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    Free ASQ Certified Six Sigma Green Belt Sample Questions

    35 free sample questions from our bank of 504+, covering every exam domain, with answers and detailed explanations. Updated September 2026.

    Domain 1: Overview: Six Sigma and the Organization

    Subdomain 1.2: Lean principles in the organization

    1.A bakery operates 480 minutes per day and customers demand 240 loaves per day. What is the takt time?

    1. A.2 minutes per loaf
    2. B.1 minute per loaf
    3. C.0.5 minutes per loaf
    4. D.4 minutes per loaf
    Show answer & explanation

    Correct answer: A2 minutes per loaf

    • A. This is correct. Dividing the 480 available minutes by the 240 loaves of daily demand gives a takt time of 2 minutes per loaf, meaning the bakery must complete a loaf every 2 minutes to keep pace with demand.
    • B. This would result from dividing demand by available time or from an arithmetic error, but it does not match 480 divided by 240.
    • C. This value is too fast for the given numbers and would only be correct if demand were 960 loaves per day, which is not the case here.
    • D. This value is too slow for the given numbers and would only be correct if demand were 120 loaves per day, which is not the case here.

    Subdomain 1.2: Lean principles in the organization

    2.A Green Belt suspects that a defect is caused by an inconsistency in how operators assemble a part, but data collected from reports is inconclusive. What should the Green Belt do next, according to lean practice?

    1. A.Walk to the assembly station and directly observe how operators perform the task
    2. B.Recreate the assembly process from memory using the process documentation on file
    3. C.Interview the shift supervisor by phone about what operators may be doing wrong
    4. D.Analyze the defect reports again using a different statistical software package
    Show answer & explanation

    Correct answer: AWalk to the assembly station and directly observe how operators perform the task

    • A. This is correct and reflects the gemba principle: going to where the work actually happens and observing operators directly reveals inconsistencies that reports and secondhand accounts cannot capture.
    • B. Working from memory and documentation alone does not reveal how the task is actually being performed on the floor, which is the gap the Green Belt needs to close.
    • C. A phone interview with a supervisor is still secondhand information about the work rather than direct observation of the operators performing the assembly.
    • D. The reports have already been described as inconclusive, so reanalyzing the same data with different software does not address the need to observe the actual work being performed.

    Subdomain 1.1: Six sigma and organizational goals

    3.A plant director is deciding whether to invest in a formal Six Sigma program instead of relying on ad hoc improvement efforts. Which of the following best explains the rationale for adopting Six Sigma?

    1. A.Reduce process variation and defects using structured, data-driven improvement projects tied to business results.
    2. B.Replace the organization's entire quality system with a single certification requirement for all employees.
    3. C.Guarantee zero defects in every process regardless of industry, product, or service complexity.
    4. D.Focus improvement efforts solely on employee satisfaction surveys instead of process performance.
    Show answer & explanation

    Correct answer: AReduce process variation and defects using structured, data-driven improvement projects tied to business results.

    • A. Six Sigma is adopted because it gives organizations a structured, statistically grounded method for reducing variation and defects, which in turn drives measurable business outcomes such as cost savings and quality gains. This is the core rationale organizations cite for investing in Six Sigma programs over unstructured efforts.
    • B. Six Sigma does not replace an organization's broader quality management system, nor does it require universal employee certification. It typically operates alongside existing quality systems, applied selectively through trained project teams.
    • C. No methodology, including Six Sigma, can guarantee zero defects; the name refers to a statistical target of very low defect rates, not an absolute guarantee. Overstating this as a certainty misrepresents how the approach actually works.
    • D. Six Sigma projects are driven by measurable process performance data, not employee satisfaction surveys alone. Satisfaction may be one input among many, but it is not the sole focus of the methodology.

    Subdomain 1.3: Design for six sigma (DFSS) methodologies

    4.A team building a new online loan application process wants to confirm that the completed workflow lets applicants actually accomplish their real goal of getting a fast, clear lending decision, not just that it matches the written technical specification. Which activity are they performing?

    1. A.Validation
    2. B.Verification
    3. C.Occurrence rating
    4. D.Control charting
    Show answer & explanation

    Correct answer: AValidation

    • A. This is correct. Checking whether the finished process truly meets the applicant's real underlying need, rather than just its written specification, is the definition of validation in DFSS terminology.
    • B. Verification would instead mean confirming the workflow matches its documented technical specification, which the scenario explicitly says is not what the team is checking here.
    • C. Occurrence rating is an FMEA scoring factor for how often a failure happens, unrelated to comparing a finished process against customer needs.
    • D. Control charting is a statistical monitoring tool used during ongoing process control, not an activity for comparing a completed design against customer needs.

    Domain 2: Define Phase

    Subdomain 2.1: Project identification

    5.An order-to-cash process starts in the sales department, moves through credit approval in finance, and ends with shipment in the warehouse. A Six Sigma team mapping this process struggles to get consistent data because each department tracks the work differently. What challenge does this scenario illustrate?

    1. A.Processes that cross multiple functional areas create data-consistency and ownership challenges because each department measures the work differently.
    2. B.The process lacks a documented SIPOC diagram, which is the only tool capable of resolving cross-department measurement differences.
    3. C.The sales department is solely responsible for the delay because it initiates the process before finance becomes involved.
    4. D.Cross-functional processes always require replacing the existing information system before any improvement work can begin.
    Show answer & explanation

    Correct answer: AProcesses that cross multiple functional areas create data-consistency and ownership challenges because each department measures the work differently.

    • A. Processes that span multiple departments commonly suffer from inconsistent measurement and unclear ownership, which is exactly this scenario.
    • B. A SIPOC diagram helps scope a process, but it is not described as the only tool that can fix measurement inconsistencies.
    • C. Blaming a single department misreads the problem; the challenge is systemic across all the functions the process crosses.
    • D. Replacing the information system is not a required or implied first step in resolving cross-functional measurement gaps.

    Subdomain 2.3: Project management basics

    6.Using the standard PERT weighted-average formula, an activity has an optimistic estimate of 4 days, a most likely estimate of 6 days, and a pessimistic estimate of 14 days. What is the expected duration?

    1. A.7 days, calculated as (optimistic + 4 times most likely + pessimistic) divided by 6
    2. B.8 days, calculated as the simple average of the three estimates
    3. C.6 days, calculated by using only the most likely estimate
    4. D.9 days, calculated as the midpoint between the optimistic and pessimistic estimates
    Show answer & explanation

    Correct answer: A7 days, calculated as (optimistic + 4 times most likely + pessimistic) divided by 6

    • A. This is correct because applying the PERT formula gives (4 + 4×6 + 14) / 6 = 42 / 6 = 7 days.
    • B. This is incorrect because a simple average of the three estimates, (4 + 6 + 14) / 3, gives 8 days, which does not match the weighted PERT formula.
    • C. This is incorrect because using only the most likely estimate ignores the optimistic and pessimistic values entirely, which defeats the purpose of the weighted estimate.
    • D. This is incorrect because averaging only the optimistic and pessimistic values, (4 + 14) / 2, gives 9 days and ignores the most likely estimate's weighting.

    Subdomain 2.3: Project management basics

    7.A Six Sigma project has reached its final review. Which of the following should the team complete as part of proper project closure? (Select all that apply)(Select 4)

    1. A.Compare the achieved results against the objectives stated in the original project charter
    2. B.Complete and archive project documentation so it can be referenced by future teams
    3. C.Capture lessons learned and share applicable insights with other parts of the organization
    4. D.Begin drafting the charter for an unrelated project the team has not yet been assigned
    5. E.Delete the historical data collected during the Measure phase to save storage space
    6. F.Review the outcome with team members and sponsors to confirm the project's objectives were met
    Show answer & explanation

    Correct answers: A, B, C, FCompare the achieved results against the objectives stated in the original project charter; Complete and archive project documentation so it can be referenced by future teams; Capture lessons learned and share applicable insights with other parts of the organization; Review the outcome with team members and sponsors to confirm the project's objectives were met

    • A. This belongs in project closure because confirming that results match the charter's original objectives is a core step in validating project success.
    • B. This belongs in project closure because archiving completed documentation ensures it is properly stored and available for future reference.
    • C. This belongs in project closure because capturing and sharing lessons learned helps other parts of the organization benefit from what the team discovered.
    • D. This does not belong because starting an unrelated project's charter is a new-project activity, not part of closing out the current one.
    • E. This does not belong because deleting collected data removes evidence needed for documentation, verification, and future reference rather than supporting proper closure.
    • F. This belongs in project closure because reviewing outcomes with the team and sponsors together confirms alignment on whether the objectives were achieved.

    Subdomain 2.2: Voice of the customer (VOC)

    8.In the Kano model, which category describes a feature that customers do not expect, but that creates disproportionate delight when it is present without causing dissatisfaction when absent?

    1. A.Must-be attribute
    2. B.Performance attribute
    3. C.Excitement (attractive) attribute
    4. D.Indifferent attribute
    Show answer & explanation

    Correct answer: CExcitement (attractive) attribute

    • A. This is incorrect because must-be attributes are expected basics whose absence causes strong dissatisfaction, the opposite of an unexpected feature that causes no dissatisfaction when missing.
    • B. This is incorrect because performance attributes raise or lower satisfaction proportionally to how much of them is provided, unlike the disproportionate delight described here.
    • C. This is correct because excitement (attractive) attributes are unexpected features that create disproportionate satisfaction when present but do not create dissatisfaction when absent, matching the description.
    • D. This is incorrect because indifferent attributes have little to no effect on satisfaction whether present or absent, which does not match a feature that creates disproportionate delight.

    Subdomain 2.4: Management and planning tools

    9.A quality team wants to show the relationship between a list of customer requirements and a list of internal process capabilities, marking the strength of each pairwise relationship in a grid layout. Which tool fits this need?

    1. A.Interrelationship digraph, which maps cause-and-effect arrows among a single set of interconnected issues.
    2. B.Activity network diagram, which sequences tasks by dependency rather than comparing two separate lists.
    3. C.Matrix diagram, which displays the relationship strength between two or more sets of items in a grid layout.
    4. D.Tree diagram, which decomposes a single objective into progressively finer sub-elements without pairwise comparison.
    Show answer & explanation

    Correct answer: CMatrix diagram, which displays the relationship strength between two or more sets of items in a grid layout.

    • A. An interrelationship digraph maps cause-and-effect among one set of issues, not the pairwise strength between two distinct lists.
    • B. An activity network diagram orders tasks by dependency and timing, which does not address comparing two lists of items.
    • C. A matrix diagram is built to lay two or more lists against each other in a grid and indicate the strength of each relationship.
    • D. A tree diagram works on one objective at a time, breaking it into finer detail rather than comparing two separate lists.

    Subdomain 2.5: Business results for projects

    10.A quality manager reviews two production lines: Line A has a DPMO of 6,210 and Line B has a DPMO of 233. Based on sigma level, which line should be prioritized first for a Six Sigma improvement project, and why?

    1. A.Line A, because its higher DPMO corresponds to a lower sigma level and a larger opportunity for defect reduction
    2. B.Line B, because its lower DPMO corresponds to a lower sigma level and therefore needs more urgent attention
    3. C.Neither line, because DPMO alone cannot be converted into a sigma level without additional cost data
    4. D.Both lines equally, because sigma level only applies to service processes and not to production lines
    Show answer & explanation

    Correct answer: ALine A, because its higher DPMO corresponds to a lower sigma level and a larger opportunity for defect reduction

    • A. Line A's DPMO of 6,210 corresponds to roughly a 4 sigma process, a lower sigma level than Line B's approximately 5 sigma performance, so Line A has the larger defect-reduction opportunity and should be prioritized.
    • B. A lower DPMO corresponds to a higher, not lower, sigma level, so Line B's 233 DPMO reflects better performance than Line A's, not a more urgent need.
    • C. DPMO can be converted to an approximate sigma level using a standard normal table and the 1.5 sigma shift, without requiring any additional cost data.
    • D. Sigma level applies equally to manufacturing and service processes, so this reasoning does not correctly explain the prioritization decision.

    Subdomain 2.5: Business results for projects

    11.True or False: A Six Sigma project sponsor announcing a newly approved project charter and directing department heads to allocate resources is an example of top-down communication.

    1. A.True
    2. B.False
    Show answer & explanation

    Correct answer: ATrue

    • A. This statement is correctly identified as true, since a sponsor issuing a decision and directive to the organization is the defining example of top-down communication.
    • B. This statement is true rather than false, because the sponsor's announcement flows from a leadership role down to the department heads who must act on it.

    Subdomain 2.6: Team dynamics and performance

    12.A Six Sigma project is running behind schedule because the team cannot get time on a production line to collect data. Which team role is primarily responsible for resolving this kind of cross-functional resource barrier?

    1. A.The Champion, who works across departments to remove organizational obstacles and secure resources for the project.
    2. B.The Green Belt, who is expected to negotiate directly with other department managers for equipment access.
    3. C.The facilitator, who manages meeting logistics and keeps team discussions focused on the agenda each week.
    4. D.The process owner, who is accountable for the process's day-to-day performance once improvements are fully implemented.
    Show answer & explanation

    Correct answer: AThe Champion, who works across departments to remove organizational obstacles and secure resources for the project.

    • A. Champions sit above the project team, typically at a management level, and their core responsibility is clearing organizational barriers like this one so the team can keep working.
    • B. Negotiating cross-department resource access falls outside a Green Belt's role; Green Belts execute project tasks and analysis under the Champion's organizational support.
    • C. A facilitator's responsibility is running effective meetings and group processes, not securing resources from other departments.
    • D. A process owner is accountable for the process after the project hands off improvements, not for resolving barriers during the project itself.

    Subdomain 2.6: Team dynamics and performance

    13.Which sequence of steps best describes the nominal group technique for prioritizing ideas?

    1. A.Members silently generate ideas individually, share them round-robin, briefly clarify, then rank or vote to build a prioritized list.
    2. B.A single leader collects ideas from each member privately and then announces the final priority list without further team input.
    3. C.Members debate ideas openly and continuously in an unstructured discussion until the loudest voices in the room converge on one idea.
    4. D.Members submit anonymous ideas online over several weeks, and the facilitator discards any idea lacking majority support immediately.
    Show answer & explanation

    Correct answer: AMembers silently generate ideas individually, share them round-robin, briefly clarify, then rank or vote to build a prioritized list.

    • A. This is the standard nominal group technique sequence: private idea generation, round-robin sharing without early debate, brief clarification, then structured ranking or voting.
    • B. Nominal group technique requires the full team to participate in ranking, not a single leader deciding priorities alone after private collection.
    • C. Nominal group technique deliberately limits open, unstructured debate to prevent louder voices from dominating, which is the opposite of what this option describes.
    • D. Nominal group technique is a structured, same-session process rather than an extended anonymous online submission process, and it does not discard ideas by simple majority before ranking.

    Domain 3: Measure Phase

    Subdomain 3.1: Process analysis and documentation

    14.A Green Belt is reviewing a production line during the Measure phase and wants to determine whether the steps operators actually follow match what is documented. Which activity best supports this goal?

    1. A.Mapping the current workflow and comparing it step by step against the written procedures and work instructions
    2. B.Calculating the process capability index from recent inspection data to check conformance to specification limits
    3. C.Building a cause-and-effect diagram with the team to brainstorm and categorize potential sources of variation
    4. D.Running a hypothesis test to compare defect rates between two shifts using sample inspection data
    Show answer & explanation

    Correct answer: AMapping the current workflow and comparing it step by step against the written procedures and work instructions

    • A. Mapping the actual workflow and checking it line by line against the documented procedures directly reveals where practice has drifted from what is written, which is exactly what a gap analysis requires.
    • B. A capability index describes how well a process meets specifications but does not compare documented steps to what operators actually do, so it does not surface procedural gaps.
    • C. A cause-and-effect diagram is a root-cause brainstorming tool used later in problem solving; it does not document or compare the current sequence of process steps.
    • D. A hypothesis test on defect rates addresses whether two shifts differ statistically, not whether the documented process matches the steps actually being performed.

    Subdomain 3.1: Process analysis and documentation

    15.While reviewing the SOP for a packaging line, a Green Belt notices operators performing an extra quality check that is not mentioned anywhere in the written procedure. What should the team do next?

    1. A.Investigate why the undocumented check exists and decide whether to formally add it to the procedure or eliminate it
    2. B.Assume the operators are not following the SOP correctly and issue a reminder to follow the documented steps exactly
    3. C.Remove the step from the line immediately since anything not written in the SOP is considered unauthorized
    4. D.Escalate the finding to senior leadership as a compliance violation requiring immediate disciplinary action
    Show answer & explanation

    Correct answer: AInvestigate why the undocumented check exists and decide whether to formally add it to the procedure or eliminate it

    • A. An undocumented step may exist for a good reason, such as catching defects the SOP missed, so the correct response is to investigate its purpose before deciding whether to formalize or remove it.
    • B. Assuming noncompliance skips the investigation step and could remove a check that is actually preventing defects, so it is premature without understanding why the step exists.
    • C. Removing the step outright without investigation risks eliminating a control that may be catching real problems the documented process does not address.
    • D. Jumping straight to disciplinary escalation treats a documentation gap as a conduct issue, which is disproportionate before the team even understands why the gap exists.

    Subdomain 3.2: Probability and statistics

    16.In probability and statistics, what does a combination calculate?

    1. A.The number of ways to select items where order does not matter
    2. B.The number of ways to arrange items where order matters
    3. C.The probability that an event will not occur
    4. D.The variance of a sample of selected items
    Show answer & explanation

    Correct answer: AThe number of ways to select items where order does not matter

    • A. Selections where order does not matter is exactly what a combination counts, such as choosing an unordered group from a larger pool.
    • B. Arrangements where order matters describes a permutation, not a combination, since permutations treat different orderings of the same items as distinct outcomes.
    • C. The probability that an event will not occur describes a complement probability, which is unrelated to counting the number of unordered groups that can be selected.
    • D. The variance of a sample describes spread around a mean, not a count of the possible unordered groupings of a set of items.

    Subdomain 3.3: Statistical distributions

    17.An inspector pulls a fixed sample of 50 circuit boards from a lot and classifies each board as defective or non-defective, with the probability of a defect assumed constant across boards. Which distribution best models the number of defective boards found?

    1. A.The binomial distribution, since each board has two possible outcomes with a constant defect probability.
    2. B.The Poisson distribution, since defects are counted over a continuous region without a fixed sample size.
    3. C.The normal distribution, since defect count is a continuous measurement with no upper bound.
    4. D.The F distribution, since the result compares the variance of two separate production lines.
    Show answer & explanation

    Correct answer: AThe binomial distribution, since each board has two possible outcomes with a constant defect probability.

    • A. With a fixed sample of 50 boards, two possible outcomes per board, and a constant defect probability, this scenario matches the binomial distribution exactly. The number of defective boards out of the fixed sample is the classic binomial count.
    • B. This scenario has a fixed sample size of 50 boards rather than an open-ended continuous region of opportunity, which rules out the Poisson model. Poisson applies when events are counted over an unbounded interval of time or space.
    • C. The defect count here is a whole number bounded between 0 and 50, not an unbounded continuous measurement. Treating it as normal would ignore the discrete, bounded nature of the count.
    • D. No comparison of variances between two production lines is described in this scenario, so the F distribution does not apply. The question asks only about the count of defects from one fixed sample.

    Subdomain 3.3: Statistical distributions

    18.A quality team records the number of defects observed in five defect categories and wants to test whether this observed distribution matches a historically expected distribution of defect types. Which distribution supports this test?

    1. A.The chi-square distribution, used to compare observed and expected category frequencies.
    2. B.The F distribution, used to compare the variances of two separate defect-category samples.
    3. C.The binomial distribution, used to model a single defect category with two outcomes.
    4. D.The normal distribution, used to model the continuous measurement of defect severity.
    Show answer & explanation

    Correct answer: AThe chi-square distribution, used to compare observed and expected category frequencies.

    • A. Comparing observed defect-category counts against an expected historical distribution is exactly the goodness-of-fit test built on the chi-square distribution. This test sums squared differences between observed and expected frequencies relative to expected counts.
    • B. The scenario compares category frequency counts, not variances between two samples, so the F distribution does not apply here. F-tests are reserved for comparing spread, not counted frequencies across categories.
    • C. The scenario involves five defect categories being compared simultaneously, not a single two-outcome classification. The binomial model only handles one category with a success/failure split, which does not fit this multi-category comparison.
    • D. The team is comparing counts of defects by category, not a continuous severity measurement. The normal distribution is not the tool used for this categorical frequency comparison.

    Subdomain 3.4: Collecting and summarizing data

    19.A process improvement team records the temperature in degrees Celsius for a chemical reaction. Why is this considered interval data rather than ratio data?

    1. A.Zero degrees Celsius does not represent a true absence of temperature
    2. B.Temperature readings cannot be ordered from lowest to highest
    3. C.Celsius values are always recorded as whole numbers only
    4. D.Temperature differences of equal size do not carry equal meaning
    Show answer & explanation

    Correct answer: AZero degrees Celsius does not represent a true absence of temperature

    • A. Because zero on the Celsius scale is an arbitrary reference point rather than a true absence of the quantity, ratios like 'twice as hot' are not meaningful, which defines interval data.
    • B. Celsius readings can absolutely be ranked from lowest to highest, so the inability to order values is not the reason this is interval rather than ratio data.
    • C. Celsius temperature can be recorded with decimal precision, so restriction to whole numbers is not a property of the scale and is not the reason for the interval classification.
    • D. Equal-sized intervals on the Celsius scale do carry equal meaning, which is exactly why it qualifies as interval data rather than a lower ordinal or nominal scale.

    Subdomain 3.4: Collecting and summarizing data

    20.A hospital wants to sample patient wait times but knows that wait times differ significantly between the morning, afternoon, and evening shifts. Which sampling method best ensures each shift is proportionally represented?

    1. A.Stratified sampling by shift
    2. B.Simple random sampling across the entire day
    3. C.Convenience sampling during the busiest hour
    4. D.Judgment sampling based on staff opinion
    Show answer & explanation

    Correct answer: AStratified sampling by shift

    • A. Dividing the day into shift-based strata and sampling within each shift guarantees that known differences between shifts are captured proportionally in the results.
    • B. Simple random sampling across the whole day could by chance under-represent one or more shifts, missing the known variation between morning, afternoon, and evening.
    • C. Sampling only during the busiest hour ignores the other shifts entirely and would not represent the full range of wait-time conditions.
    • D. Selecting data based on staff opinion introduces subjective bias and does not guarantee proportional representation of each shift's wait times.

    Subdomain 3.5: Measurement system analysis (MSA)

    21.A plant manager reviews a GR&R report showing %GRR of 8%, ndc of 7, and no bias detected against a certified reference standard. A supplier's competing gage shows %GRR of 22% and ndc of 4. Which gage should the manager select for controlling a tight-tolerance process, and why?

    1. A.The first gage, since its %GRR and ndc both clearly meet the acceptable thresholds
    2. B.The second gage, since a higher %GRR always means better sensitivity to small changes
    3. C.Either gage, since ndc has no real effect on a measurement system's usability
    4. D.Neither gage, since a bias study alone cannot confirm a measurement system is capable
    Show answer & explanation

    Correct answer: AThe first gage, since its %GRR and ndc both clearly meet the acceptable thresholds

    • A. An 8% %GRR is under the 10% acceptable threshold and an ndc of 7 exceeds the minimum of 5, and with no bias detected, the first gage meets all the standard criteria for a capable measurement system on a tight-tolerance process.
    • B. A higher %GRR means more of the total variation is consumed by measurement error, not better sensitivity; the 22% result places the second gage in the marginal band, which is worse, not better, than the first gage.
    • C. Ndc directly reflects how finely a gage can distinguish between parts, and the second gage's ndc of 4 falls short of the minimum of 5, making it a meaningful factor in the selection decision.
    • D. The scenario reports a full set of GR&R metrics, not just a bias study, and the first gage's %GRR, ndc, and bias results together are sufficient to judge it capable for this application.

    Subdomain 3.6: Process and performance capability

    22.Which capability indices are calculated using long-term (overall) standard deviation rather than short-term (within-subgroup) standard deviation? (Select all that apply.)(Select 2)

    1. A.Cp
    2. B.Cpk
    3. C.Pp
    4. D.Ppk
    5. E.Short-term sigma level
    Show answer & explanation

    Correct answers: C, DPp; Ppk

    • A. Cp is a short-term index and is calculated using the within-subgroup standard deviation, not the overall long-term variation.
    • B. Cpk is also a short-term index and uses the within-subgroup standard deviation to measure capability under stable, immediate conditions.
    • C. Pp uses the overall standard deviation calculated from the full long-term dataset, which is what distinguishes it from its short-term counterpart Cp.
    • D. Ppk uses the overall long-term standard deviation combined with the process mean's distance to the nearer limit, distinguishing it from the short-term Cpk.
    • E. The short-term sigma level is derived from the short-term Cpk value and therefore reflects within-subgroup variation, not the overall long-term standard deviation.

    Domain 4: Analyze Phase

    Subdomain 4.1: Exploratory data analysis

    23.Which of the following statements about correlation and causation are correct? (Select all that apply.)(Select 4)

    1. A.A strong correlation coefficient shows two variables tend to move together but does not by itself prove one causes the other.
    2. B.A lurking variable can create a strong correlation between two variables that have no direct causal link.
    3. C.Any correlation coefficient above 0.90 is sufficient proof that a causal relationship exists between the variables.
    4. D.Establishing causation typically requires additional evidence, such as a controlled experiment, beyond correlation alone.
    5. E.A correlation coefficient near zero always means the two variables have no relationship of any kind.
    6. F.Temporal precedence, where the cause happens before the effect, is one piece of evidence supporting a causal claim.
    Show answer & explanation

    Correct answers: A, B, D, FA strong correlation coefficient shows two variables tend to move together but does not by itself prove one causes the other.; A lurking variable can create a strong correlation between two variables that have no direct causal link.; Establishing causation typically requires additional evidence, such as a controlled experiment, beyond correlation alone.; Temporal precedence, where the cause happens before the effect, is one piece of evidence supporting a causal claim.

    • A. This statement is correct. A strong correlation coefficient shows two variables tend to move together but is not, by itself, proof that a change in one variable directly causes a change in the other.
    • B. This statement is correct. A third, unmeasured factor can independently drive two variables in the same direction, producing a strong correlation between them even though neither one causes the other.
    • C. This statement is incorrect. No fixed threshold of correlation strength, including 0.90, is sufficient proof of causation on its own; causation requires additional evidence beyond the size of the correlation coefficient.
    • D. This statement is correct. Establishing that one variable causes another typically requires controlled experimentation or other supporting evidence, since correlation alone cannot rule out lurking variables or reverse causation.
    • E. This statement is incorrect. A correlation coefficient near zero rules out a linear relationship but not a real non-linear or curved relationship, so it does not guarantee the variables are unrelated in every sense.
    • F. This statement is correct. Showing that the proposed cause reliably occurs before the proposed effect is one supporting piece of evidence used when building a case for causation, though it is not sufficient alone.

    Subdomain 4.2: Hypothesis testing

    24.A Green Belt runs a paired-comparison t-test on operator error counts measured before and after a new work instruction, using the same ten operators. The test returns a p-value of 0.30 at alpha = 0.05. What should be concluded?

    1. A.Fail to reject the null hypothesis; there is no significant change in error counts
    2. B.Reject the null hypothesis; the work instruction significantly reduced error counts
    3. C.Fail to reject the null hypothesis; the work instruction definitely had no effect
    4. D.Reject the null hypothesis; paired samples in this test are not independent of each other
    Show answer & explanation

    Correct answer: AFail to reject the null hypothesis; there is no significant change in error counts

    • Fail to reject the null hypothesis; there is no significant change in error counts. Because the p-value of 0.30 exceeds alpha, there is insufficient evidence to reject the null hypothesis of no difference. The data simply do not provide strong enough evidence of a change in error counts.
    • Reject the null hypothesis; the work instruction significantly reduced error counts. A p-value above alpha does not support rejecting the null hypothesis, so this conclusion is not justified by the result. The evidence here is too weak to claim a significant reduction.
    • Fail to reject the null hypothesis; the work instruction definitely had no effect. Failing to reject the null hypothesis means the evidence is insufficient to detect a difference, not that no effect definitely exists. A true effect could still be present but undetected due to limited power.
    • Reject the null hypothesis; paired samples in this test are not independent of each other. Paired samples are intentionally not independent, since the design pairs each operator's before and after measurement to control for individual variation. This is a feature of the paired design, not a reason to reject the null hypothesis.

    Subdomain 4.3: Additional analysis methods

    25.In gap analysis, an improvement team compares the current state and a target future state against predefined metrics to size the performance gap that needs to be closed.

    1. A.True
    2. B.False
    Show answer & explanation

    Correct answer: ATrue

    • A. This statement is true because gap analysis is specifically defined as comparing a measured current state to a desired future state using predefined metrics to quantify the size of the gap.
    • B. This statement is false to select only if the comparison ignored predefined metrics or skipped either the current or future state, which is not how gap analysis is performed.

    Domain 5: Improve Phase

    Subdomain 5.1: Design of experiments (DOE)

    26.The bakery study has two factors, temperature (325°F, 375°F) and bake time (20, 30 minutes), tested in a full factorial design. Which of the following is one of the treatments in this design?

    1. A.Baking at 375°F for 30 minutes, since this pairs one specific level of each factor together.
    2. B.Baking at 325°F and then again at 375°F on the same tray during a single oven cycle.
    3. C.Measuring moistness twice for the same cake using two different moisture meters.
    4. D.Recording the average moistness across all four temperature-and-time combinations.
    Show answer & explanation

    Correct answer: ABaking at 375°F for 30 minutes, since this pairs one specific level of each factor together.

    • A. A treatment is one unique combination of factor levels, and pairing 375°F with 30 minutes is exactly one such combination in this two-factor design.
    • B. Running two temperature levels together on the same tray in one cycle confounds the factor levels rather than defining a single treatment.
    • C. Measuring the same cake twice with different meters is a measurement system comparison, not a treatment defined by factor levels.
    • D. Averaging moistness across all combinations summarizes overall results and does not identify a single treatment.

    Subdomain 5.1: Design of experiments (DOE)

    27.Which of the following are basic terms used to describe the structure of a designed experiment? (Select all that apply.)(Select 4)

    1. A.Factor
    2. B.Response
    3. C.Treatment
    4. D.Block
    5. E.Control chart
    6. F.Correlation coefficient
    Show answer & explanation

    Correct answers: A, B, C, DFactor; Response; Treatment; Block

    • A. A factor is one of the basic building blocks of a designed experiment, describing an independent variable being studied.
    • B. A response is a basic DOE term describing the measured outcome the experiment is designed to explain.
    • C. A treatment is a basic DOE term describing one unique combination of factor levels tested in the study.
    • D. A block is a basic DOE term describing a grouping used to control for a known nuisance variable.
    • E. A control chart is a process monitoring tool from the Control phase, not a term describing the structure of a designed experiment.
    • F. A correlation coefficient is a statistic describing association between two variables and is not one of the basic structural terms of DOE.

    Subdomain 5.2: Implementation planning

    28.A team generates seven candidate layouts for a new workstation, quickly builds rough cardboard mockups of the top three, and has operators try each one, refining the design between attempts based on what fails. This process is an example of:

    1. A.Try-storming
    2. B.Simulation
    3. C.Proof of concept
    4. D.Control plan review
    Show answer & explanation

    Correct answer: ATry-storming

    • A. Generating multiple ideas, narrowing to a few, and rapidly building and testing rough prototypes while refining based on early failures matches the defined stages of try-storming.
    • B. Simulation involves a computer or mathematical model of the process rather than physically building and testing cardboard mockups with real operators.
    • C. A proof of concept typically validates a single idea's feasibility, not an iterative cycle of generating, narrowing, and rapidly testing multiple physical mockups.
    • D. A control plan review examines how an already-implemented improvement is being sustained, which happens after implementation, not during concept generation and testing.

    Subdomain 5.2: Implementation planning

    29.A Green Belt team is deciding between running a pilot test and performing a simulation to evaluate a proposed change to a chemical batching process. Which factor would most strongly favor choosing simulation over a physical pilot?

    1. A.Running the change on real equipment carries a high safety or contamination risk
    2. B.The team wants direct evidence of operator acceptance of the new procedure
    3. C.The team needs to observe unplanned real-world variation the model cannot capture
    4. D.Regulatory approval requires evidence collected from an actual production run
    Show answer & explanation

    Correct answer: ARunning the change on real equipment carries a high safety or contamination risk

    • A. When testing a change on real equipment could create safety hazards or contamination, a mathematical or computer-based simulation lets the team evaluate outcomes without exposing people or product to that risk.
    • B. Operator acceptance and behavior can only be observed by having real people interact with the actual changed process, which requires a physical pilot rather than a simulation model.
    • C. Unplanned real-world variation, such as equipment quirks or human factors, is precisely what a simulation model cannot capture, making a physical pilot the better choice for this concern.
    • D. Regulatory bodies that require evidence from an actual production run are asking for real operating data, which only a physical pilot test can provide.

    Subdomain 5.3: Lean tools

    30.A cable manufacturer redesigns a connector so it is shaped asymmetrically and can only be plugged in one correct way, making a reversed connection physically impossible. This redesign is an example of which lean tool?

    1. A.Poka-yoke
    2. B.Kanban
    3. C.Standard work
    4. D.5S
    Show answer & explanation

    Correct answer: APoka-yoke

    • A. Shaping the connector so an incorrect orientation is physically impossible is a classic poka-yoke, since it prevents the error from occurring rather than relying on inspection to catch it.
    • B. Kanban is a signaling mechanism for replenishing materials based on consumption, unrelated to redesigning a part's shape to prevent a connection error.
    • C. Standard work documents the sequence and timing operators follow, which does not involve physically redesigning a component to prevent misassembly.
    • D. 5S organizes and cleans the workplace, which does not address preventing a specific assembly error through part geometry.

    Subdomain 5.3: Lean tools

    31.What best describes 'continuous flow' as a lean production technique?

    1. A.Moving units through each process step one at a time with minimal waiting between steps
    2. B.Producing large batches at each station before moving them to the next process
    3. C.Storing finished goods in a central warehouse until customer orders arrive
    4. D.Scheduling every station independently based on its own local forecast
    Show answer & explanation

    Correct answer: AMoving units through each process step one at a time with minimal waiting between steps

    • A. Continuous flow, often called one-piece flow, moves individual units directly from one process step to the next with minimal queuing or waiting, reducing work-in-process and cycle time.
    • B. Producing large batches before moving them forward describes batch-and-queue production, which continuous flow is specifically designed to eliminate.
    • C. Storing finished goods centrally until orders arrive describes a make-to-stock warehousing approach, not the step-by-step movement that defines continuous flow.
    • D. Scheduling each station independently based on its own forecast describes disconnected push scheduling, which is the opposite of the synchronized, connected movement in continuous flow.

    Domain 6: Control Phase

    Subdomain 6.1: Statistical process control (SPC)

    32.On a control chart, six consecutive points show a steady upward trend even though no single point falls outside the control limits. How should this pattern be interpreted?

    1. A.As a special cause signal, since a trend indicates a systematic shift is affecting the process
    2. B.As common cause variation, since none of the individual points exceed the calculated control limits
    3. C.As a measurement error, since true process data cannot show six consecutive increases in a row
    4. D.As evidence that the control limits were calculated incorrectly and now must be widened further
    Show answer & explanation

    Correct answer: AAs a special cause signal, since a trend indicates a systematic shift is affecting the process

    • A. A sustained run or trend across several consecutive points is statistically unlikely under pure common cause variation, even when every point stays inside the control limits. Pattern-based rules like a steady trend flag a special cause that warrants investigation.
    • B. Staying inside the control limits is not the only test for control chart interpretation; nonrandom patterns such as trends and runs are separate out-of-control signals. Treating this trend as ordinary variation would miss a real systematic shift.
    • C. Consecutive increases are a legitimate and well-documented out-of-control pattern in SPC theory, not evidence of measurement error. Dismissing the trend as a data artifact would overlook a genuine process signal.
    • D. Control limits reflect the process's historical common cause variation and are not adjusted just because a nonrandom pattern appears. Widening them would mask the systematic shift instead of prompting an investigation into its cause.

    Subdomain 6.1: Statistical process control (SPC)

    33.A textile mill inspects rolls of fabric of different lengths each day and counts the total number of flaws found per roll, then normalizes the flaw count by the length inspected. Which chart fits this situation?

    1. A.u chart, since it tracks average defects per unit of inspection area when the amount inspected varies
    2. B.c chart, since it tracks the total defect count when every inspected unit is the same fixed size
    3. C.np chart, since it tracks the number of defective rolls found among a fixed inspection sample size
    4. D.X-bar and S chart, since it tracks a continuous measurement collected from subgroups larger than eight units
    Show answer & explanation

    Correct answer: Au chart, since it tracks average defects per unit of inspection area when the amount inspected varies

    • A. Because roll lengths vary from day to day, normalizing the flaw count by the amount inspected keeps the chart meaningful across different inspection sizes, which is exactly the role the u chart plays.
    • B. This chart assumes every inspected unit is the same fixed size, but the fabric rolls here vary in length, so a chart that does not normalize for inspection amount would not fit this varying-size situation.
    • C. This chart requires a constant sample size and classifies whole units as defective or not, but the mill is instead counting individual flaws per roll of varying length, not classifying entire rolls as pass or fail.
    • D. Flaw counts are discrete attribute data, not a continuous measurement, so a variables chart built for measured dimensions collected in large subgroups does not apply to this counting scenario.

    Subdomain 6.2: Sustain improvements

    34.Three months after a process change was implemented, an audit finds that new hires are still performing the old, pre-improvement steps. What does this most likely indicate?

    1. A.The training plan did not cover onboarding for new hires, so they learned the outdated steps from tenured coworkers.
    2. B.The control chart's reaction plan was not triggered when the process drifted out of control.
    3. C.The wrong document revision was mistakenly approved during the document-control review.
    4. D.The measurement system used to verify weld strength was not recalibrated on schedule.
    Show answer & explanation

    Correct answer: AThe training plan did not cover onboarding for new hires, so they learned the outdated steps from tenured coworkers.

    • A. This is correct because new hires performing outdated steps points to a gap in onboarding training rather than a monitoring, document-approval, or calibration issue.
    • B. Nothing in the scenario mentions a control chart signal being missed; the finding is specifically about staff performing outdated steps.
    • C. There is no indication the wrong document version was approved; the problem described is that people are not following the current process, which points to training.
    • D. Gage calibration affects measurement accuracy, not whether new hires know and follow the correct process steps.

    Subdomain 6.3: Lean tools for process control

    35.What does the lean concept of Jidoka refer to in a controlled production process?

    1. A.Building in automatic detection of abnormalities so equipment or workers stop the process until the defect is corrected.
    2. B.Assigning a dedicated inspector to manually check every finished unit before it leaves the production line.
    3. C.Scheduling equipment overhauls on a fixed annual calendar to prevent long-term wear and tear.
    4. D.Posting daily output targets on a shared board so every shift can compare actual results to the plan.
    Show answer & explanation

    Correct answer: ABuilding in automatic detection of abnormalities so equipment or workers stop the process until the defect is corrected.

    • A. Jidoka, or autonomation, means building automatic abnormality detection into a process so it halts on its own until the defect is fixed, preventing bad output from continuing downstream.
    • B. Relying on a dedicated inspector to manually check finished units is a form of end-of-line inspection, which is the reactive approach Jidoka is designed to replace.
    • C. Scheduling overhauls on a fixed annual calendar describes a planned maintenance activity, not the automatic defect-detection behavior that defines Jidoka.
    • D. Posting output targets for shift comparison is a visual management practice, distinct from Jidoka's automatic stop-on-defect mechanism.

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