with the process that should be addressed. Ignoring such points could lead to further quality issues and potential defects.

Question 18

The following data occurs chronologically from left to right: $$\begin{array} { | l | l | l | l | l | l | } 
\hline 15.2 & 19.7 & 16.0 & 11.1 & 14.8 & 14.5 \
\hline
\end{array}$$
The number of runs up and down is:
A) 2.
B) 3.
C) 4.
D) 5.
E) none of these.

Accepted Answer

A run is a sequence of consecutive numbers that are either all increasing or all decreasing. The sequence has runs: 15.2 to 19.7 (up), 19.7 to 16.0 (down), 16.0 to 11.1 (down), 11.1 to 14.8 (up), and 14.8 to 14.5 (down), totaling 4 runs.

Question 19

_______ variation is a variation whose cause can be identified.
A) Assignable
B) Controllable
C) Random
D) Statistical
E) Theoretical

Accepted Answer

Assignable variation, also known as special cause variation, is a variation that can be traced back to a specific cause or source. This type of variation occurs outside the normal range of expected variation and can be controlled or eliminated by identifying and addressing the root cause. In contrast, random variation (C) is a result of ordinary fluctuations in a process and cannot be attributed to a specific cause. Controllable (B) and statistical (D) variations are not as accurate as assignable variation. Theoretical variation (E) is not a commonly used term in statistical process control.

Question 20

Consider the following information: $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Observations } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Num. of defects } & 10 & 18 & 13 & 15 & 9 & 12 \
\hline
\end{array}$$
The number of runs up and down for the preceding data is:
A) 3.
B) 4.
C) 5.
D) 6.
E) none of these.

Accepted Answer

A "run" is defined as a sequence of consecutive observations that are either all increasing or all decreasing. Looking at the data above, we can see that there are 5 runs:
- Runs up: 10, 18, and 13
- Runs down: 15, 9, and 12
Therefore, the answer is choice (C) 5.

Quiz 14: Quality Control

The process capability index (Cpk) may mislead if: (I) the process is not stable. (II) the process output is not normally distributed. (III) the process is not centered.

A control chart used to monitor the number of defects per unit is the:

Which of the following relationships must always be incorrect?

A shift in the process mean for a measured characteristic would most likely be detected by a:

Which of the following is not a step in the control process?

The purpose of control charts is to:

A plot below the lower control limit on the range chart: (I) should be ignored since lower variation is desirable. (II) may be an indication that process variation has decreased. (III) should be investigated for assignable cause.

A time-ordered plot of sample statistics is called a(n) ______ chart.

Consider the following information: $\begin{array} { | l | c | c | c | c | c | c | } \hline \text { Observations } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Num. of defects } & 10 & 18 & 13 & 15 & 9 & 12 \\\hline\end{array}$ The number of runs above and below the sample median is:

If a process is performing as it should, it is still possible to obtain observations which are outside of which limits? (I) tolerances (II) control limits (III) process variability

The range chart (R-chart) is most likely to detect a change in:

The traditional view is that the optimum level of inspection is where the:

The probability of concluding that assignable variation exists when only random variation is present is: (I) the probability of a Type I error. (II) known as the alpha risk. (III) highly unlikely. (IV) the sum of probabilities in the two tails of the normal distribution.

The following data occurs chronologically from left to right: $\begin{array} { | l | l | l | l | l | l | } \hline 15.2 & 19.7 & 16.0 & 11.1 & 14.8 & 14.5 \\\hline\end{array}$ The number of runs above and below the sample median is:

A point which is outside of the lower control limit on an R-chart:

The following data occurs chronologically from left to right: $\begin{array} { | l | l | l | l | l | l | } \hline 15.2 & 19.7 & 16.0 & 11.1 & 14.8 & 14.5 \\\hline\end{array}$ The number of runs up and down is:

_______ variation is a variation whose cause can be identified.

Consider the following information: $\begin{array} { | l | c | c | c | c | c | c | } \hline \text { Observations } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Num. of defects } & 10 & 18 & 13 & 15 & 9 & 12 \\\hline\end{array}$ The number of runs up and down for the preceding data is: