Answer Key
Certified Lean Six Sigma Black Belt Assessment
Belt Assessment
OPEN SOURCE SIX SIGMA ASSESSMENT
Open Source Six Sigma, LLC
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Information Sheet
Name
Contact
Division
Class
Date
Correct Answers Marked in Bold Dark Blue Define…
1. Sigma is a symbol that is used to identify Standard Deviation:
True | False
2. What item below best describes variation in a process?
A. Points not centrally located outside the Mean
B. A cluster of outcomes located at one Center Point
C. How tightly all the various outcomes are clustered around the average
D. The overall calculated point cluster to the right of the Mean
3. A concept used to best describe a performance of a process relative
to a specification limit is called:
A. Sigma level
B. Standard Deviation
C. Median Class
D. Hypothesis Testing
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 1 4. The ________ _________ refers to how tightly all the various outcomes are
clustered around the average.
process variation OR Standard Deviation – either is acceptable
5. The __________ __________ is the distance between the Mean and the
point of inflection on the Normal curve:
Standard Deviation
6. Error Proofing devices is part of what COPQ categories:
A. Supplier
B. External
C. Prevention
D. Internal
7. When looking at COPQ, labor savings and scrap reductions are
categorized as soft savings:
True | False
8. The items below are all examples of hard savings except:
A. Hidden Factory Costs Reduction
B. Lowered Inventory Carrying Costs
C. Regaining Lost Sales
D. Cycle Time Improvements lowering overtime hours paid
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 2 9. What is the main difference between FTY and RTY:
A. There is no difference
B. RTY reveals losses from rework
C. RTY captures resource consumption
D. FTY captures amount of rework
10. Specifically within Six Sigma change in performance comes from
identifying and controlling:
A. Independent variables
B. Dependent variables
C. Controlled variables
D. Transparent variables
11. A type of bar graph used to help prioritize processes:
A. Time Series Plot
B. Process Alignment Graph
C. Pareto Analysis
D. Process Elimination Chart
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 3 12. Match each name below with the correct formula.
Binomial > A | DPU > B | RTY > D
Poisson > C |
13. Sigma is a measure of deviation. The mathematical formula for the
Standard Deviation of a population is ________(C)
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 4 14. The higher a sigma level the better the performance:
True |False
15. Corporation XYZ operates at a yield of 93.2%. Therefore this
Corporation is operating at what sigma level:
A. 3 sigma
B. 3.5 sigma
C. 2 sigma
D. 4 sigma
16. According to our definition of RTY, which of the following items best
describes the purpose of RTY:
A. A function of Y=f(x)
B. Reveals losses due to rework steps
C. Isolates the increase throughput
D. Determines incremental Growth
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 5 17. The Japanese terms for 5S are: (Check all that apply)
A. Seiri
B. Saki
C. Seiton
D. Sukiaki
E. Seiso
F. Seiketsu
G. Shitsuke
H. Shenzen
18. If we produce more than is needed by the next step in the process or
more than the customer needs this is an example of which element of
waste:
A. Overproduction
B. Correction (defects)
C. Inventory
D. Motion
E. Overprocessing
F. Conveyance
G. Speed
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 6 19. A small distribution warehouse moves a single crate of product thirteen
times before it is finally loaded for shipment, this is an example of which
one of the seven elements of waste:
A. Correction (defects)
B. Inventory
C. Motion
D. Overprocessing
E. Conveyance
F. Waiting
20. The Japanese word for waste is hudat:
True |False
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 7 Measure…
21. Two data type exist known as, ______________________ and Variable:
Attribute
22. The difference between the largest observation and the smallest
observation in the data set is known as_______________. Range
23. The ____________________ is the average squared deviation of each
individual data point from the Mean: Variance
24. A Belt is constructing a FMEA, also known as Failure Modes
________________ Analysis for the identified independent variables.
Effect OR Effects
25. Gage R&R tries to determine if the measurement system has good
_______________________ and Reproducibility. Repeatability
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 8 26. Stability of a gauge is defined as error being a function of time and is
measured in terms of ___________________ Deviation. Standard
27. The difference in Bias values across the process range is known
as_______________________. Linearity
28. A population is a collection of all the individuals of interest and the
population has its own statistics:
True |False
29. A Black Belt was entering data into MINITABTM. The data being entered
is the name of the countries that his company supplies product to. This is
an example of:
A. Nominal Scale Data
B. Ration Scale Data
C. Continuous Data
D. Ordinal Scale Data
30. Interquartile Range is the difference between the 25th percentile and
the 50th percentile:
True|False
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 9 31. Which item listed below is NOT necessary to determine Process
Capability for a process with a continuous output:
A. Shape of process data distribution (e.g. Normal Distribution)
B. Process Mean
C. Process Standard Deviation
D. Presence of Special Causes of solely Common Causes
E. Interquartile range of the process
F. Specification limit or limits
32. What is the estimated probability of a process to give a result within +/3 Standard Deviations from the Mean for a normally distributed process:
A. 68.27%
B. 99.73%
C. 100.%
D. 95.45%
33. The variation in measurements obtained with one instrument used
several times by one appraiser on a single part´s one characteristic is:
A. Repeatability
B. Bias
C. Linearity
D. Reproducibility
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 10 34. For a crossed Gage R&R study, if 8 parts are being analyzed by 4
quality technicians and each technician tests each part 3 times, how
many total times is each part being measured in the study:
A. 4
B. 12
C. 24
D. 96
35. Which types of MSA studies are paired correctly?: (Check all that
apply)
A. Destructive variable gage R&R and Crossed Study
B. Destructive variable gage R&R and Nested Study
C. Nondestructive variable gage R&R and Crossed Study
D. Nondestructive variable gage R&R and Nested Study
36. What does Cp tell you: (Check all that apply)
A. What is possible if your process is perfectly centered
B. Process Potential
C. Process Performance
D. Relative ratio of the process variation to the specifications´ range
E. The best your process can be
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 11 37. The purpose of using Ppk is: (Check all that apply)
A. Assess process performance
B. How well the process is actually running
C. Process capability relative to specification limits
D. To see if your process is perfectly centered relative to the calculated
Pp
E. Evaluate process without Special Causes
38. Which statements are true for Process Capability of real world
processes with Normal Distributions: (Check all that apply)
A. Cp is always less than or equal to Pp for the same process
B. The more a process becomes centered, the Cpk or Ppk increases
C. The Ppk is always equal or less than the Pp for the same process
D. A Cp of 3 means very little product (less than 1%) is out of specification
E. Cp and Cpk are for short term data sets
F. If the overall sigma level increases, the Ppk or Cpk increases
G. The selected Normality test indicated a P-value less than 0.05 when
the process distribution was tested
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 12 39. Using the partial Z table below, how many pieces in a week are
expected to not satisfy customer requirements of the following process.
Upper specification limit: 60 Lower specification limit: 40 Mean of the
process: 54 Process Standard Deviation: 3 Weekly production: 652 pieces
Z-table:
Z
area
A. 0.00
0
0.500
B. 0.33
0.1
0.460
0.5
0.309
1.0
0.159
1.5
0.067
2.0
0.023
6.7
0.000
C. 15
D. 44
E. 196
F. 300
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 13 40. Given the following data set, calculate the appropriate capability
statistics for this process that was taken from one machine operated by
one operator in the last 30 minutes of his shift. Select the answer showing
the best and appropriate capability statistics.
Data:
6.9 4.6 2.4 5.8 7.6 7.6 7.2 3.9 9.3 4.9
Process specification:
LSL = 0.5
USL = 10.0
A. Cp = 0.69 and Cpk = 0.58
B. Pp = 0.74 and Ppk = 0.62
C. Cp = 0.74 and Cpk = 0.62
D. Cpk = 0.58 and Ppk = 0.62
E. Cp = 0.74 and Cpk = 0.62 and Pp = 0.74 and Ppk = 0.62
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 14 Analyze… 41. Multi-vari Studies are a graphical tool that display patterns of data
performed _____________ where the process is studied in its natural
unchanged state:
A. with an experimental design
B. as a passive study
C. with active changes by the team
D. with a histogram analysis
42. Between unit or Cyclical variation can be displayed as: (Check all
that apply)
A. Variation among consecutive pieces
B. Variation among groups of pieces
C. Variation among consecutive batches
D. Variation among the completed product
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 15 43. Some different types of error that exist in statistics are: (Check all that
apply)
A. Error in sampling
B. Bias in sampling
C. Error in measurement
D. Lack of measurement validity
E. Power validity
F. Insufficient sample size
44. The purpose of Hypothesis Testing is:
A. To make some inference or educated guess about the population
B. To form a conclusion by guessing
C. To calculate identifiable causes
D. To find new problems
45. T-tests in its various forms are used to: (Check all that apply)
A. Compare a Mean against a target
B. Compare Means from two different samples
C. Compare sample distributions types
D. Compare paired data
E. Compare sample variances
F. Compare Medians of different samples
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 16 46. Levene´s test of equal variance is used to compare the estimated
population Standard Deviations from two or more samples with nonnormal distributions:
True | False
47. For a Skewed Distribution, the appropriate statistic to describe the
central tendency is:
A. Mean
B. Median
C. Mode
48. When conducting a Hypothesis Test using continuous data, the proper
sample size depends on the practical difference to be detected and the
inherent variation in the process:
True | False
49. Contingency tables are used to:
A. Illustrate one tail proportion
B. Compare more than two sample proportions with each other
C. Contrast the outliers under the tail
D. Analyze the ´´what if´´ scenario
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 17 50. Read the following word problem:
After conducting a one-sample Z test, the sample gives a test statistic z
closest to:
A. -.77
B. -.11
C. 0.77
D. 0.11
51. Read the following word problem:
The alternative hypothesis in the above example is:
A. The Mean time is equal to 45 minutes
C. The Mean is less than 45 minutes
D. The Mean is greater than 45 minutes
E. The Mean is less than or equal to 45 minutes
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 18 52. Read the following word problem:
After conducting a one-sample Z-test, the data indicates a z-score closest
to:
A. 0.00
B. 0.82
C. 0.83
D. 0.97
E. 0.99
53. Read the following word problem
A. State the Practical Problem:
B. If the average cost per desktop is $2,100 or less, then the purchase
manager will upgrade the office with new desktops
C. If the average cost per desktop is greater than $2,100, then the
purchase manager will upgrade the office with new desktops
D. Only if the average cost per desktop is $1,951, then the purchase
manager will upgrade the office with new desktops
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 19 54. If the average cost per desktop is less than $242, then the purchase
manager will upgrade the office with new desktops
Read the following word problem:
The alternative hypothesis stated in the above example is:
A. The Standard Deviation is equal to $242
B. The Mean is greater than $2100
C. The Mean is equal to $1951
D. The Mean is less than $2100
E. The Mean is less than $2193
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 20 55. Read the following word problem:
After conducting a one-sample Z-test, the data indicates a Z-score of:
A. 4.93
B. 4.35
C. -4.35
D. -4.93
E. -7.07
56. Read the following word problem:
The statistical Degrees of Freedom for this example is:
A. 2
B. 19
C. 20
D. 21
E. 1
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 21 57. Read the following word problem
After conducting the appropriate one-sample T-test, the t statistic is
closest to:
A. -3.38
B. -2.62
C. -2.14
D. 2.15
58. Read the following word problem
Using the alpha level and the DF (Degrees of Freedom), what is the
critical-T for a 2-sided test as required in this case:
A. 1.833
B. 2.228
C. 2.262
D. 6.314
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 22 59. Read the following word problem
The distributor fails to reject the null hypothesis stating the average
sales/month is equal to $12,000:
True|False
60. The use of Proportion versus a Target tests:
A. If the process proportion equals some desired value
B. If the process proportion equals some value range
C. If the target is current
D. If the proportion of the tail is equal
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 23 Improve…
61. Which statements are true about the regression shown below? (Check
all that apply)
Fitted Line Plot
Y = 130.5 - 0.8714 KNOB-C
S
R-Sq
R-Sq(adj)
110
6.52267
36.0%
32.5%
Y
100
90
80
70
30
35
40
KNOB-C
45
50
A.
B.
C.
D.
When Knob C increases, the output Y increases.
The slope of the equation is a positive 130.5
The predicted output Y is close to 104 when Knob C is set to 30.
Over 30% of the variation of the output is explained by the
independent variable with the Linear Regression.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 24 62. Multiple regressions are best used for:
A. Non-linear relationships between an X and a Y.
B. Uncertainty in the slope of the linear relationship between an X and a
Y.
C. Relationships with no correlations found between an X and a Y.
D. Relationships between Y and two or more X’s.
E. Replacing the use of a designed experiment.
63. Which statements are correct about residuals from a proper,
statistically correct linear regression analysis? (Check all that apply)
A.
B.
C.
D.
E.
F.
All of the residuals will be within 3 Standard Deviations of the residuals.
Most residuals are within 2 Standard Deviations of the residuals.
The errors or residuals are Normally Distributed.
The variance of the errors varies significantly across the process range.
The sum of the residuals are zero.
The residual, as defined by MINITABTM, is equal to the predicted value
subtracted from the observed value.
64. Which statement is most correct about Regression Analysis?
A. A Regression with an R2 and R2 adj. greater than 80% is required for a
statistically valid conclusion.
B. If the correlation was insignificant, the Linear Regression should be
significant with the same data.
C. A multiple Linear Regression includes interaction effects.
D. Non-linear Regressions can explain curvature with more statistical
confidence than Linear Regressions.
E. A Regression explains why X changes the Y with the mathematical
expression.
F. A correlation does not explain causation but a Regression Analysis with
a statistically valid mathematical equation does explain causation.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 25 65. Which relationships can be modeled with a Regression Equation?
(Check all that apply)
A.
B.
C.
D.
E.
Simple Linear
Quadratic
Cubic
Multiple Linear
Logarithmic
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 26 66. Which statements are true for the Regression Analysis shown below?
(Check all that apply)
Regression Analysis: Y versus KNOB-C
The regression equation is Y = 130 - 0.871 KNOB-C
Predictor
Coef
SE Coef
T
P
130.50
11.39
11.46
0.000
-0.8714
0.2737
-3.18
0.005
Constant
KNOB-C
S = 6.52267
R-Sq = 36.0%
R-Sq(adj) = 32.5%
Analysis of Variance
Source
DF
SS
MS
F
P
1
431.14
431.14
10.13
0.005
Residual Error
18
765.81
42.55
Total
19
1196.95
Regression
Unusual Observations
Obs
KNOB-C
Y
Fit
SE Fit
Residual
St Resid
14
50.0
75.00
86.93
2.80
-11.93
-2.02R
18
29.0
98.00
105.22
3.66
-7.22
-1.34 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
A.
B.
C.
D.
E.
Two observations are having a large influence on the Regression.
Two observations have standardized residuals larger than 2.
20 observations were used in this Regression Analysis.
18 residuals or errors are in the Regression Analysis.
This Regression has statistical significance assuming the residuals follow
the assumptions of a residual analysis.
F. 19 observations were used in this Regression Analysis.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 27 67. Which statements are correct for the Regression Analysis below?
(Check all that apply)
Regression Analysis: Tons mined versus Personnel hours
The regression equation is
Tons mined = 4.359 + 0.000310 Personnel hours
S = 0.0559431
R-Sq = 39.2%
R-Sq(adj) = 33.1%
Analysis of Variance
Source
DF
SS
MS
F
P
1
0.0201823
0.0201823
6.45
0.029
Error
10
0.0312964
0.0031296
Total
11
0.0514787
Regression
A. This Regression is an example of simple Linear Regression.
B. This Regression is statistically significant because the P-value is less
than 0.05 and the residuals are appropriate.
C. This Regression is statistically insignificant because Rsquared is much
less than 80%.
D. The independent variable is “tons mined”.
E. If each month was one observation value, 11 months of data was used
to analyze for this Regression.
68. Which statements are true about multiple Regressions? (Check all that
apply)
A.
B.
C.
D.
E.
F.
Multiple Regressions are a form of experimentation.
The X’s are assumed to be independent of each other.
The X’s are assumed to not be correlated.
The residuals or errors are assumed to be Normally Distributed.
Interactions are NOT included in multiple Linear Regressions.
R2 and the statistical confidence of the coefficients are impacted by
the measurement error of the inputs or X’s.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 28 69. Which statements are correct about the Regression below? (Check all
that apply)
Fitted Line Plot
No. of customers per hour = - 0.416 + 0.1526 Outside temperature
+ 0.04166 Outside temperature**2
No. of customers per hour
70
50
40
30
2.91382
98.6%
98.4%
20
10
0
-10
S
R-Sq
R-Sq(adj)
60
Regression
95% CI
95% PI
80
0
10
20
30
Outside temperature (deg C)
40
A. The independent variable is the outside temperature.
B. The Regression is an example of a cubic equation.
C. With at least 95% confidence, we can expect less than 30 customers
per hour when the outside temperature is 21 deg C.
D. If the outside temperature was to increase from 20 to 30 deg C, the
number of customers per hour should increase by nearly 20.
E. If the outside temperature increases, the expected number of
customers per hour would increase.
F. If the outside temperature was 35 deg C, with 95% confidence we
would expect a minimum of 48 customers per hour. © Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 29 70. Which statements are correct about the DOE factorial plot output
shown below? (Check all that apply)
Cube Plot (data means) for Distance
8.20
4.55
3.35
1.50
1
Stop Angle
5.15
2.40
1
2.10
Fulcrum
0.90
-1
-1
-1
Start Angle
1
A. The 3 factors were operated at 3 levels each.
B. The highest distance was achieved with the start angle at the low level
while the fulcrum and stop angle were at the high level.
C. The design indicated above is a 32 factorial design.
D. The fulcrum and start angle are at the low level for the lowest distance
achieved.
E. All factors had 2 levels in the experiment.
F. The average distance achieved when all factors were at the high level
is 4.55.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 30 71. Which statements are correct about the factorial plot shown above?
(Check all that apply)
Main Effects Plot (data means) for Distance
Main Effects Plot (data means) for Distance
5.0
4.0
4.5
Mean of Distance
Mean of Distance
4.5
5.0
3.5
3.0
2.5
2.0
4.0
3.5
3.0
2.5
2.0
-1
1
Fulcrum
-1
1
Stop Angle
A. When the stop angle increases from low to high level, the distance
increases.
B. The coefficient of the fulcrum is positive related to the output of
distance.
C. The coded coefficient is larger for the fulcrum than the stop angle
related to the output of distance.
D. These plots prove a statistically significance factor with 95%
confidence.
E. These plots are an example of interaction plots.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 31 72. Which statements are correct for the plot shown above for the 23 full
factorial design with no replicates or center points? (Check all that apply)
Interaction Plot (data means) for C8
7
S
6
B
-1
1
Mean
5
4
3
2
1
R
-1
1
C
A. 4 experimental runs make the Mean for the point indicated by R.
B. 2 experimental runs make the mean for the point indicated by S.
C. S indicates when the factor C is at the low level and the second
factor is at the high level.
D. Some interaction exists between these 2 factors.
E. The design has a total of 8 experimental runs.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 32 73. Which statements are true about fractional factorial designs? (Check
all that apply)
A. Half fractional experiments do not exist for those with only 2 factors.
B. Quarter fractional experiments can exist for those with 4 factors.
C. Resolution V or higher designs are desired unless the experiment is for
screening purposes.
D. A half fractional design for 5 factors has the same number of
experimental runs as a full factorial design for 4 factors assuming no
repeats or replicates or center points.
E. The danger with fractional factorial designs is the consequence of the
main effects always being confounded with 2-way effects to reduce
the number of experimental runs
74. Which statements are true about experimental designs? (Check all
that apply)
A. Experimental designs include RSM, full factorials, and fractional
factorials
B. If an experimental design was created with no replicates on the corner
points and center points were added, the number of experimental runs
is larger than the same design without center points.
C. Fractional factorial designs have too few runs to obtain a
mathematical expression between the output(s) of interest and the
statistically significant inputs.
D. A fractional factorial or full factorial 2-level design can give the
experimenter a mathematical expression between the output(s) of
interest and the statistically significant inputs.
E. All fractional factorial designs for experiments with 7 or fewer factors
have some aliasing or confounding.
F. A resolution III design is an appropriate design for optimizing a process.
G. An experimental design should not have more than one output
because of the difficulty in selecting factor levels.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 33 75. Which statement best describes why experimental runs are
randomized?
A. The inspection or testers will not know what results to expect so the
experimental design is best as a blind study.
B. The randomized experimental design does not allow the operators or
technicians involved with the study to predict the course of the study.
C. A randomized experiment prevents orthogonality of an experiment’s
results.
D. Noise within the experimental study is spread across the effects and
interactions giving greater statistical confidence.
E. Randomized experiments are usually faster to execute within the
process.
76. What are some reasons for all factors’ main effect being statistically
insignificant in a DOE? (Check all that apply)
A. The DOE should have had Center Points added.
B. Not enough replicates to give statistical confidence
C. The levels for the factors were too small to create an effect with
statistical confidence.
D. The levels for the factors were too large and the process output had an
undetected local maximum or minimum.
E. The measurement system error was too large relative to the changes in
the process output.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 34 77. Which statements are correct about the MINITABTM output from an
analysis of this DOE? (Check all that apply)
Factorial Fit: Yield versus Temp, Supplier
Estimated Effects and Coefficients for Yield (coded units)
Term
Effect
Coef
SE Coef
T
P
61.1250
0.1847
330.94
0.000
23.4500
11.7250
0.1847
63.48
0.000
0.0000
0.0000
0.1847
0.00
1.000
Temp*Supplier
10.0500
5.0250
0.1847
27.21
0.000
S = 0.738805
R-Sq = 99.75%
Constant
Temp
Supplier
R-Sq(adj) = 99.69%
Analysis of Variance for Yield (coded units)
Source
DF
Seq SS
Adj SS
Adj MS
F
P
Main Effects
2
2199.61
2199.61
1099.80
2014.91
0.000
2-Way Interactions
1
404.01
404.01
404.01
740.17
0.000
Residual Error
12
6.55
6.55
0.55
Pure Error
12
6.55
6.55
0.55
15
2610.17
Total
A. The total number of factors studied in the experimental design was 2.
B. The total number of factors studied in the experimental design cannot be
confirmed with this output.
C. The number of experimental runs in this experiment is 15.
D. The number of experimental runs in this experiment is 16.
E. The number of residuals, defined as the modeled or expected value
subtracted from the observed value, is 12.
F. The number of residuals, defined as the modeled or expected value
subtracted from the observed value, is 13.
G. The number of residuals, defined as the modeled or expected value
subtracted from the observed value, is 16.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 35 78. Which statements are correct about the Pareto chart of effects from
MINITABTM’s analysis of an experimental design. (Check all that apply)
Pareto Chart of the Effects
(response is % react, Alpha = .10)
3.78
F actor
A
B
C
D
E
B
D
BD
DE
E
N ame
A
B
C
D
E
Term
CE
A
AB
BC
BE
AE
AD
AC
CD
C
0
5
10
Effect
15
20
Lenth's PSE = 1.875
A. The number of experimental runs are 15 in this experiment.
B. Factor B has the largest effect on the output measured in the
experiment.
C. Factor C has the smallest effect on the output measured in the
experiment’s results.
D. Main effects B, D, and E and 2-way interactions BD and DE should be
retained in the mathematical model if the alpha is set to 10%
E. Main effects B, D, and E and 2-way interactions BD and DE should
be retained in the mathematical model if the alpha is set to 90%
F. Main effects C and A and the 2-way interactions AB, BC, BE, AE, AD,
AC, and CD, and CD should be retained in the mathematical
model if the alpha is set to 10%.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 36 79. Which statements are correct for the output graph from a MINITABTM
analysis of a designed experiment? (Check all that apply)
Normal Probability Plot of the Standardized Effects
(response is % Reacted, Alpha = .05)
99
B
95
90
Percent
F actor
A
B
C
D
E
BD
D
80
Effect Ty pe
Not Significant
Significant
70
60
50
40
30
N ame
F eed
C ataly st
A gitation
Temp
C oncentration
20
E
10
5
1
DE
-10
-5
0
5
10
Standardized Effect
15
20
A. The factor with the largest absolute value effect is Catalyst.
B. The main effect with the largest impact that reduces % reacted is
Concentration. An effect is defined as the impact when going from
the low level to high level for a factor.
C. The factors without an effect on the output with 95% confidence
include Feed and Agitation
D. The largest factor that increases the % reacted the most is Catalyst.
E. We are certain no other factors were in the experimental design
because of this probability plot.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 37 80. If the response is the output from the experimental design, which
statements are true about the design shown above? (Check all that
apply)
A.
B.
C.
D.
E.
F.
G.
The experimental design has 4 Center Points.
The design has 2 levels for each factor.
This design is a half-fractional design.
This design has 2 replicates at the Corner Points.
The resolution of this design is undeterminable.
This design is orthogonal.
The Adv main effect is confounded with the Bev*Des 2-way
interaction because it is a resolution III design.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 38 Control…
81. What is the most frequent reason for selecting the base factor for a
steepest ascent design?
A. The statistically significant factor has the largest absolute value
coefficient
B. The statistically significant factor has the smallest absolute value
coefficient
C. The statistically significant factor is easy to alter
D. The factor is involved in an interaction but not a statistically significant
main effect
82. If the Belt has found a good, statistically significant model from the last
full factorial design, what is the main reason a steepest ascent design be
considered in the project?
A. 4 factors were found to be statistically significant
B. The desired process output was not yet found within the original design
space
C. The project target was achieved but the project wants to further
improve the process
D. The DOE indicated curvature because Center Points were included
and the local, desired maximum was within the original design space.
83. Advanced Capability Analysis for defects per unit is not possible within
MINITABTM.
True | False
84. Advanced Capability Analysis for % defective is possible within
MINITABTM.
True | False
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 39 85. Which statements are correct about the advanced capability analysis
shown below? (Check all that apply)
U C har t
Defect Rate
1
0.45
0.4
0.30
U C L=0.3008
0.15
_
U =0.1738
DP U
Sample C ount P er Unit
Capability Analysis of defective reports
LC L=0.0468
0.00
1
4
7
10
13 16 19
Sample
22
25
0.3
0.2
0.1
70
28
90
Sample Size
110
Tests performed w ith unequal sample sizes
C umulative DP U
Dist of DP U
S ummary S tats
0.20
(using 95.0% confidence)
M ean DP U :
Low er C I:
U pper C I:
M in DP U :
M ax DP U :
Targ DP U :
DP U
0.18
0.16
0.1738
0.1586
0.1901
0.0935
0.4375
0.1000
0.14
5
10
15
20
Sample
25
30
Tar
12
9
6
3
0
0.
10 . 15 .2 0 .25 . 30 .3 5 .40 . 45
0 0 0 0 0 0 0
A.
B.
C.
D.
This is a Poisson Capability Analysis
The average DPU with 95% confidence is between 0.16 and 0.19
The DPU does not seem to vary depending on sample size
The process shows only one instance of being out of control statistically
so we have confidence in the estimated DPU of this process.
E. The maximum DPU in one observation was nearly 0.195.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 40 86. Process Capability is discussed in the Control Phase. Why is Process
Capability considered in the Control Phase of a Six Sigma project?
(Check all that apply)
A. Process Capability is a way of predicting future performance when
a stable process exists.
B. Special Causes reduce Predictability and Process Capability
measures process Predictability relative to specifications.
C. Process Capability uses the same equations for Normal and Nonnormal processes
D. If the process is Non-normal the type of distribution must be
remembered when monitoring a process in the Control Phase. This
type of Non-normal Distribution must be known to run a proper
process Capability Analysis.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 41 87. What statements are true from the process shown below in the
Capability Analysis? (Check all that apply)
Process Capability Sixpack of Wine(ml)
Xbar C har t
C apability H istogr am
Sample Mean
UCL=223.184
222
LSL
USL
S pecifications
LS L 215
U S L 225
_
_
X=220.611
220
218
LCL=218.038
1
3
5
7
9
11
13
15
17
19
216
Sample Range
R C har t
220
226
LCL=0
1
3
5
7
9
11
13
15
17
19
215
Within
S tD ev 2.10115
Cp
0.79
C pk
0.7
220
215
5
10
Sample
220
225
230
C apability P lot
Last 2 0 Subgr oups
225
Values
224
_
R=5.32
5
0
A.
B.
C.
D.
E.
222
Nor mal P r ob P lot
A D : 0.134, P : 0.979
UCL=10.67
10
218
15
20
Within
O v erall
O v erall
S tD ev 2.10797
Pp
0.79
P pk
0.69
C pm *
S pecs
The process is stable and in control.
The process is properly assumed to be a Normal process.
The Mean of the process is 5.32
This Capability Analysis used subgroups.
More of the wine bottles are over filled than under filled.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 42 88. Which statements are true about the process shown above? (Check
all that apply)
Process Capability of Weight
Calculations Based on Largest Extreme Value Distribution Model
LSL
USL
P rocess Data
LS L
215
Target
*
USL
225
S ample M ean 221.126
S ample N
120
Location
219.715
S cale
2.42756
O v erall C apability
Pp
0.48
PPL
1.02
PPU
0.29
P pk
0.29
E xp. O v erall P erformance
P P M < LS L
934.43
P P M > U S L 107194.67
P P M Total 108129.09
O bserv ed P erformance
P P M < LS L
0.00
P P M > U S L 133333.33
P P M Total 133333.33
216
219
222
225
228
231
A. The initial focus for this project would be to determine why the
weights are so frequently too low.
B. The majority of the process is within specification.
C. This process is described with the Weibull Distribution.
D. The Ppk is much less than 1.0
E. The process has more problems with variation than Centering.
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 43 89. Lean tools can keep help sustain a process improvement or be a good
basis for taking “Noise” out of the system prior to the completion of the
Measure Phase. The most basic of all Lean tools that support the other
Lean tools is best known as:
A.
B.
C.
D.
E.
Kanbans
Kaizens
Kaikaku
5S
Standardized work instructions
90. The foundation of a Visual Factory is:
A.
B.
C.
D.
Technically skilled workers
Work space with active 5S
Inventory control
Breakthrough projects
91. Examples of items necessary to support standardized work include:
(Check all that apply)
A.
B.
C.
D.
E.
Availability of required tools and supplies where and when needed
Machines continually operating to reduce the labor cost per piece
Zero inventory to prevent Muda of excess inventory
Labeled inventory of in-process stock
Consistent flow of work across the process
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 44 92. Which basic tool listed below should be the last tool attempted at a
process step that has variation causing Special Causes in the Six Sigma
project?
A.
B.
C.
D.
Kanban
Kaizen
SPC
Poka-Yoke
93. Which are examples of defect prevention to consider in your
execution of the Control Phase of your project? (Check all that apply)
A.
B.
C.
D.
E.
Poka-Yoke or Mistake Proofing
Monte Carlo simulation
FMEA
Robust product design
Negotiate new specification limits from customers
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 45 94. Which statement is most correct for the above process shown below?
If the process wants to be 95% confident of a defect free process, where
should we maintain the input if the output must be less than 6.
Fitted Line Plot
Output2 = 10.81 - 0.2826 Input3
12
Regression
95% PI
10
S
R-Sq
R-Sq(adj)
Output2
8
0.575981
96.1%
96.0%
6
4
2
0
0
A.
B.
C.
D.
E.
F.
10
20
Input3
30
40
The input3 must be greater than 20
The input3 must be greater than 17
The input3 must be greater than 12
The input3 must be less than 20
The input3 must be less than 17
The input3 must be less than 12
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 46 95. Every process has causes of variation commonly known as: (Check all
that apply)
A.
B.
C.
D.
Common
Insignificant
Special
Uneducated
96. SPC charts typically incorporate Control Limits indicating Special
Causes of what width from the Center Line?
A.
B.
C.
D.
+/- 2 sigma
+/- 3 sigma
+/- 4.5 sigma
+/- 6 sigma
98. Subgroups are used in which types of SPC charts? (Check all that
apply)
A.
B.
C.
D.
Xbar charts
R charts
MR charts
nU charts
99. Which SPC chart should be selected with the following conditions:
attribute output with no Poka-Yoke available and the tracking of %
defective desired with a sample size across the 25 tellers?
A.
B.
C.
D.
E.
NP chart
P chart
U chart
C chart
I-MR chart
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 47 100. Which tests for Special Causes was violated that would have
prompted an action from the OCAP in the above SPC chart? (Check all
that apply)
Xbar-R Chart of Part1, ..., Part5
35
Sample M ean
U C L=33.07
30
_
_
X=26.33
25
20
LC L=19.59
1
6
11
16
21
26
Sample
31
36
41
46
1
U C L=24.72
Sample Range
24
18
_
R=11.69
12
6
0
LC L=0
1
6
11
16
21
26
Sample
31
36
41
46
A.
B.
C.
D.
One point was greater than 3 sigma from the Center Line
9 points in a row were on the same side of the Center Line
6 points in a row were all consecutively increasing or all decreasing
8 points in a row were greater than one sigma from either side of
the Center Line
E. No tests were violated for either the within or between group
variation
© Open Source Six Sigma, LLC Individual use only, unauthorized reproduction and distribution is strictly prohibited. 48