Examination Paper of Six Sigma Black Belt
CERTIFIED SIX SGMA BLACK BELT
Examination paper
____________________________________________________
Guideline for paper
. Total no of question is 75
. The minimum passing marks is 40%
. Section-A (50 Question) carries 1 mark each.
. Section-B (25 Question) carries 2 marks each
. Answer all the question.
Section A Total: 100 marks
1. A frequent cause of system sub optimization is:
a. Optimizing individual process
b. Failing to draw a system flow chart
c. Using data with outliers
d. Failing to consider the normal distribution
2. Dr. W Edwards Deming:
a. Lectured in Japan after World War II
b. Was an author of several books in the US
c. Lectured widely in the US
d. Is considered an expert in the quality field
e. All of the above
f. None of the above
3. Successful Six Sigma project always:
a. Use designed experiments
b. Impact the bottom line of the enterprise
c. Are completed in a short time frame
d. All of the above
e. non of the above
4. Proposed Six Sigma projects that are not in some way liked to organizational goals:
a. Will typically be short term
b. Use statistical inference
c. Have a high risk of failure
d. Should not be approved
e. non of the above
Examination Paper of Six Sigma Black Belt
5. Dr. Joseph M.Juran:
a. Lectured in Japan after World War II
b. Was an author of several books in the US
c. Lectured widely in the US
d. Is considered an expert in the quality field
e. All of the above
f. None of the above
6. A project whose definition does not include performance metrics:
a. Will typically be short term
b. Use statistical inference
c. Have a high risk of failure
d. Should not be approved
e. Non of the above
7. An important step in determining the VOC is:
a. Establish viable or comprehensive process feedback loops
b. Ascertain the principles that are values of the corporation
c. Identify the customer
d. Measure the virtual operating continuum potential
e. all the above
f. None of the above
8. Quality function deployment is a tool to aid in:
a. Analyzing non-paired data
b. determining if quality procedures being followed on the shop floor
c. ascertaining which processes are functioning correctly
d. Liking customer requirements to product features
e. All of the above
f. None of the above
9. A process produced 1394 units. During this time 11 defects were detected. The rolled
throughput yield (RTU) is approximately:
a. 0.992
b. 7.89
c. 0.00789
d. 1.008
e. All of the above
f. None of the above
10. The x2 distribution is:
a. Symmetric
b. Left skewed
c. Right skewed
Examination Paper of Six Sigma Black Belt
d. Normal
e. Uniform
11. The mean of a Poisson distribution is 2.94. Its standard is:
a. Not enough information is given
b. 1.71
c. 8.64
d. 74.7
e. 1.31
12. Calculate the estimated variance of the population from which the following values have
been randomly selected: 2.8 2.7 2.6 2.9 2.8 2.8 2.8
a. .095
b. .009
c. .088
d. .008
13. An advantage of using standard deviation rather than range for measuring dispersion of a
large sample is that:
a. Standard deviation has a simpler formula
b. Calculators have a standard deviation key but not a range Key
c. Standard deviation uses information from each measurement
d. Range calculation are not normally distributed
14. Data are collected in Xy pairs and a scatter diagram shows the points are grouped very close
to a straight line that tips down on its right hand end. A reasonable value for the coefficient of
correlation is:
a. .8
b. 0
c. -.9
d. 1
e. 1.3
f. -1.8
15. The mean, median and mode of a distribution have the same value. What can be said about
the distribution?
a. It is exponential
b. It is normal
c. It is uniform
d. None of the above
16. Approximately what percent of the data values are smaller than the mean?
a. 25%
b. 50%
Examination Paper of Six Sigma Black Belt
c. 75%
d. None of above
17. A normal probability plot is used to:
a. Determine whether the distribution is normal
b. Plot Z value
c. Determine process capability
d. It percent out of specification
18. As opposed to earlier emphases lean manufacturing tends to stress:
a. Making value added activities more efficient
b. Eliminating, Simplifying or reducing non-value added activity.
19. Work performed by the payroll department is considered value added activity:
a. True
b. False
20. In the theory of constraints the “Subordinate” step refers to:
a. A listing of sub-processes
b. Reducing the rate for some processes
c. The portion of the process flow chart that depends on the main flow
d. The less important product or service stream
e. None of the above
21. A team wants a technique for displaying the connection between various customer need and
various features on a product. They should use:
a. Written and diagrammed work instruction
b. Flow chart and process maps
c. Cause and effect diagrams
d. Pareto chart
e. Relationship matrix
22. A team wants a technique for obtaining a large number of possible reasons for excess
variation in a dimension. They should use:
a. Written and diagrammed work instructions
b. Flow chart and process maps
c. Cause and effect diagrams
d. Pareto chart
e. Relationship matrix
Use the following for problem 23-26: The average yield from a small batch process has been
83%. A new catalyst is available which is designed to increase average yield by at least 5
percentage points. A sample of 45 batches is run with the new catalyst.
The average yield of this sample is 90% and the standard deviation of the sample yields is 2.8%.
Examination Paper of Six Sigma Black Belt
A hypothesis test with <= 0.05 will be used to determine whether the sample data indicate that
the new catalyst does increase the average yield by at least 5 percentage points.
23. This will be a:
a. Left-tail test
b. Right-tail test
c. Two-tail test
24. The critical value(s) is-are:
a. 1.645
b. 1.96
c. ±1.645
d. ±1.96
25. The critical test statistic is approximately:
a. 4.79
b. 6.71
c. 2.08
d. 5.44
26. The null hypothesis should be:
a. Rejected
b. Not rejected
c. Accepted
27. The word takt is closest to the theory of constraints word:
a. Drum
b. Buffer
c. Rope
d. Constraint
28. The team development stage characterized by expression of individual opinions and ides
often without regard for team objectives is known as:
a. Performing
b. Norming
c. Conflicting
d. Storming
e. Brainstorming
29. Nominal Group technique is used to:
a. Help a group reach consensus
b. Generate a group on new ides
c. Provide a consistent stable group leadership
d. Provide a name for the group
Examination Paper of Six Sigma Black Belt
30. A Six Sigma project designed to solve a particular problem needs a definition/scope
statement to help avoid:
a. Going beyond the problem into other problem
b. Failing to cover the entire problem
c. Misunderstanding and disagreement between team members regarding problem boundaries
d. All of the above
c. None of the above
31. An example of a project metric would be:
a. The decrease in defect occurrence
b. The decrease in product cost
c. The decrease in cycle time
d. All the above
32. SMED is an acronym for activity that:
a. Involve housekeeping in the work area
b. Makes mistake of a certain type impossible
c Emphasizes the pull of the customer
d. Reduces set up the time
e. None of the above
f. All of the above
33. A correct statement about the relationship between the terms parameter and statistic is:
a. A population statistic is more accurate than a parameter
b. A sample parameter is used to estimate a statistic
c. A sample statistic is used to estimate a population parameter
d. Standard deviation calculation requires both statistics and parameters
34. A and B are events. P(A) = 0.80 and P(B) = 0.90:
a. Events A and B are disjoint or mutually exclusive
b. Events A and B are not disjoint or mutually exclusive
c. P (A and B) = 0
d. P(A and B) = 1.7
35. Find the mean, median and mode of the following data set:9, 11, 12, 14, 18, 18, 18, 20, 23:
a. 15.5, 18, 18
b. 15, 14, 18
c. 14, 16, 18
d. 15, 12, 18
e. 15.5, 16, 18
36. The diagram of 50 randomly selected shafts have a mean of 1.525 and standard deviation of
0.006 find the 95% lower confidence limit for the population mean.
a. 1.523
Examination Paper of Six Sigma Black Belt
b. 1.524
c. 1.525
d. 1.526
e. 1.527
37. In a certain sampling situation, a=0, b=0.08. the power of the sampling plan this case is:
a. 0
b. 0.08
c. 1.00
d. 0.92
38. A newspaper article describes a high positive correlation between obesity and orange juice
consumption among six-year-olds. Parents who restrict he use of orange juice for their children
have:
a. Made a type I error
b. Made a type II error
c. Misunderstood margin of error
d. Confused correlation with causation
39. A principle advantage of fractional factorial experimental designs is:
a. Reduced cost
b Improved accuracy
c. Increased confounding
d. Higher confidence level
e. Reduced probability of type II error
40. A principle disadvantage of fractional factorial experimental designs is:
a. Reduced cost
b Improved accuracy
c. Increased confounding
d. Higher confidence level
e. Reduced probability of type II error
41. In an experimental design context, replications refer to:
a. Duplicating experimental result at another location
b. Repeating a test with the same factor levels
c. Obtaining the same or similar result from different factors
d. Repeating an experiment but using at least one different factor level
42. find the upper control limit for a range chart if n=4 and the average range is 2.282
a. 2.282
b. 4.564
c. 5.208
d. 3.423
Examination Paper of Six Sigma Black Belt
43. An x-bar control chart been established with control limits of 3.245 and 3.257, n=5. An
engineer collects the following sample and plots the average on the control chart:3.257, 3.256,
3.258, 3.259
a. The process is out of control
b. The process is not out of control
c. The engineer misused the control chart
d. The control limits are incorrect
44. TEIZ is an acronym which refers to:
a. A set of problem solving tools
b. An organization of quality professionals
c. An experiment using transitional results
d. A Russian general responsible for creative thinking
45. A robust design is one which;
a. Has high reliability
b. Has low maintenance frequency
c. Is simple to manufacture’
d. Is resistant to varying environmental condition
46. A team has completed a brainstorming session that has generated a large number of ideas in
natural groupings. Which tool is most appropriate?
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
47. A team has been asked to reduce the occurrence of a particular defect. They begin by
brainstorming all possible causes using a:
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
Examination Paper of Six Sigma Black Belt
48. a team wants to make a schedule for a project showing which takes must be done
sequentially and which may be done simultaneously. Which tool is most appropriate?
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
49. A complex system has many causes and effects. These may be illustrated on which of the
following:
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
50. An experiment is conducted by checking the effect that three different pressures have on the
surface appearance of a product. Ten item items are produced at each of the three pressures. The
number of replications, factors and levels are:
a. 10, 3, 2
b. 10, 2, 3
c. 2, 3, 3
d. 10, 1, 3
e. 10, 3, 1
Examination Paper of Six Sigma Black Belt
Section B
51. A factorial experiment has three factors. Each factor has three levels. The number of test
combinations or runs is:
a. 9
b. 6
c. 27
d. 36
e. 33
Use the following for problem 52-54: A product specification or tolerance is 180-200. A sample
of 100 parts has an average of 188 and standard deviation of 6. Assume the population is
normally distributed.
52. What percent of population falls below the lower specification limits?
a. 9.18%
b. 22.66%
c. 6.68%
d. 1.83%
53. Find cp
a. 2.00
b. 0.56
c. 1.33
d. 0.44
54. Find cpk
a. 2.00
b. 0.56
c. 1.33
d. 0.44
Use the following for problem 55 and 56. The following data have been collected.
Find the least squares regression equation of the type y=mx + b or y = b0 + b1 x:
x 6 8 10
y 1 3 4
55. Find the value of m or b1:
a. 0.25
b. 0.63
c. 0.75
d. 1.22
56. Find the value of b or b0:
a. 3.33
b. -3.33
Examination Paper of Six Sigma Black Belt
c. 4.08
d. -4.08
e. 1.24
f. -1.2
Use for problems 57-59:
A B Res.
1 20
2 30
3 40
4 50
57. Calculate the main effect of factor A:
a. 20
b. 25
c. 30
d. 40
e. None of the above
58. Calculate the interaction effect:
a. 20
b. 25
c. 30
d. 40
e. None of the above
59. If it is desirable to maximize the response R, the following levels should be used:
a. A+ and B+
b. A+ and Bc.
A- and B+
d. A- and Be.
None of the above
60. A control chart will be used to monitor the number of scratches on a product. The following
data have been collected:
Number of
Scratches
6 5 7 5 6
Sample size 120 110 111 128 110
The appropriated control chart to use is:
a. x-bar and R
b. Median
c. Individual and moving range
- -
- +
+ -
+ +
Examination Paper of Six Sigma Black Belt
d. p
e. np
f. u
g. c
61. The temperature in a storage location is logged once every 30 minutes. The control chart that
is appropriate for displaying these values is:
a. x-bar and R
b. Median
c. Individual and moving range
d. p
e. np
f. u
g. c
62. a control chart is to be use to display the number of non-conducting diodes. Each point on the
chart represents the number of bad diodes in a box of 1000. The appropriate control chart to use
is
a. x-bar and R
b. Median
c. Individual and moving range
d. p
e. np
f. u
g. c
Use the following for problems 63-69:
A team is asked to determine whether printer #2 prints typical company documents faster than
printer # 1. The team decides to use the paired t hypothesis test. They select eight documents and
print each on each printer, assuming that the differences are normally distributed. The results:
Document # Time Reqd, sec
Ptr #1 Ptr #2
1 4.2 3.9
2 5.6 5.5
3 2.8 2.9
4 7.1 6.7
5 11.5 11
6 8.2 8.1
7 12.3 11.8
8 13.5 13
Examination Paper of Six Sigma Black Belt
63. Find the average difference d bar:
a. 0.2875
b. 0.3502
c. 0.2714
d. 0.2295
64. Find sd:
a. 0.2875
b. 03502
c. 0.2714
d. 0.2295
65. Is this a left-tail or two-tail test?
a. No
b. Left-tail
c. Right-tail
d. Two-tail
66. if a=0.5, what is the critical value?
a. 2.365
b. 2.306
c. 1.860
d. 1.895
67. What is the value of the test statistic?
a. 0.898
b. 1.251
c. 3.57
d. 0.429
e. none of the above
68. If the value of the test statistic had been 0.185, what action should have been taken regarding
the null hypothesis?
a. Rejected
b. accepted
c. None of the above
d. All of the above
69. if the value of the statistic had been 7.03, what action should been taken regarding the null
hypothesis
a. Rejected
b. accepted
c. None of the above
d. All of the above
Examination Paper of Six Sigma Black Belt
Use for questions 70-72:
Here is an experimental design with result:
A B C
Responses
1
- - +
10 11 10
2 - + -
22 20 23
3 + + +
34 36 37
4 + - -
26 25 25
70. This experimental design is:
a. Full factorial
b. Half factorial
c. Quarter factorial
d. None of the above
71. The number of factors, levels and replications:
a. 3, 3, 3
b. 2, 3, 2
c. 3, 2, 2
d. 3, 2, 3
e. 2, 2, 2
f. None of the above
72. An indication of the experimental error is available because the design has:
a. Multiple replications
b. Multiple levels
c. Multiple factors
73. The average number of defects is 21.6. Find the upper control limit for the c.chart.
a. 26.4
b. 24.6
c. 18.8
d. 26.2
e. None of the above
74. An x-bar and R chart is used to monitor a process. One week ago a new type of raw material
was introduced and since that 60 points have been plotted on the x bar chart and all are in the
middle third of the chart. The corresponding 60 points on the R chart are all below the average.
The indicates that:
a. The operator has been plotting the points incorrectly
Examination Paper of Six Sigma Black Belt
b. It is time to recalibrate the gage used
c. It is time to recalculate the control limits
d. The material manager should be asked to go back to the previous raw material so the chart will
more accurately reflect process
75. Here is a partial ANOVA table. Use a= 0.05.
Source SS Df Ms Fstatistic Fcritical
A 1200 6 x y Z
B 900 6
A x B 180 3
Error 100 10
The value of x, y and z should be:
a. 200, 20, 3.00
b. 12, 1.2, 4.06
c. 200.20, 4.06
d. None of the above
CERTIFIED SIX SGMA BLACK BELT
Examination paper
____________________________________________________
Guideline for paper
. Total no of question is 75
. The minimum passing marks is 40%
. Section-A (50 Question) carries 1 mark each.
. Section-B (25 Question) carries 2 marks each
. Answer all the question.
Section A Total: 100 marks
1. A frequent cause of system sub optimization is:
a. Optimizing individual process
b. Failing to draw a system flow chart
c. Using data with outliers
d. Failing to consider the normal distribution
2. Dr. W Edwards Deming:
a. Lectured in Japan after World War II
b. Was an author of several books in the US
c. Lectured widely in the US
d. Is considered an expert in the quality field
e. All of the above
f. None of the above
3. Successful Six Sigma project always:
a. Use designed experiments
b. Impact the bottom line of the enterprise
c. Are completed in a short time frame
d. All of the above
e. non of the above
4. Proposed Six Sigma projects that are not in some way liked to organizational goals:
a. Will typically be short term
b. Use statistical inference
c. Have a high risk of failure
d. Should not be approved
e. non of the above
Examination Paper of Six Sigma Black Belt
5. Dr. Joseph M.Juran:
a. Lectured in Japan after World War II
b. Was an author of several books in the US
c. Lectured widely in the US
d. Is considered an expert in the quality field
e. All of the above
f. None of the above
6. A project whose definition does not include performance metrics:
a. Will typically be short term
b. Use statistical inference
c. Have a high risk of failure
d. Should not be approved
e. Non of the above
7. An important step in determining the VOC is:
a. Establish viable or comprehensive process feedback loops
b. Ascertain the principles that are values of the corporation
c. Identify the customer
d. Measure the virtual operating continuum potential
e. all the above
f. None of the above
8. Quality function deployment is a tool to aid in:
a. Analyzing non-paired data
b. determining if quality procedures being followed on the shop floor
c. ascertaining which processes are functioning correctly
d. Liking customer requirements to product features
e. All of the above
f. None of the above
9. A process produced 1394 units. During this time 11 defects were detected. The rolled
throughput yield (RTU) is approximately:
a. 0.992
b. 7.89
c. 0.00789
d. 1.008
e. All of the above
f. None of the above
10. The x2 distribution is:
a. Symmetric
b. Left skewed
c. Right skewed
Examination Paper of Six Sigma Black Belt
d. Normal
e. Uniform
11. The mean of a Poisson distribution is 2.94. Its standard is:
a. Not enough information is given
b. 1.71
c. 8.64
d. 74.7
e. 1.31
12. Calculate the estimated variance of the population from which the following values have
been randomly selected: 2.8 2.7 2.6 2.9 2.8 2.8 2.8
a. .095
b. .009
c. .088
d. .008
13. An advantage of using standard deviation rather than range for measuring dispersion of a
large sample is that:
a. Standard deviation has a simpler formula
b. Calculators have a standard deviation key but not a range Key
c. Standard deviation uses information from each measurement
d. Range calculation are not normally distributed
14. Data are collected in Xy pairs and a scatter diagram shows the points are grouped very close
to a straight line that tips down on its right hand end. A reasonable value for the coefficient of
correlation is:
a. .8
b. 0
c. -.9
d. 1
e. 1.3
f. -1.8
15. The mean, median and mode of a distribution have the same value. What can be said about
the distribution?
a. It is exponential
b. It is normal
c. It is uniform
d. None of the above
16. Approximately what percent of the data values are smaller than the mean?
a. 25%
b. 50%
Examination Paper of Six Sigma Black Belt
c. 75%
d. None of above
17. A normal probability plot is used to:
a. Determine whether the distribution is normal
b. Plot Z value
c. Determine process capability
d. It percent out of specification
18. As opposed to earlier emphases lean manufacturing tends to stress:
a. Making value added activities more efficient
b. Eliminating, Simplifying or reducing non-value added activity.
19. Work performed by the payroll department is considered value added activity:
a. True
b. False
20. In the theory of constraints the “Subordinate” step refers to:
a. A listing of sub-processes
b. Reducing the rate for some processes
c. The portion of the process flow chart that depends on the main flow
d. The less important product or service stream
e. None of the above
21. A team wants a technique for displaying the connection between various customer need and
various features on a product. They should use:
a. Written and diagrammed work instruction
b. Flow chart and process maps
c. Cause and effect diagrams
d. Pareto chart
e. Relationship matrix
22. A team wants a technique for obtaining a large number of possible reasons for excess
variation in a dimension. They should use:
a. Written and diagrammed work instructions
b. Flow chart and process maps
c. Cause and effect diagrams
d. Pareto chart
e. Relationship matrix
Use the following for problem 23-26: The average yield from a small batch process has been
83%. A new catalyst is available which is designed to increase average yield by at least 5
percentage points. A sample of 45 batches is run with the new catalyst.
The average yield of this sample is 90% and the standard deviation of the sample yields is 2.8%.
Examination Paper of Six Sigma Black Belt
A hypothesis test with <= 0.05 will be used to determine whether the sample data indicate that
the new catalyst does increase the average yield by at least 5 percentage points.
23. This will be a:
a. Left-tail test
b. Right-tail test
c. Two-tail test
24. The critical value(s) is-are:
a. 1.645
b. 1.96
c. ±1.645
d. ±1.96
25. The critical test statistic is approximately:
a. 4.79
b. 6.71
c. 2.08
d. 5.44
26. The null hypothesis should be:
a. Rejected
b. Not rejected
c. Accepted
27. The word takt is closest to the theory of constraints word:
a. Drum
b. Buffer
c. Rope
d. Constraint
28. The team development stage characterized by expression of individual opinions and ides
often without regard for team objectives is known as:
a. Performing
b. Norming
c. Conflicting
d. Storming
e. Brainstorming
29. Nominal Group technique is used to:
a. Help a group reach consensus
b. Generate a group on new ides
c. Provide a consistent stable group leadership
d. Provide a name for the group
Examination Paper of Six Sigma Black Belt
30. A Six Sigma project designed to solve a particular problem needs a definition/scope
statement to help avoid:
a. Going beyond the problem into other problem
b. Failing to cover the entire problem
c. Misunderstanding and disagreement between team members regarding problem boundaries
d. All of the above
c. None of the above
31. An example of a project metric would be:
a. The decrease in defect occurrence
b. The decrease in product cost
c. The decrease in cycle time
d. All the above
32. SMED is an acronym for activity that:
a. Involve housekeeping in the work area
b. Makes mistake of a certain type impossible
c Emphasizes the pull of the customer
d. Reduces set up the time
e. None of the above
f. All of the above
33. A correct statement about the relationship between the terms parameter and statistic is:
a. A population statistic is more accurate than a parameter
b. A sample parameter is used to estimate a statistic
c. A sample statistic is used to estimate a population parameter
d. Standard deviation calculation requires both statistics and parameters
34. A and B are events. P(A) = 0.80 and P(B) = 0.90:
a. Events A and B are disjoint or mutually exclusive
b. Events A and B are not disjoint or mutually exclusive
c. P (A and B) = 0
d. P(A and B) = 1.7
35. Find the mean, median and mode of the following data set:9, 11, 12, 14, 18, 18, 18, 20, 23:
a. 15.5, 18, 18
b. 15, 14, 18
c. 14, 16, 18
d. 15, 12, 18
e. 15.5, 16, 18
36. The diagram of 50 randomly selected shafts have a mean of 1.525 and standard deviation of
0.006 find the 95% lower confidence limit for the population mean.
a. 1.523
Examination Paper of Six Sigma Black Belt
b. 1.524
c. 1.525
d. 1.526
e. 1.527
37. In a certain sampling situation, a=0, b=0.08. the power of the sampling plan this case is:
a. 0
b. 0.08
c. 1.00
d. 0.92
38. A newspaper article describes a high positive correlation between obesity and orange juice
consumption among six-year-olds. Parents who restrict he use of orange juice for their children
have:
a. Made a type I error
b. Made a type II error
c. Misunderstood margin of error
d. Confused correlation with causation
39. A principle advantage of fractional factorial experimental designs is:
a. Reduced cost
b Improved accuracy
c. Increased confounding
d. Higher confidence level
e. Reduced probability of type II error
40. A principle disadvantage of fractional factorial experimental designs is:
a. Reduced cost
b Improved accuracy
c. Increased confounding
d. Higher confidence level
e. Reduced probability of type II error
41. In an experimental design context, replications refer to:
a. Duplicating experimental result at another location
b. Repeating a test with the same factor levels
c. Obtaining the same or similar result from different factors
d. Repeating an experiment but using at least one different factor level
42. find the upper control limit for a range chart if n=4 and the average range is 2.282
a. 2.282
b. 4.564
c. 5.208
d. 3.423
Examination Paper of Six Sigma Black Belt
43. An x-bar control chart been established with control limits of 3.245 and 3.257, n=5. An
engineer collects the following sample and plots the average on the control chart:3.257, 3.256,
3.258, 3.259
a. The process is out of control
b. The process is not out of control
c. The engineer misused the control chart
d. The control limits are incorrect
44. TEIZ is an acronym which refers to:
a. A set of problem solving tools
b. An organization of quality professionals
c. An experiment using transitional results
d. A Russian general responsible for creative thinking
45. A robust design is one which;
a. Has high reliability
b. Has low maintenance frequency
c. Is simple to manufacture’
d. Is resistant to varying environmental condition
46. A team has completed a brainstorming session that has generated a large number of ideas in
natural groupings. Which tool is most appropriate?
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
47. A team has been asked to reduce the occurrence of a particular defect. They begin by
brainstorming all possible causes using a:
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
Examination Paper of Six Sigma Black Belt
48. a team wants to make a schedule for a project showing which takes must be done
sequentially and which may be done simultaneously. Which tool is most appropriate?
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
49. A complex system has many causes and effects. These may be illustrated on which of the
following:
a. Matrix diagram
b Cause and effect diagram
c. Process decision program chart
d. Affinity diagram
e. Activity network diagram
f. Tree diagram
g. Prioritization matrix
h. Matrix diagram
i. Interrelationship digraph
50. An experiment is conducted by checking the effect that three different pressures have on the
surface appearance of a product. Ten item items are produced at each of the three pressures. The
number of replications, factors and levels are:
a. 10, 3, 2
b. 10, 2, 3
c. 2, 3, 3
d. 10, 1, 3
e. 10, 3, 1
Examination Paper of Six Sigma Black Belt
Section B
51. A factorial experiment has three factors. Each factor has three levels. The number of test
combinations or runs is:
a. 9
b. 6
c. 27
d. 36
e. 33
Use the following for problem 52-54: A product specification or tolerance is 180-200. A sample
of 100 parts has an average of 188 and standard deviation of 6. Assume the population is
normally distributed.
52. What percent of population falls below the lower specification limits?
a. 9.18%
b. 22.66%
c. 6.68%
d. 1.83%
53. Find cp
a. 2.00
b. 0.56
c. 1.33
d. 0.44
54. Find cpk
a. 2.00
b. 0.56
c. 1.33
d. 0.44
Use the following for problem 55 and 56. The following data have been collected.
Find the least squares regression equation of the type y=mx + b or y = b0 + b1 x:
x 6 8 10
y 1 3 4
55. Find the value of m or b1:
a. 0.25
b. 0.63
c. 0.75
d. 1.22
56. Find the value of b or b0:
a. 3.33
b. -3.33
Examination Paper of Six Sigma Black Belt
c. 4.08
d. -4.08
e. 1.24
f. -1.2
Use for problems 57-59:
A B Res.
1 20
2 30
3 40
4 50
57. Calculate the main effect of factor A:
a. 20
b. 25
c. 30
d. 40
e. None of the above
58. Calculate the interaction effect:
a. 20
b. 25
c. 30
d. 40
e. None of the above
59. If it is desirable to maximize the response R, the following levels should be used:
a. A+ and B+
b. A+ and Bc.
A- and B+
d. A- and Be.
None of the above
60. A control chart will be used to monitor the number of scratches on a product. The following
data have been collected:
Number of
Scratches
6 5 7 5 6
Sample size 120 110 111 128 110
The appropriated control chart to use is:
a. x-bar and R
b. Median
c. Individual and moving range
- -
- +
+ -
+ +
Examination Paper of Six Sigma Black Belt
d. p
e. np
f. u
g. c
61. The temperature in a storage location is logged once every 30 minutes. The control chart that
is appropriate for displaying these values is:
a. x-bar and R
b. Median
c. Individual and moving range
d. p
e. np
f. u
g. c
62. a control chart is to be use to display the number of non-conducting diodes. Each point on the
chart represents the number of bad diodes in a box of 1000. The appropriate control chart to use
is
a. x-bar and R
b. Median
c. Individual and moving range
d. p
e. np
f. u
g. c
Use the following for problems 63-69:
A team is asked to determine whether printer #2 prints typical company documents faster than
printer # 1. The team decides to use the paired t hypothesis test. They select eight documents and
print each on each printer, assuming that the differences are normally distributed. The results:
Document # Time Reqd, sec
Ptr #1 Ptr #2
1 4.2 3.9
2 5.6 5.5
3 2.8 2.9
4 7.1 6.7
5 11.5 11
6 8.2 8.1
7 12.3 11.8
8 13.5 13
Examination Paper of Six Sigma Black Belt
63. Find the average difference d bar:
a. 0.2875
b. 0.3502
c. 0.2714
d. 0.2295
64. Find sd:
a. 0.2875
b. 03502
c. 0.2714
d. 0.2295
65. Is this a left-tail or two-tail test?
a. No
b. Left-tail
c. Right-tail
d. Two-tail
66. if a=0.5, what is the critical value?
a. 2.365
b. 2.306
c. 1.860
d. 1.895
67. What is the value of the test statistic?
a. 0.898
b. 1.251
c. 3.57
d. 0.429
e. none of the above
68. If the value of the test statistic had been 0.185, what action should have been taken regarding
the null hypothesis?
a. Rejected
b. accepted
c. None of the above
d. All of the above
69. if the value of the statistic had been 7.03, what action should been taken regarding the null
hypothesis
a. Rejected
b. accepted
c. None of the above
d. All of the above
Examination Paper of Six Sigma Black Belt
Use for questions 70-72:
Here is an experimental design with result:
A B C
Responses
1
- - +
10 11 10
2 - + -
22 20 23
3 + + +
34 36 37
4 + - -
26 25 25
70. This experimental design is:
a. Full factorial
b. Half factorial
c. Quarter factorial
d. None of the above
71. The number of factors, levels and replications:
a. 3, 3, 3
b. 2, 3, 2
c. 3, 2, 2
d. 3, 2, 3
e. 2, 2, 2
f. None of the above
72. An indication of the experimental error is available because the design has:
a. Multiple replications
b. Multiple levels
c. Multiple factors
73. The average number of defects is 21.6. Find the upper control limit for the c.chart.
a. 26.4
b. 24.6
c. 18.8
d. 26.2
e. None of the above
74. An x-bar and R chart is used to monitor a process. One week ago a new type of raw material
was introduced and since that 60 points have been plotted on the x bar chart and all are in the
middle third of the chart. The corresponding 60 points on the R chart are all below the average.
The indicates that:
a. The operator has been plotting the points incorrectly
Examination Paper of Six Sigma Black Belt
b. It is time to recalibrate the gage used
c. It is time to recalculate the control limits
d. The material manager should be asked to go back to the previous raw material so the chart will
more accurately reflect process
75. Here is a partial ANOVA table. Use a= 0.05.
Source SS Df Ms Fstatistic Fcritical
A 1200 6 x y Z
B 900 6
A x B 180 3
Error 100 10
The value of x, y and z should be:
a. 200, 20, 3.00
b. 12, 1.2, 4.06
c. 200.20, 4.06
d. None of the above
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