SIX SIGMA CONTROL - Online Project Management Nigeria · Why are variable control chart subgroup sizes ... separation of within time from time to time variation A. II and ... fact

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SIX SIGMA – CONTROL

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1. An X and R chart was prepared for an operation using twenty samples with five

pieces in each sample; X was found to be 33.6 and R was 6.20. During

production, a sample of five was taken and the pieces measured 36, 43, 37, 25,

and 38. At the time, this sample was taken:

A. Both the average and range were within control limits

B. Neither the average nor range were within control limits

C. Only the average was outside control limits

D. Only the range was outside control limits

Correct Answer: D

Justification: This question requires a calculation of the X and R control limits and a

comparison to the sample data and answers.

Equations:

Solution:

For the sample data:

X = 35.8, R = 18. Thus, the X chart is in control but the R chart is not.

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2. Which of the following control charts are most sensitive to small but gradual drifts

in process?

I. X – R charts

II. CuSum charts


III. EWMA charts

IV. Moving average charts

A. I and II only

B. I and III only

C. II and III only

D. III and IV only

Correct Answer: C

Justification: Both CUSUM and exponentially weighted moving average charts can

detect small sustained changes in a process.

If continued for some time, these small changes will be apparent on which of the

following control charts are most sensitive to small but gradual drifts in process?

If continued for some time, these small changes will be apparent on X – R charts and

moving averages as well. However, the word “most” in the question prevents their

selection.

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3. What does the parameter λ stand for when plotting a EWMA chart?

A. The variance

B. The depth of memory

C. The time that a sample is taken

D. The number of observations to be monitored

Correct Answer: B

Justification: This is a straight knowledge question. λ is a weighting factor which

determines the rate at which older data is included into the EWMA statistic. λ is a

reflection of the depth of memory of the EWMA chart.

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4. A process is checked by inspection of random samples of four shafts after a

polishing operation, and X and R charts are maintained. A person making a spot

check picks out two shafts, measures them accurately, and plots the value of


each on the chart. Both points fall just outside the control limits. He advises the

department foreman to stop the process. This decision indicates that:

A. The process level is out of control

B. Both the level and dispersion are out of control

C. The process level is out of control but not the dispersion

D. The person is not using the chart correctly

Correct Answer: D

Justification: This question requires a basic understanding of the use of an X – R chart

and a review of the answers. No estimation of process dispersion can be made from the

facts in this question. The X chart was based on a sample size of four shafts. If an

individual reading is plotted, then an erroneous decision could easily be made. The

person is using the chart incorrectly.

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5. The factor D4 in X bar and R control charts is used to:

A. Determine the upper control limit of a range chart

B. Establish the control limits for the average chart

C. Correct the bias in estimating the population

D. Determine the lower control limit of a range chart

Correct Answer: A

Justification: This question requires knowledge of control chart limits and a review of

the answers.

UCLR = D4R

Answers B and C are filler. The D4 factor is a multiplier which establishes the distance

between the mean and the upper control limit of a range chart.

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6. Pre-control starts a process specifically centered between:

A. Process limits

B. Specification limits


C. Normal distribution limits

D. Three-sigma control limits

Correct Answer: B

Justification: Pre-control starts a stable process specifically centered between

specification limits. From earlier capability studies, it has been determined that the

normal distribution will be at or inside the specification limits.

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7. An operator takes a routine sample using the pre-control method and notes that

the first piece is within specifications but not within target. What does the

operator do next?

A. Stops the process and adjusts it

B. Checks a second sample

C. Confirms that the next 5 consecutive pieces are within target

D. Continues to run

Correct Answer: B

Justification: While running a process an operator samples 2 consecutive pieces. If the

first is within target, the second piece is not checked. If the first piece is not within

target, the second piece is checked in order to make a run or adjust decision.

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8. Certain Six Sigma improvement efforts have resulted in the need to replace the

existing measurement system and others have not. What could be reasons for

staying with an existing system?

I. It’s precise enough

II. No better equipment exists

III. The current measurement is based on count data

IV. The improvement has not been successful

A. I only

B. II and III only

C. I, II and IV only


D. I, II, III and IV

Correct Answer: D

Justification: Not all improvement is based on variable measurements. Attribute data

may be used. Sometimes there are low tech ways of checking high tech improvements.

In most cases, improvement in products and processes require that the measurement

system be re-analyzed. However, all item choices are valid reasons for staying with an

existing system.

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9. The control chart that is most sensitive to variations in a measurement is:

A. p chart

B. np chart

C. c chart

D. X bar and R chart

Correct Answer: D

Justification: The p chart is the most sensitive attribute chart but the variable X bar – R

chart is the most sensitive control chart.

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10. Why are variable control chart subgroup sizes general 3, 4, 5 or 6?

I. Larger subgroup sizes would permit an opportunity for process changes

with the subgroup

II. They fit onto traditional chart paper very well

III. They are large enough so that averages of data will follow the normal

distribution

IV. They permit a separation of within time from time to time variation

A. II and III only

B. I and II only

C. I, III and IV only



Correct Answer: C

Justification: The weakest selection is item III. Control chart paper was developed to

support a logical control chart sample size. Sample sizes should not be chosen to fit a

handy form. The other items have merit.

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11. You have just returned from a two-week vacation and are going over with your

QC manager, the control charts which have been maintained during your

absence. He calls your attention to the fact that one of the X bar-charts shows

the last 50 points to be very near the center line. In fact, they all seem to be

within about one sigma of the center line. What explanation would you offer him?

A. Somebody “goofed” in the original calculation of the control limits.

B. The process standard deviation has decreased during the time the last 50

samples were taken and nobody thought to recompute the control limits.

C. This is a terrible situation. I’ll get on it right away and see what the trouble is. I

hope we haven’t produced too much scrap.

D. This is fine, the closer the points are to the center line the better our control.

Correct Answer: B

Justification: Answer C is obviously incorrect. If the X bar (average) was sellable

before your vacation, it will be sellable now. Implied in the question is the fact that the

charts has been maintained for some time and that other charts have been plotted.

Thus, answer A appears to be a weak choice. Answer D may be correct, in part, if the

average is at the desired location. Since 50 samples are involved, the control limits

should have been recalculated to reflect a reduced range (and standard deviation).

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12. The most common subgrouping scheme for X – R control charts is to separate

the variation:

A. Within stream versus stream to stream

B. Within time versus time to time

C. Within piece versus piece to piece

D. Inherent process versus error of measurement

Correct Answer: B


Justification: A multitude of techniques such as stratified studies, error of

measurement and multi-vari charts can be used to segment all of the answer choices.

However, X – R charts generally compare within time to over time variation.

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13. The sensitivity of a p-chart to changes in quality is:

A. Equal to that of a range chart

B. Equal to that of a chart for averages

C. Less than that of a c chart

D. Greater than that of a u chart

Correct Answer: D

Justification: The X-bar and R chart (Average – Range Chart) is the most sensitive to

changes in quality. Thus, answers A and B are false. The most sensitive attribute chart

is the p chart. Thus, answer C is false and D is true.

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14. Considering that all of the following terms have benefits, which would LEAST

likely affect product quality?

A. Muda

B. 5S

C. Lean Manufacturing

D. Total Productive Maintenance

Correct Answer: C

Justification: The elimination of unnecessary storage, transport and handling makes

Muda a positive influence on quality. The same can be said for 5S because of the

organizational controls on the system. TPM minimizes start-ups and shutdown which

create scrap.

The lean manufacturing approach also helps quality (less handling, etc.) but it would

tend to affect items like delivery more.

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15. Which of the following Japanese techniques is most clearly identified with small

incremental change?

A. Kaizen

B. Kanban

C. Poka-yoke

D. 5S strategy

Correct Answer: A

Justification: The term Kaizen is associated with small incremental changes. Although

a “Kaizen blast” can speed things up a great deal. Kanban is a process flow control

mechanism, 5S deals with workplace organization, and Poka-yoke means to mistake

proof a process.

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16. Review the following 5S elements and identify the step that is being referenced.

Determine who has missing items

Create a name and location for everything

Use aisle and material placement markings

Use labels, tool boards and color codes

A. Sort

B. Straighten

C. Scrub

D. Systematize

Correct Answer: B

Justification: The only two logical elements (or steps) are straighten and systematize.

A close review of the statements indicates that the straighten step is being described.

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17. Given that resistors are produced in lots of 1000, and that the average number of

defective resistors per lot is 12.7, what are the upper and lower limits for the

control chart appropriate for this process?

A. LCL = 2.0 UCL = 23.4

B. LCL = 3.8 UCL = 20.2


C. LCL = 0.031 UCL = 0.131

D. LCL = 1.5 UCL = 26.7

Correct Answer: A

Justification: When the sample size is constant, a c (count of non-conformances) chart

is appropriate for attributes data (good or bad). The control limits for a c chart are based

on the average number of non-conformances (c bar). The control limits are calculated

using the expression:

LCL, UCL = C ± 3√C

For this problem the limits are:

LCL = 12.7 - 3(3.56) = 2.0

UCL = 12.7 + 3(3.56) = 23.4

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18. If points on a c chart are outside of the control limits and we wish to set up a

control chart for future production:

A. More data are needed

B. Discard those points falling outside the control limits, for which you can

identify an assignable cause, and revise the limits

C. Check with production to determine the true process capability

D. Discard those points falling outside the control limits and revise the limits

Correct Answer: B

Justification: Answer A: normally twenty five data points are sufficient to establish c-

chart control limits. Answer C: production may not know the true process capability.

Answer D: we cannot discard points outside the control limits if the reason is unknown.

They may recur. Answer B is the correct option.

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19. Control limits are set at the three-sigma level because:

A. This level makes it difficult for the output to get out of control

B. This level establishes tight limits for the production process


C. This level reduces the probability of looking for trouble in the production

process when none exists

D. This level assures a very small type II error

Correct Answer: C

Justification: Answer A is incorrect because the control limits come from the process

data itself. Assuming that assignable causes do not occur, the control limits are not

“tight”. This level assures a very small type I error (calling the process out of control

when it is in control).

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20. What two distinct types of variation are noted in control charts?

A. Random and chance

B. Special and assignable

C. Chance and assignable

D. Normal and random

Correct Answer: C

Justification: The two varieties of variation are chance and assignable. Chance

variation is also referred to as normal or random (among others). Assignable variation is

also called special or non-normal.

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21. A process is checked at random by inspection of samples of four shafts after a

polishing operation, and X bar and R charts are maintained. A person making a

spot check measures two shafts accurately, and plots their range on the R chart.

The point falls just outside the control limit. He advises the department foreman

to stop the process. This decision indicates that:

A. The process level is out of control

B. The process level is out of control but not the dispersion

C. The person is misusing the chart

D. The process dispersion is out of control

Correct Answer: D


Justification: No estimation can be made of the process average. Thus, answers A

and C are eliminated. It’s true that the person is not using the chart correctly but, if two

samples exceed the upper control limit on the range chart, taking two more samples will

not make the results better. The process dispersion is out of control.

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22. Identify the LEAST likely result of adopting standardized work procedures:

A. They tend to minimize variability

B. They are a basis for training

C. They assure marketplace success

D. They preserve know-how and expertise

Correct Answer: C

Justification: Note that a negative response is requested. Standardized procedures

can help with the consistency of a process but they do not assure marketplace success.

Many other factors like technology, customer preference, marketing strategies, etc.

affect consumer preference.

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23. When using a control chart, a point plotting within the limits on the chart is:

A. The equivalent of type I error

B. The equivalent of type II error

C. The equivalent of accepting the hypothesis that the process is in control

D. The equivalent of not rejecting the hypothesis that the process is in control

Correct Answer: D

Justification: If the points on a control chart fall within the limits, and do not form a non-

random pattern, the process is assumed to be in a state of statistical control. The null

hypothesis is never accepted, rather, there is not sufficient evidence to reject it. A plot

within limits is neither a type I nor type II error.

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24. In control chart theory, the distribution of the number of defects per unit follows

very closely the:

A. Normal distribution


B. Binomial distribution

C. Chi-square distribution

D. Poisson distribution

Correct Answer: D

Justification: The normal distribution relates to variable (not attribute) data. The chi-

square distribution is used to make inferences regarding population variances. The

binomial distribution is the assumed distribution for defectives. The Poisson distribution

is the assumed distribution for defects.

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25. You are plotting a control chart and the last two of three points are greater than 2

sigma, four out of the last five points are beyond 1 sigma and eight successive

points are on one side of the center line; you should:

A. Stop the process immediately

B. Take more readings and continue to plot

C. Write a discrepancy notice to the supervisor

D. Investigate to determine what has changed

Correct Answer: D

Justification: Using any set of interpretation rules, there has been a significant change

in the process. If an X-bar chart or attribute chart is being plotted, there is evidence of a

shift, trend or drift in the process. If an R chart is being charted, the variability has

changed significantly.

Answers B and C are extremely weak responses. Answer A might be appropriate

depending upon your authority and the critical nature of the process. Answer D is

appropriate and required in this case.

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26. Overproduction, scrap, waiting, and excess motion are all forms of:

A. TPM

B. Muda

C. Kanban

D. CFM


Correct Answer: B

Justification: The question states four of the major seven forms of Muda (waste).

Kanban, total productive maintenance, and continuous flow manufacturing have some

influence on waste areas but do not directly address them all.

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27. A number of charts have been devised to plot and control small production runs.

Which charting tool can display a number of variables on a single chart?

A. Short run charts

B. Individual/ moving range charts

C. Moving average/moving range charts

D. Pre-control charts

Correct Answer: A

Justification: Answer D is a distractor. Although multi-vari charts might be a good

choice, it’s not listed as an answer option. A number of short run charts can be adapted

to show high and low values for a number of variables on a single chart.

Individual/moving range and moving average/moving range charts would be very messy

if they showed multiply variables on the same chart.

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28. Compute the upper control limit for an S chart, based on a sample size of 10, if

the process is in control with a mean of 40 and a sample standard deviation of 7.

A. 12.0

B. 13.3

C. 15.7

D. 21.0

Correct Answer: A

Justification: The upper control limit for an S chart can be approximated by:

UCLS = B4 (S) B4 for n = 10 = 1.72

UCLS = (1.7) (7)

UCLS = 12.04


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29. Which of the following techniques does NOT necessarily compliment the visual

factory concept?

A. Kanban

B. Tool boards

C. 5S

D. Poka-yoke

Correct Answer: D

Justification: Poka-yoke is mistake proofing and is not necessarily a visual factory

concept. However, some visual factory concepts do compliment and assist Poka-yoke.

Choices A, B and C are visual factory concepts.

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30. The tool/technique most widely used by a number of automotive manufactures

that supply products to Toyota is called:

A. Kanban

B. Muda

C. Poka-yoke

D. An Andon board

Correct Answer: A

Justification: The question is describing the kanban system of signals and control.

Muda (waste) and Poka-yoke (mistake proofing) are out of step with the question. The

Andon board is a lighted overhead display showing current status and problems. This is

a subset of the visual factory (relatively minor).

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31. If two-sigma limits are substituted for conventional three-sigma limits on a control

chart, which of the following occurs?

A. Decrease in alpha risk

B. Increase in beta risk

C. Increase in alpha risk

D. Increase in sample size


Correct Answer: C

Justification: A type I or alpha risk is to reject a true hypothesis. In this case, we are

substituting 2.0 sigma boundaries for 3.0 sigma boundaries. There is an increased

probability of rejecting (or acting on) normal variation and calling it abnormal. There is

an increased alpha risk.

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32. There are several different varieties of median control charts. If median values

and ranges are plotted, what would be expected to be different than experienced

with an X bar – R chart for the sample size? Assume that control limits are used.

A. The middle value would be circled on the median chart

B. The range chart would have different control limits

C. The median control limits would be wider apart

D. The lower limit on the range chart could not be zero

Correct Answer: C

Justification: The median value might be circled in the data but would not be circled on

the median chart (with this type of chart). The range chart would be identical to an X Bar

– R chart of the same sample size (eliminates answers B and D). The control limit

factors for the median chart are slightly larger than for a traditional X bar charts, making

the control limits wider.

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33. A process is in control at X = 100, R = 7.3 with n = 4. If the process level shifts to

101.5, with the same range, what is the probability that the next X point will fall

outside the old control limits:

A. 0.016

B. 0.029

C. 0.122

D. 0.360

Correct Answer: A

Justification: This question requires the calculation of the upper control limit, the

treatment of this control limit as a specification limit, the determination of an upper Z

value and thus the projected failure rate after the process shifts.


Equations:

Where,

SX = standard deviation for the control chart

3SX for the control chart = A2R = 5.33. Thus, SX = 1.78.

The following drawing will help with the Z value failure rate calculation. Note the UCL

becomes an USL.

Under the normal curve,

The failure rate is 0.0158.

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34. A short run means chart, as suggested by Bothe, requires which of the following

conditions?

I. That mean values be converted into Z values

II. That no traditional interpretation rules apply

III. That the control limits be ± A2

A. I only

B. II and III only

C. I and III only

D. I, II and III

Correct Answer: C

Justification: Using some math magic, Bothe converts data into Z values and the

control limits into ± A2. With this plotting arrangement, traditional control chart

interpretation rules apply.

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35. An investigation of the total product or process variability indicates that the single

largest element is quite often:

A. Dependent on the process itself

B. The error of measurement

C. Time to time variation

D. Stream to stream variation

Correct Answer: A

Justification: For any given process or product, answers B, C and D could all be true.

Additionally, a lot to lot or piece to piece variation could be the major culprit. All of this

logic makes answer A the best choice.

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36. If a value of one is used for λ in a EWMA chart, what will be the outcome?

A. The chart becomes meaningless

B. Only older data would be considered

C. The variance of the EWMA statistic cannot be calculated


D. The plot becomes a Shewhart chart

Correct Answer: D

Justification: λ is normally set between 0.2 and 0.3. The actual value is somewhat

arbitrary. If a value of 1.0 is selected, then only most recent measurements influences

the EWMA. That is, the plot degrades to a Shewhart chart.

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37. Which control chart is normally used when monitoring the number of

nonconformities per unit?

A. c chart

B. X bar chart

C. np chart

D. u chart

Correct Answer: D

Justification: The u chart is used to monitor the number of nonconformities per unit.

This is also considered the average number of defects/unit. There is nothing in the

question that states that the sample size is fixed.

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38. Which of the following charts does NOT require the averaging of variable data?

A. Moving average chart

B. X bar – R chart

C. mX – mR chart

D. Multi-vari chart

Correct Answer: D

Justification: Note that this question is asking for a negative response. The multi-vari

chart plots non-averaged individual values.

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39. If the specification limits are narrower than the control limits, then:

I. The process is not capable


II. The process is considered to be out of control if a point falls beyond the

specification limits

III. The specification limits replace the control limits on the chart

A. I only

B. I and II only

C. II and III only

D. I, II and III

Correct Answer: A

Justification: If the specification limits are narrower than the control limits, then the

process is not capable. As a rule of thumb, the process capability, Cp should be at least

1.3.

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40. The advantages of pre-control charting do NOT include:

A. Use of the specification tolerance directly

B. Very simple operator instructions

C. A permanent record of process adjustments

D. Applications for attribute or visual characteristics

Correct Answer: C

Justification: Note that the question is requesting a negative response. One of the

disadvantages of pre-control is the lack of a paper trail, indicating when process

adjustments were made.

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41. Which of the following indicate an out of control condition?

I. A trend of 9 points in an upward direction

II. 10 consecutive points above or below the center

III. 2 or 3 consecutive points outside the 2-sigma warning limits

A. I and II only


B. II and III only

C. I and III only

D. I, II and III

Correct Answer: D

Justification: There are many ways a control chart can exhibit an out of control

condition. The most popular rules were summarized by the Western Electric Company:

(1) 1 point outside the 3-sigma limits

(2) A trend of 8 points in an upward or downward direction

(3) 8 consecutive points on 1 side of the center line

(4) 4 of 5 consecutive points beyond 1-sigma limits

(5) 2 of 3 consecutive points beyond 2-sigma limits

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42. Since CuSum charts are more complicated to operate than Shewhart control

charts, what is the most logical reason for using them at all?

I. They require less data

II. They can be computer generated

III. They can detect smaller shifts in the process mean

A. I only

B. II and III only

C. I and III only

D. I, II and III

Correct Answer: B

Justification: All of the statements I – III are true. However, the most important reason

for CuSum charts is item III. Since there is no answer selection for item III only, then

another answer must be considered important. The question writer suggests that the

rapid computer generation of CuSum charts is also important to their expanded use.

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43. The best chart for analyzing volatile data, like stock market averages or

commodity prices, would be:

A. EWMA

B. CuSum

C. Moving average

D. Short run

Correct Answer: C

Justification: The question describes an application for the moving average chart. With

the moving average chart, the data is smoothed so that true trends can be analyzed.

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44. As with the 7 quality management tools, the Japanese concept of workplace

organization, 5S, has been Americanized. Of the five original tools, which two are

hardest to find in the American system?

A. Seiko and Seiton

B. Seiton and Seiso

C. Seiketso and Shitsuke

D. Seiko and Seiso

Correct Answer: C

Justification: There are several versions of Americanized 5S systems. They can

include Sort, Straighten, Scrub, Shine, Systematize, Standardize and Safety (and

others). The items in the American version appear to be directed mainly at the system

with implications for operator responsibility. The Japanese version includes Seiketso

(personal cleanliness) and Shitsuke (personal discipline) that are directed at the

individual. These are only obliquely covered in the USA version.

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45. What charting technique is useful for looking at a process for trends after

smoothing of data has occurred?

A. X bar – R chart

B. Moving average chart

C. Multi-vari chart

D. np chart


Correct Answer: B

Justification: The Multi-vari and np charts do not apply to this question. Although data

is “averaged” in an X bar – R chart, it is not intentionally smoothed as with a moving

average chart.

A moving average chart is useful for data (like the stock market) in that there is a

smoothing of short term information from an erratic process.

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46. In which one of the following is the use of an X bar and R chart liable to be most

helpful as a tool to control a process:

A. The machine capability is wider than the specification

B. The machine capability is equal to the specification

C. The machine capability is somewhat smaller than the specification

D. The machine capability is very small compared to the specification

Correct Answer: C

Justification: A control chart is not a useful tool in controlling a process if the capability

is wider than specification. An X bar – R control chart may not be necessary if the

capability (spread) is very small compared to the process. In this case, a pre-control

chart may be selected (or first and last piece inspection). Answer B is not a bad choice.

Answer C is a much better choice.

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47. In a hypothetical situation, if all within time, piece to piece, and measurement

variation were removed from a process, what would be left?

A. Nothing it would all be eliminated

B. Inherent process variation

C. Product spread

D. Time to time variation

Correct Answer: B

Justification: This question requires familiarity with variation breakdown or rational

subgrouping. What would be left is inherent process (short term machine or human)

variation. Answers A, C and D are all distractors.


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48. As applied to a Six Sigma environment, how would control chart variables be

selected?

I. From CTQ characteristics

II. From KPIVs

III. From KPOVs

IV. From non-critical KPIVs and KPOVs

A. I and IV only

B. I, II and III only

C. II, III and IV only

D. I, II, III and IV only

Correct Answer: B

Justification: Control chart characteristics in a Six Sigma world would be selected from

critical to quality customer characteristics as well as key process input and output

variables. There are too many non-critical items to be considered for control charting. If

variables are non-critical they probably wouldn’t be key variables in the first place.

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49. The identification of key process input and output variables can come from:

I. DOE results

II. Customer surveys

III. ANOVA methods

IV. Customer requirements

A. I and II only

B. II and III only

C. I, II and IV only


Correct Answer: D


Justification: Actually all items (I – IV) can identify key process variables.

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50. If we drew a large number of samples from a controlled process, we would not be

surprised to discover:

I. Some differences among the values of the sample means

II. A distribution of sample means around some central value

III. That many sample means differ from the process average

A. I only

B. II only

C. I and III only

D. I, II and III

Correct Answer: D

Justification: Items I – III are all correct statements regarding sampling principles,

control chart theory and statistical inference.

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51. What % of product should fall between the P – C lines (green zone) on a pre-

control chart, assuming that the process is stable?

A. 60.0%

B. 68.4%

C. 86.0%

D. 95.4%

Correct Answer: C

Justification: This is a straight knowledge question. The P – C lines are established to

capture 86% of the data. The other answer choices are distractors.

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52. You look at a process and note that the chart for averages has been in control. If

the range suddenly and significantly increases, the mean will:

A. Usually increase


B. Stay the same

C. Always decrease

D. Occasionally show out of control of either limit

Correct Answer: D

Justification: This question requires a review of the answers. If the range significantly

increases, then more spread in individual readings is occurring. The mean will not

always increase or decrease. The mean will not necessarily stay the same.

Occasionally it may exceed either control limit.

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53. Which of the following types of control charts has the largest average run length

for small shifts in the process mean?

A. X bar

B. Cumulative sum

C. EWMA

D. Dodge-Romig

Correct Answer: A

Justification: The average run length, ARL, is the average number of plotted points to

obtain a point outside the control limits. For a Shewhart chart, with 3-sigma limits, the

ARL is 370 (1/0.0027) if the process is in control. Shewhart charts are insensitive to

small shifts in the mean. Cumulative-sum charts (CuSum), and Exponentially weighted

moving average charts, (EWMA), are much better at detecting small shifts in the mean.

Since an X bar chart is a Shewhart chart, answer A is correct. Dodge – Romig is a

sampling technique.

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54. On the production floor, parts being produced measure 0.995 – 1.005. The

specification requires the parts to be 0.995 – 1.005. Which of the following

techniques would NOT be particularly useful in trying to improve and control the

process?

A. Pre-control

B. ANSI/ASQ Z1.4

C. Short run charts


D. R charts

Correct Answer: B

Justification: This question requires a general knowledge of a number of statistical

tools plus a review of the answers. The key phrase is “would NOT be useful”.

Even if all of the tools presented are not understood, a CSSBB student should

recognize that an attribute sampling plan ANSI/ASQ Z1.4 is out of place in a variable

measurement application.

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55. If six consecutive samples were taken from a process and measured precisely,

one would still expect to find differences. What type of variation would be most

difficult to determine?

A. Lot to lot variation

B. Piece to piece variation

C. Inherent process variation

D. Error of measurement

Correct Answer: A

Justification: The small sample size would make it impossible to provide a high level of

confidence in the results. However, measurement error, inherent process variation and

piece to piece variation are obtainable. Lot to lot variation would not be detectable

unless carefully planned for (which is not indicated in the question).

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56. If a process is truly in control, what is the probability of observing a run violation

of seven or more consecutive points on either side of the X bar chart centerline?

A. 1/32

B. 1/64

C. 1/128

D. 1/256

Correct Answer: B


Justification: The odds of observing seven consecutive readings on the upper side of

an X bar chart is (1/2)7 or 1/128. However, there is a similar probability of getting such a

run on the lower side of an X bar chart. Therefore, 1/128 + 1/128 = 1/64. This is why

some quality texts suggest that the run rule be extended to 8 or 9 consecutive points.

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57. In addition, to determining if a process is in statistical control, what other

applications can be made from variable control chart data?

I. Determining if changes made to the system were effective

II. Determining the natural tolerance range of the process

III. Determining when corrective action is necessary

IV. Determining if inspection costs can be minimized

A. I and III only

B. I, III and IV only

C. II and III only


Correct Answer: D

Justification: Items I and III are straightforward applications of control charting.

Additionally, control chart data can often be used to determine the tolerance range of

the process (that is, a continuous process capability determination). If a process shows

good control and is well within specification limits, then control chart monitoring can be

substituted for inspection. All items are correct.

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58. Which of the following control charts are more efficient than an X-bar chart at

detecting small shifts in the mean?

I. CuSum

II. EWQR

III. EWMA

A. I only


B. II and III only

C. III only

D. I and III only

Correct Answer: D

Justification: The cumulative sum (CuSum), and exponentially weighted moving-

average (EWMA), charts are more efficient than the X bar chart at detecting small shifts

in the process mean. Item II is a distractor.

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59. An X bar control chart is based on a sample size of 4. An operator mistakenly

plots the value of a single observation on the control chart. This point:

A. Will not cause any mis-judgments if the process is in control

B. Will always be plotted near the center line of the control chart

C. Will cause the associated R chart to show an out of control condition

D. Increases the probability of the process being labeled out of control

Correct Answer: D

Justification: The standard deviation of a sample mean of 4 is ½ the standard

deviation of the individuals. This is because the standard deviation of the sampling

distribution is inversely proportional to the square root of the sample size. In this case,

the square root of 4 is 2. Since the standard deviation of individual measurements is

twice that of the average of a sample of 4, the corresponding limits on an X bar control

chart would be twice as wide as those for the average from a sample of 4 points. Thus,

plotting a single observation increases the probability of the point falling outside the

control limits when the process is in control.

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60. If a process is out of control, the theoretical probability that a single point on the

X bar chart will fall between plus one sigma and upper control limits is:

A. 0.2240

B. 0.1587

C. Unknown

D. 0.3413

Correct Answer: C


Justification: This question can be a little tricky. The key phrase is “out of control”. If

the process were in control, a simple Z value determination would yield 0.1587 as the

correct answer. Since the process is out of control, the answer is unknown.

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61. Total productive maintenance involves coordinated group activities for greater

equipment effectiveness. Which of the following elements are also included?

I. Predictive maintenance

II. Preventative maintenance

III. Increased machine reliability

IV. Ease of maintenance

A. I and II only

B. II and III only

C. II, III and IV only


Correct Answer: D

Justification: In addition to utilizing operators for certain routine maintenance activities,

TPM considers and utilizes all of the items (I – IV) choices.

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62. About 9 months after embarking on a Six Sigma effort, a company moved from

measurement with traditional mikes and verniers to digital mikes and two piece

linear scales. Why was this action necessary?

A. They probably wanted to show prospective customers their level of

measurement precision

B. If changes were made they did not want to be caught “asleep at the switch”

C. Processes have improved and they needed finer product measurements

D. This would be required in the control phase of the DMAIC process

Correct Answer: C

Justification: Let’s assume that process improvements mandated more precise

measurements. Answer D is a very weak distractor.


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63. An R chart is most closely related to a:

A. c chart

B. S chart

C. u chart

D. X bar chart

Correct Answer: B

Justification: An R chart is used to monitor process variance. The range, the difference

between the largest and smallest measures in the sample, is used as an estimate of the

variance or standard deviation. The S chart is also used to monitor process variance,

except the standard deviation, S, is estimated directly, rather than using the range

method. This method is recommended when the sample size is large, n > 10, and when

the sample size is variable (The range method quickly loses accuracy as the sample

size increases).

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64. Standard work as visualized by the Japanese means:

I. Working harder

II. Working safer

III. Working productively

IV. Working under extreme constraints

A. I and II only

B. III and IV only

C. II and III only

D. I and IV only

Correct Answer: C

Justification: Standardized work in Japan means that the process is being controlled

not the workers. To them, a standard defines the process methods that are safest and

easiest for the workers and the most cost-effective and productive for the company.

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65. What type of control chart employs a V-mask?

A. EWMA

B. Moving average

C. CuSum

D. Short run

Correct Answer: C

Justification: A V-mask was widely used with a CuSum chart before the advent of

computers. The chart can now be generated with or without a V-mask.

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66. When using a pre-control chart, it’s possible to have two consecutive samples

outside of the target area but inside of the specification. What is the expectation

that two consecutive samples would both fall between the target area and the

specification limit on the high side?

A. 1/7

B. 1/49

C. 1/196

D. 1/98

Correct Answer: C

Justification: In the CSSBB Primer it is stated that the chance that two parts will fall

outside either P – C line is 1/7 times 1/7, or 1/49. However, there are four ways that this

can occur, based on pure probability:

Two consecutive on the high side is 1/196 probability

Two consecutive on the low side is 1/196 probability

One high/one low (or vice versa) is 2/196 probability

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67. What is the inherent danger in using an X bar and sigma chart with a sample size

of 25?

A. Finding appropriate control limit factors

B. Interpreting the chart properly


C. Recording 25 data points in the data table

D. Capturing too much variation in the sample

Correct Answer: D

Justification: Where applicable, sample sizes of 25 or more can be collected. Control

limit factors are readily available. Most of these charts are constructed by computer

programs so data tables are not an issue. There is a danger of capturing too much

variation in the sample. Thus, answer D is the best choice. If answer D is valid then, and

only then, should answer B be a concern.

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68. An X-bar chart has shown control for a long time. You see that points for the last

50 samples are all very near the center line on the chart. In fact, they are all

within one sigma of the center line. This probably indicates that:

A. It is a desirable situation

B. It is an undesirable situation

C. The process standard deviation has decreased during the time the last 50

samples were taken

D. The control limits are incorrectly computed

Correct Answer: C

Justification: Answer B is the least likely choice because the process standard

deviation (sample range) may have decreased. Answer A may be correct but it’s not

known if X-bar is the desired target. Answer D could be correct but it is unlikely if the

chart has been maintained for a long time. Answer C is the best choice.

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69. American visitors to an aluminum plant in Japan were given white gloves to wear.

What category of the 5S program was being displayed?

A. Sort

B. Scrub

C. Straighten

D. Standardize

Correct Answer: B


Justification: This is a form of white glove or white rag inspection. It emphasized the

importance of the scrub (shine and clean) portion of the 5S approach.

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70. A process is running under pre-control conditions and two consecutive pieces

have been sampled. The first piece is measured to be in the green zone. What is

the probability that the second piece will be measured to be in the red or yellow

zones?

A. Zero

B. 1/49

C. 1/98

D. 1/196

Correct Answer: A

Justification: Maybe zero is a bad choice because some idiot may always choose to

measure a sample when taken. However, if the first sample is within target the second

piece should not be measured.

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