Deck 5: Certified Six Sigma Black Belt

Question 1

Which statement(s) are incorrect for the Regression Analysis shown here? (Note: There are 2 correct answers).

A) The air-fuel ratio explains most of the TurbineOutput variation
B) The Regression explains over 98% of the process variation
C) This Multiple Linear Regression has three statistically significant independent variables
D) If the air-fuel ratio increases by 1, the TurbineOutput more than triples
E) The SteamExitTemp explains the most variation of the TurbineOutput

Answer 1

D,E

Question 2

Fractional Factorial designs are used to reduce the ____________ because the number of runs has been lowered.

A) Time and cost of experiments
B) Number of people involved
C) Number of data measurement points
D) Output summary

Answer 2

A

Question 3

A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade.  The purchasing manager is depending on the Belt's effort requiring that the average cost of an internal critical raw material component be less than or equal to $4,200 in order to stay within budget.  Using a sample of 35 first article components, a Mean of the new product upgrade price of $4,060, and a Standard Deviation of $98 was estimated. Select the answer that best states the Practical Problem.

A) If the average cost per component is $4,200 or less, then the purchase manager will introduce the new product upgrade with new components.
B) If the average cost per component is greater than $4,200, then the purchase manager will introduce the new product upgrade with new components.
C) Only if the average cost per product upgrade is $4,060, will the purchase manager introduce new product upgrades with new components.
D) If the average cost per new product upgrade is less than $180, then the purchase manager will introduce the new product upgrade with new components.

Answer 3

C

Question 4

Which of these might contribute to similar distributions having Unequal Variance?

A) Extreme tails
B) Outliers
C) Multiple Modes
D) All of the above

Question 5

Which statement is NOT correct about the Fitted Line Plot shown here?  

A) The independent variable is the reactant
B) If the reactant was 6 units, with 95 % confidence we would expect a minimum yield of 100 units
C) With at least 95% confidence, we can expect less than 10 units of Yield when the reactant is at a value of 1
D) A reactant value between 2 and 4 units yields around 20 to 40
E) When the reactant increases, the expected yield would increase

Question 6

When a Belt decides to use written procedures and visual controls to improve the consistency of the tasks that must occur in the process he is improving he has utilized the _________________ activity of 5S.  

A) Sustaining
B) Sorting
C) Standardizing
D) Straightening

Question 7

A Full Factorial experiment using a 3 level 3 factor approach has been proposed to test the viability of an extrusion machine experiment. How many treatment combinations will this approach involve?

A) 6
B) 9
C) 27
D) 54

Question 8

When a Belt conducts a Linear Correlation Analysis and finds that as an X increases the Y also increase then he has proven a ______________ correlation.

A) Negative
B) Positive
C) Monomial
D) Single alignment

Question 9

A Factorial Experiment based on a Level 2 Design with 6 factors would require 16 runs to fully assess the interactions.

Question 10

When doing Hypothesis Testing on Non-normal data Belts will use a ________________ to compare more than two sample proportions to each other.

A) Z score Table
B) Sakami Table
C) Mean-to-Mode Analysis
D) Contingency Table

Question 11

A valid mathematical Regression represents all of the characteristics shown except ___________________________.

A) The residuals when plotted follow a Normal Distribution
B) The sum of the residuals is zero
C) All of the standardized residuals will be within ±3 Standard Deviations
D) Most standardized residuals are within ±2 Standard Deviations

Question 12

SPC Charts are used extensively in different business and decision-making environments.  In this example a vendor is being selected based on speed of delivery. Which of the conclusions would help you pick a vendor for your needs regarding lead-time of delivery from your vendors? (Note: There are 4 correct answers).

A) Vendor A with a much shorter lead time in delivery
B) Vendor B as it has a better consistency (lower variance) on lead time
C) Vendor B as Vendor A shows a situation out of control as shown in red
D) Vendor B as the Control Limits are much narrower than Vendor A
E) Vendor B with higher lead time, but a process with much narrower Control Limits

Question 13

When a Belt properly analyzes the results of an experiment he must examine the Residuals in expectation of finding all of the following except _________.

A) Some Residuals higher than others
B) Some Residuals lower than others
C) All Residuals within 2 Standard Deviations of the Mean
D) Residuals will represent a Linear Regression

Question 14

A valid Multiple Linear Regression (MLR) is characterized by all of these except _______________________.  

A) It is an assumption that the X's (inputs) are not correlated to each other
B) The X's (inputs) are assumed to be independent of each other
C) MLR is conducted based on a deliberate form of experimentation
D) The Residuals from MLR analysis have to be Normally Distributed

Question 15

It would be more likely than not for a Belt conducting a Regression Analysis to find that the _______________________.

A) r2 value is smaller than the absolute value of r
B) Correlation Coefficient equals r2
C) Coefficient of Determination is less than r2
D) Correlation Coefficient equals r divided by 2

Question 16

Screening experiments are the proper choice when a Belt is faced with the situation of highly Fractional Factorial Designs.

Question 17

Which statement(s) are most correct for the Regression Analysis shown here?

A) The Regression explains 50.8% of the process variation
B) The air-fuel ratio explains most of the TurbineOutput variation
C) This Simple Linear Regression explains 98+% of the process variation
D) This Multiple Linear Regression has four statistically significant independent variables

Question 18

Which statement(s) are correct about the Regression shown here? (Note: There are 2 correct answers).

A) The dependent variable is the outside temperature
B) The relationship between outside temperature and number of customers per hour is a Linear Regression
C) The dashed lines indicate with 95% confidence where all of the process data should fall between
D) The dashed lines indicate with 95% confidence the estimate for the Quadratic Regression Line
E) The predicted number of customers per hour is close to 5 if the outside temperature is 10 deg C

Question 19

Fractional Factorial Designs are used to analyze factors to model the output as a function of inputs if Hypothesis Testing in the Analyze Phase was inadequate to sufficiently narrow the factors that significantly impact the output(s).

Question 20

Which statement(s) are correct about the DOE Factorial plot output here? (Note: There are 3 correct answers).

A) Two factors were operated at 3 levels each
B) The highest tool age was achieved with metal hardness at high level while keeping the cutting speed at the low level
C) The design indicated above is a 32 factorial design
D) The cutting speed and cutting angle are at the low level for the least tool age achieved
E) All factors had 2 levels in the experiment

Question 21

A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade.  The purchasing manager is depending on the Belt's effort requiring that the average cost of an internal critical raw material component be less than or equal to $3,600 in order to stay within budget.  Using a sample of 42 first article components, a Mean of the new product upgrade price of $3,200 and a Standard Deviation of $180 was estimated. Based on the data provided, the Z value for the data assuming a Normal Distribution is?

A) 1.11
B) 2.22
C) 4.30
D) 5.42

Question 22

Since Normality is required if we intend to use the data collected as a predictive tool. To test for Normality of data we must determine if the P-value is ___________.

A) Equal to 0.05
B) Less than 0.05
C) Greater than 0.05
D) Greater than 0.5

Question 23

A statistical test or Hypothesis Test is performed to reject or fail to reject a stated hypothesis and it converts the Practical Problem into a Statistical Problem.

Question 24

When the Inputs, X's, for your process are Normally Distributed about the Mean, the Outputs, Y's, will always be Normally Distributed.

Question 25

To properly analyze the variables impacting the output of a process we need to collect data that represents at least 80% of the variation in the process and assure ourselves we are collecting data from all three types of variation which are _______________.

A) Within, Between and Temporal
B) Within, Between and Temporary
C) Without, Above and Below
D) Induced, Natural and Unavoidable

Question 26

From the variance F-test shown above, which of these conclusions is/are valid?

A) The variance between the class score distribution is significantly different
B) The variance between the class score distribution is not significantly different
C) This test applies only to Normal Distributed data at 99 % confidence
D) This test applies only to Non-normal Data at 99 % confidence
E) There are not enough data points to make any statistical conclusions

Question 27

On a _________________ a Belt screens variables, or various inputs, to analyze their relative impact on the output of concern.

A) X-Y Matrix
B) Weighted Scale
C) Multi-Vari Chart
D) Poisson Chart

Question 28

Some of the sources for different types of error that can be quantified using Statistical Analysis are ___________________.

A) Error in sampling
B) Bias in sampling
C) Error in measurement
D) All of these answers are correct

Question 29

Following process modifications, the Null Hypothesis states that no improvement to the process has occurred. If we discover the Null Hypothesis Test was rejected when it was false that would be a(n) ________________________.

A) Alpha Error
B) Type I Error
C) Type II Error
D) Type III Error

Question 30

Statistical Difference is the magnitude of difference or change required to distinguish between a true difference, brought about by change or improvement, and one that could have occurred by chance.  

Question 31

To be an effective Lean Six Sigma practitioner one must understand the difference between ___________________________.  

A) ANOVA and the Analysis of Variance
B) Nonparametric tests and tests of Non-normal Data
C) F-test and test of variances of 2 samples
D) Practical and Statistical significance

Question 32

The validity of the decision made with Hypothesis Testing is dependent upon all of these except ___________________.  

A) Beta risk
B) Alpha risk
C) Range of data
D) Sample size

Question 33

For a Normal Distribution as samples size increases the Range in Mean and Standard Deviation decrease relative to the Mean and Standard Deviation of the population.

Question 34

The Normal Distribution is considered to be the most important distribution in statistics and, among other things is defined as having a total area under the curve of 1, is mounded and symmetrical and the Mean, Median and Mode are _____________.

A) All evenly divisible by 3
B) Twice the Standard Deviation
C) Within 10% of each other
D) The same number

Question 35

A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade.  The purchasing manager is depending on the Belt's effort requiring that the average cost of an internal critical raw material component be less than or equal to $4,200 in order to stay within budget.  Using a sample of 35 first article components, a Mean of the new product upgrade price of $4,060, and a Standard Deviation of $98 was estimated. The Alternative Hypothesis in the above example is?

A) The Standard Deviation is equal to $300.
B) The Mean is less than $4,320.
C) The Mean is equal to $4,060.
D) The Mean is less than $4,200.
E) The Mean is greater than $ 4,200.

Question 36

Time is always the metric on the horizontal scale of a(n) ___________ Chart.

A) Pareto
B) Xbar
C) Multi-Vari
D) NP

Question 37

A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade.  The purchasing manager is depending on the Belt's effort requiring that the average cost of an internal critical raw material component be less than or equal to $3,800 in order to stay within budget.  Using a sample of 38 first article components, a Mean of the new product upgrade price of $3,680, and a Standard Deviation of $120 was estimated.  In order to increase the Long Term Z value to 5, what is the maximum long term variation in pricing the Belt can accept for his upgraded critical raw material component?

A) $6
B) $12
C) $24
D) $48

Question 38

Sally and Sara sell flower pots at their garage sale.  Sally motivates Sara mentioning that they will sell a minimum of 15 pots per day if the outside temperature exceeds 60o F.  From a sample, whose population is assumed to follow a Normal Distribution, taken for 30 days at 60 degrees or more an average of 13.6 pots per day were sold with a Standard Deviation of 0.7 pots. For the sales accomplished above, what test would validate if they met their requirements?

A) F Test
B) Test for Equal Variance
C) Chi Square Test
D) One-Sample t-Test

Question 39

When conducting a Hypothesis Test using Continuous Data the proper sample size is influenced by the extent to which we need to assess a Difference to be detected and the inherent variation in the process.  

Question 40

A Belt is analyzing data and upon creation of the graphical analysis sees multiple modes. One of the primary reasons this could occur is because the process has experienced a ____________________.

A) Significant change from one shift to another
B) Sizable Measurement System error
C) Catastrophic failure of some sort
D) Any one of these

Question 41

Relative to a Design of Experiments the term Collinear refers to variables being a ________________ of each other.

A) Linear combination
B) Directly parallel
C) Mirror image
D) None of the above

Question 42

If an experiment has 5 factors and no replicates for a 2-level Experimental Design with 16 experimental runs which statement(s) are correct? (Note: There are 3 correct answers).

A) The Main Effects for the 5 factors are not aliased or confounded but the 2-way interactions are confounded with the 3-way interactions
B) The Main Effects are confounded with only 4-way interactions
C) The Experimental Design is half-fractional
D) The experiment has 8 experimental runs with the first factor at the high level
E) The experiment has only 4 experimental runs with the 5th factor at the high level

Question 43

Each of the items listed would impact the Process Capability for a process with a continuous output except ___________________.  

A) Shape of process data distribution (e.g. Normal Distribution)
B) Process Technology
C) Process Standard Deviation
D) Seasonal variation in process

Question 44

A ___________ problem in the Measurement System suggests that there is a lack of consistency in the measurement over time.

A) Linearity
B) Bias
C) Stability
D) Magnitude

Question 45

Accuracy can be assessed in several ways and a fairly accurate means of measurement is visual comparison.

Question 46

The Lean toolbox includes all of the following items except __________.      

A) Poke-Yoke
B) Standard Operating Procedures
C) Kaizen
D) 5S the work area

Question 47

Appropriate measures means that measurements are ______________.  

A) Representative
B) Sufficient
C) Contextual
D) Relevant
E) All of these answers are correct

Question 48

Measurement __________ is defined as the difference between the observed and the expected values for a given set of data.

A) Breadth
B) Linearity
C) Range
D) Bias

Question 49

Questions that can be best answered by a Visual Factory include all of these except _____________________.  

A) Are setups optimized for lower scrap levels?
B) Can extra inventory be seen easily?
C) Can changeover challenges be recognized?
D) Are unneeded tools or supplies easily noted?

Question 50

What aspects of Measurement Systems Analysis (MSA) studies are applicable when the process used to measure does not damage the part?

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

Question 51

What is the Ppk of a process with a spread of 24 units, an average of 68, an upper limit of 82 and a lower limit of 54?

A) 1.68
B) 2.00
C) 4.00
D) 4.42

Question 52

How many experimental runs exist in a Full Factorial and fully randomized design for 5 factors with 2 replicates for the Corner Points and no Center Points?  The factors in the experiment are only at 2-levels.  

A) 10
B) 128
C) 256
D) 64

Question 53

For Attribute Data, Process Capability is defined as the average proportion of nonconforming products.

Question 54

In a good Measurement System the most variation will be with part-to-part measurements.  What should you do if the majority of variation is associated with the Gage R&R assuming the gage is technically capable?

A) Focus on fixing the Repeatability and Reproducibility of the measurement device
B) Purchase a new machine
C) Focus on trimming the Part-to-Part variation
D) Run another MSA test with the machine

Question 55

With Measurement System Analysis we are concerned with two issues that impact the potential variability of the data. They are ____________ and Accuracy.

A) Spread
B) Reliability
C) Precision
D) Deflection

Question 56

An operator is measuring the distance between two points. Which is most likely to be influenced by the operator?

A) Precision of the measurement
B) Accuracy of the measurement
C) Calibration of the instrument
D) All of these answers are correct

Question 57

When we compare short-term and long-term Capability which of these is true?

A) Cp is better for the short term
B) Both short-term and long-term performance are alike
C) Performance tends to improve over time
D) Cp is better for the long-term

Question 58

Which statements are correct about the advanced Capability Analysis shown here? (Note: There are 3 correct answers).  

A) This is a Poisson Capability Analysis.
B) The average DPU with 95% confidence is between 0.024 and 0.0295.
C) The DPU does not seem to vary depending on sample size.
D) 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 0.0753.

Question 59

An operator checks that all boxes being packed contain enough products to fill the box.  However, each box getting filled has a different number of products in it.  This is a Reproducibility problem, not a Repeatability problem.

Question 60

The reported Cpk for a process with an average of 104 units, a spread of 18 units and upper and lower specification limits of 122 and 96 units would be?

A) 0.5
B) 0.89
C) 1.00
D) 2.00

Question 61

If a Six Sigma project was to reduce changeover times and the team found the project success was decreasing over time since changeover times began to creep back up, which Lean tools should be considered in the Control Phase to reestablish and sustain the project success?  

A) Improve the lighting to assure adequate visibility
B) Confirm a Visual Factory exists to assure proper communication of status of machines
C) Implement Kanbans to assure enough inventory for the process step
D) Reword the standardized work instructions to use active verbs and not passive phrases

Question 62

If you can Poka-Yoke a defect out of the process entirely then you do not need use SPC on the characteristic of interest in the defect.  

Question 63

The Hardware Store ordered ten lawn mower from the manufacturer and just before shipping the manufacturer found one to have a motor that wouldn't start.  For the manufacturer this would be categorized as what type of cost?

A) Internal Failure Costs
B) External Failure Costs
C) Prevention Costs
D) Appraisal Costs

Question 64

One of the foundations of Lean Six Sigma is the concept that the output of a process (Y) is influenced by the process inputs (X's) and is commonly shown as which formula?

A) Y = Z(X2)
B) Y = f(X3)
C) Y = f(Xn)
D) Y = g(X+ 1.5)

Question 65

If a process has subgroups for Variable data and the process runs for a long period of time, then the best pair of SPC Charts to use would be an Xbar and _________.  

A) NP Chart
B) Individuals Chart
C) R Chart
D) C Chart

Question 66

When a Belt creates a Process Map she will use a __________________ to depict a decision point requiring a Yes or No decision.

A) Circle
B) Square
C) Diamond
D) Rectangle

Question 67

Range Charts are the technique used to determine if ______________ are occurring within the subgroups of the SPC Charts.

A) Common Causes
B) Special inspections
C) Unnatural forces
D) Special Causes

Question 68

For a Kanban to be successful which of these must occur?  

A) Consistent cycle times
B) Fairly stable process demand of product or service
C) Low defect rate of incoming product or service
D) All of the above

Question 69

A Belt has determined that the inventory of repair parts at a rework station can be reduced by 45%.  According to Cost of Poor Quality (COPQ) definitions inventory reduction would be considered _______________.  

A) Soft Savings
B) COPQ efficiency
C) Median Savings
D) Hard Savings

Question 70

Kaizens or Kaikakus and Six Sigma projects are intended to create breakthrough, significant process improvement versus minor, incremental improvements.  

Question 71

Six Sigma is a business improvement discipline whose fundamental view is based on a _________ oriented approach of the business.

A) Profit
B) Performance
C) Process
D) Predatory

Question 72

When we gather information for the Voice of the Business we are primarily interested in information concerning the _____________ of the business.

A) Advertising budget
B) Market share
C) Profitability
D) Ownership

Question 73

Special Cause Variation falls into which two categories? (Note: There are 2 correct answers).

A) Natural
B) Short term
C) Assignable
D) Pattern

Question 74

Much of the Six Sigma methodology is used to identify and remove causes for _____________ .

A) Process Variation
B) Material Costs
C) Excess Inventory
D) Lost Sales

Question 75

Using this partial Z Table, how many units from a month's production run are expected to not satisfy customer requirements for the following process? Upper specification limit: 7.2 Lower specification limit: 4.3 Mean of the process: 5.9 Standard Deviation: 0.65 Monthly production: 450 units

A) 3
B) 7
C) 10
D) 12

Question 76

When variation is removed from the output of a process then the process customer can have more confidence in the experience that results from the process.

Question 77

Common and Special Cause ______________ are the focus of Statistical Process Control.  

A) Prediction
B) Ideation
C) Capability
D) Variation

Question 78

Which of these items are not part of what is necessary for successful Kaizens?      

A) Good lighting
B) Management support
C) Operator support
D) Analysis tools

Question 79

The distance between the Mean of a data set and the Point of Inflection on a Normal curve is called the _______________.

A) Curve Spread
B) Standard Deviation
C) Numerical Average
D) Data Breadth

Question 80

Customers make their decisions based on Features, Integrity (of the seller) Delivery and ___________?

A) Color
B) Expense
C) Season
D) None