Lean Six Sigma Green Belt Practice Exam — All Questions

A process inspects 500 units, each having 8 opportunities for a defect, and finds 20 defects. What is the DPMO?

• a.2,500
• b.40,000
• c.250
• d.5,000✓

DPMO = defects / (units x opportunities) x 1,000,000 = 20 / (500 x 8) x 1,000,000 = 20 / 4,000 x 1,000,000 = 5,000. Each answer that ignores the opportunity count or the scaling factor is incorrect.

Defects Per Unit (DPU) is calculated as:

• a.Total number of defects divided by total number of units✓
• b.Total number of defects times 1,000,000
• c.Number of units divided by number of defects
• d.Defects divided by the number of opportunities only

DPU = total defects / total units, a simple ratio of how many defects occur per unit produced. Multiplying by a million or dividing by opportunities describes DPMO or DPO, not DPU.

Using the common long-term sigma table (with the 1.5-sigma shift), a process operating at approximately 66,807 DPMO corresponds to what sigma level?

• a.2 sigma
• b.4 sigma
• c.3 sigma✓
• d.6 sigma

On the standard shifted sigma table, roughly 66,807 DPMO equals about a 3-sigma process (about 93.3% yield). Six sigma is about 3.4 DPMO and four sigma is about 6,210 DPMO.

Which type of data is 'the number of scratches found on each painted panel'?

• a.A specification limit
• b.Nominal data with no order
• c.Continuous (variable) data
• d.Discrete (attribute/count) data✓

Counts of defects are discrete attribute data because they take whole-number values. Continuous data (like length or weight) can take any value on a scale, and a count is not a specification limit.

In a Measurement System Analysis (Gage R&R), 'reproducibility' refers to the variation caused by:

• a.The natural variation of the manufacturing process
• b.Different appraisers measuring the same part with the same gage✓
• c.The same appraiser measuring the same part repeatedly
• d.The width of the specification tolerance

Reproducibility is the appraiser-to-appraiser (between-operator) variation. The same appraiser repeating a measurement is repeatability, and neither describes process variation or the tolerance itself.

A detailed process map (flowchart) built in the Measure phase primarily helps the team to:

• a.See the actual sequence of steps, decisions, and hand-offs where defects and delays may occur✓
• b.Prove a cause-and-effect relationship with statistics
• c.Calculate the correlation coefficient
• d.Set the project's overall financial budget and forecast the expected annual savings it will produce

A process map documents the real flow of steps, decisions, and hand-offs, exposing rework loops, bottlenecks, and non-value-added activity to investigate. It is a visualization tool, not a statistical proof.

On a standard flowchart, a diamond symbol represents a:

• a.Start or end point
• b.Process or activity step
• c.Stored document
• d.Decision point with alternative paths✓

The diamond is the decision symbol, branching the flow (e.g., yes/no). Rectangles are process steps, rounded shapes/ovals are terminators (start/end), and other symbols denote documents or storage.

A value stream map (VSM) differs from a basic flowchart because it also:

• a.Captures material and information flow plus data like cycle time, wait time, and inventory to reveal value-added vs. non-value-added time✓
• b.Replaces the need for any measurement
• c.Shows only the decision points and the branching logic of the process, without any cycle-time, inventory, wait-time, or material-flow information at all
• d.Is used exclusively in the Define phase

A VSM overlays process flow with timing and inventory data, separating value-added from non-value-added time and exposing lead-time waste. A basic flowchart shows steps but not this Lean timing/flow data.

A swim-lane (deployment) flowchart is especially useful when the team needs to:

• a.Show which person, role, or department performs each step and where hand-offs occur✓
• b.Rank defects by frequency
• c.Estimate the standard deviation
• d.Compute the process sigma level directly from its collected defect and opportunity data

Swim-lane maps assign each step to a lane (role/department), making hand-offs and accountability visible — a common source of delay and error. They clarify who does what, not statistical spread.

A spaghetti diagram is used to reveal:

• a.The number of defects per million opportunities
• b.The probability distribution of a variable
• c.The physical movement/travel path of people, material, or product through a workspace✓
• d.The statistical correlation between two process factors plotted together on a scatter diagram

A spaghetti diagram traces physical travel paths on a floor plan, exposing excess motion and transportation waste. It targets layout/motion, not statistical distributions or DPMO.

Continuous (variable) data is best described as data that:

• a.Is always recorded as a simple pass-or-fail outcome with no possible values in between the two
• b.Can take any value on a continuous scale, such as length, weight, time, or temperature✓
• c.Can only be whole-number counts
• d.Has categories with no order

Continuous data is measured on a scale and can, in principle, take infinitely many values between two points (e.g., 3.72 seconds). Counts and pass/fail outcomes are discrete/attribute data.

Which of the following is an example of attribute (discrete) data?

• a.The temperature of an oven in degrees
• b.The number of defective units in a batch of 100✓
• c.The elapsed cycle time for each unit, measured in seconds
• d.The precise weight of each unit in grams

A count of defective units takes whole-number values, making it discrete/attribute data. Weight, temperature, and time are measured on continuous scales.

On the nominal-ordinal-interval-ratio hierarchy, a NOMINAL scale is one where values:

• a.Have a true zero and support ratios
• b.Are labels or categories with no inherent order, such as machine A, B, or C✓
• c.Are ranked in a meaningful and consistent order running from lowest to highest
• d.Have equal intervals but no true zero

Nominal data names categories without order (colors, machine IDs, defect types). Ordinal adds rank order, interval adds equal spacing without a true zero, and ratio adds a true zero.

A customer-satisfaction rating of 'poor, fair, good, excellent' is an example of which measurement scale?

• a.Interval — equal spacing and no true zero
• b.Ratio — a scale that has equal intervals and a meaningful, non-arbitrary true zero point
• c.Nominal — unordered categories
• d.Ordinal — categories that have a meaningful rank order but unequal/undefined intervals✓

Ordinal scales rank categories ('good' > 'fair') but the gaps between ranks are not necessarily equal. Nominal has no order; interval and ratio require equal, quantifiable intervals.

Temperature measured in degrees Celsius is an example of which scale, because it has equal intervals but no meaningful true zero (0 C does not mean 'no temperature')?

• a.Interval✓
• b.Nominal
• c.Ratio
• d.Ordinal

Interval scales have equal spacing but an arbitrary zero, so differences are meaningful but ratios are not (20 C is not 'twice as hot' as 10 C). A true zero (like weight in kg) would make it a ratio scale.

Length in centimeters, where 0 cm means 'no length' and 20 cm is genuinely twice 10 cm, is an example of which scale?

• a.Ratio✓
• b.Ordinal
• c.Interval
• d.Nominal

Ratio scales have equal intervals and a true zero, so both differences and ratios are meaningful. Weight, length, time, and count share this property; interval scales (like Celsius) lack the true zero.

Compared with attribute data, continuous data is generally preferred for analysis because it:

• a.Provides more information per data point, so smaller sample sizes can detect change✓
• b.Never requires a measurement system analysis
• c.Is always easier and cheaper to collect
• d.Eliminates essentially all measurement error and removes the need for any gage study

Continuous measurements carry more information than pass/fail counts, so fewer samples are needed to detect a shift and capability can be assessed directly. It still requires MSA and is not always cheaper to collect.

In simple random sampling, every item in the population has:

• a.An equal and independent chance of being selected✓
• b.No chance unless it is at the start of the batch
• c.A selection chance that is directly proportional to its physical size
• d.A guaranteed place if it is defective

Random sampling gives each unit an equal, independent probability of selection, minimizing selection bias. Stratified and systematic methods impose structure; convenience sampling introduces bias.

Stratified sampling is most appropriate when the population:

• a.Is perfectly uniform with no subgroups
• b.Contains fewer than three total items and therefore cannot be divided into any subgroups
• c.Contains distinct subgroups (strata) and you want each represented proportionally✓
• d.Must be sampled by taking every 10th item

Stratified sampling divides the population into meaningful subgroups (shifts, machines, suppliers) and samples each so all are represented. This reduces variability from known differences between strata.

Selecting every 20th unit off a production line is an example of:

• a.Simple random sampling
• b.Systematic sampling✓
• c.Stratified sampling
• d.Convenience sampling

Systematic sampling selects items at a fixed interval (every kth unit). It is easy on a line but can be biased if the interval coincides with a cyclical pattern in the process.

A 'rational subgroup' is chosen so that:

• a.Variation within the subgroup is maximized on purpose
• b.It always contains exactly one measurement
• c.Variation within the subgroup reflects only common cause, so special-cause shifts appear between subgroups✓
• d.It always contains the entire population of units produced during the studied period, leaving nothing unsampled

Rational subgrouping collects samples close in time/condition so within-subgroup variation captures only natural (common-cause) noise; differences between subgroups then flag special causes. This principle underlies control-chart subgrouping.

All else equal, increasing the sample size in a study:

• a.Increases the systematic measurement bias that is present in the collected data
• b.Reduces the standard error and increases the power to detect a real effect✓
• c.Guarantees the data will be normally distributed
• d.Has no effect on the precision of estimates

Larger samples shrink the standard error (which scales with 1/sqrt(n)) and raise statistical power, making estimates more precise and real effects easier to detect. It does not create normality or fix bias.

A numerical summary calculated from a SAMPLE (such as the sample mean x-bar) is called a:

• a.Specification
• b.Census
• c.Parameter
• d.Statistic✓

A statistic describes a sample (x-bar, s), while a parameter describes the whole population (mu, sigma). Samples are used to estimate the usually unknown population parameters.

The overall purpose of Measurement System Analysis (MSA) is to:

• a.Write the final control plan and reaction procedures the process owner will use to sustain the gains after closure
• b.Rank the causes of defects
• c.Design the improvement experiment
• d.Confirm the data are trustworthy by quantifying measurement-system error before using the data to make decisions✓

MSA verifies that the measurement system is accurate and precise enough that observed variation reflects the process, not the gage or appraiser. Without trustworthy data, later analysis is unreliable.

In MSA terms, 'accuracy' and 'precision' differ in that accuracy concerns:

• a.How close measurements are to the true value, while precision concerns how close repeated measurements are to each other✓
• b.The number of appraisers, while precision concerns the number of parts
• c.The color of the measuring gage, while precision concerns the physical size, shape, and weight of the measuring instrument
• d.The sample size, while precision concerns the population size

Accuracy is closeness to the true/reference value (related to bias); precision is the tightness of repeated readings (related to repeatability/reproducibility). A gage can be precise yet inaccurate, or vice versa.

In a Gage R&R study, 'repeatability' is the variation observed when:

• a.Different operators measure different parts
• b.The SAME operator measures the SAME part multiple times with the SAME gage✓
• c.Different operators measure the same part
• d.The upper and lower specification limits are changed partway through the study

Repeatability (equipment variation) is the variation from one appraiser measuring one part repeatedly with one gage. Variation between different appraisers is reproducibility.

In MSA, 'bias' refers to:

• a.The variation observed between different operators who are measuring the same parts
• b.The difference between the average measured value and the true/reference value✓
• c.The spread of repeated measurements
• d.The number of distinct categories

Bias is a systematic offset — the gap between the measurement average and a known reference value. Spread relates to precision/repeatability, and operator differences relate to reproducibility.

'Linearity' in a measurement system describes:

• a.Whether the data are normally distributed
• b.How many operators are involved
• c.How the gage's bias changes across the operating range of measurements✓
• d.The elapsed time between two successive scheduled calibrations of the gage

Linearity assesses whether bias stays consistent across the range (e.g., accurate at low values but biased at high values). It is a form of accuracy evaluated over the measurement range, distinct from stability over time.

'Stability' of a measurement system refers to:

• a.Whether the measurement of the same part stays consistent over time✓
• b.The correlation between two variables
• c.The total number of parts and operators that are included in the gage study
• d.The tolerance width of the specification

Stability is consistency of measurements of the same reference across time, often tracked on a control chart of a master part. Drift signals the gage needs recalibration or maintenance.

By common AIAG guidelines, a Gage R&R result under 10% (of study variation or tolerance) is considered:

• a.Acceptable — the measurement system is generally adequate✓
• b.Practically impossible for any real measurement system to actually achieve
• c.Unacceptable — the gage must be scrapped
• d.Marginal — acceptable only for rough work

A %GRR below 10% indicates an acceptable measurement system. The 10-30% band is marginal (may be acceptable depending on cost/criticality), and above 30% is unacceptable.

A Gage R&R result of 22% is typically judged as:

• a.Marginal — may be acceptable depending on application, cost, and criticality✓
• b.Unacceptable — must be rejected outright
• c.Fully acceptable with no concerns
• d.A clear sign that the parts being measured are themselves defective and out of spec

A %GRR between 10% and 30% falls in the marginal band; acceptability depends on the importance of the measurement and the cost to improve it. Under 10% is acceptable; over 30% is unacceptable.

A Gage R&R result of 45% indicates that:

• a.The underlying production process is fully capable, centered, and needs no further work
• b.The measurement system is acceptable
• c.The sample size was too large
• d.The measurement system is unacceptable and must be improved before trusting the data✓

A %GRR above 30% means the measurement system contributes too much variation to be trusted and must be improved (better gage, training, or method) before the data can be used. It says nothing directly about process capability.

In a Gage R&R study, the total gage variation (R&R) is composed of:

• a.The number of appraisers times the number of parts
• b.The specification width minus the mean
• c.Repeatability and reproducibility combined✓
• d.Only the part-to-part variation

Gage R&R combines repeatability (equipment variation) and reproducibility (appraiser variation): total variance = repeatability variance + reproducibility variance. Part-to-part variation is the process spread, kept separate from gage error.

The 'number of distinct categories' (ndc) reported in a Gage R&R should generally be at least:

• a.2
• b.1
• c.5✓
• d.3

An ndc of 5 or more means the measurement system can reliably distinguish enough different levels of the parts to be useful. ndc = 1.41 x (part variation / gage variation); a value below 5 signals poor discrimination.

For pass/fail (attribute) inspection, the appropriate MSA is:

• a.A capability study using Cpk
• b.An attribute agreement analysis, checking whether appraisers agree with each other and with a known standard✓
• c.A histogram of the defects
• d.A full designed experiment (DOE) run across several factors and levels to fully model the entire response surface

Attribute agreement analysis evaluates whether inspectors classifying good/bad agree among themselves (reproducibility), with themselves on repeats (repeatability), and with the correct standard. Cpk applies to continuous data.

'Discrimination' (resolution) of a measurement device refers to:

• a.The number of operators in the study
• b.The distance between control limits
• c.The systematic measurement bias that is built into the device
• d.The smallest increment the device can detect and display✓

Discrimination is the finest increment a gage can read; a common rule is that resolution should be at most one-tenth of the process variation or tolerance so the gage can 'see' the variation being measured.

A process produces 1,200 units, each with 5 opportunities for a defect, and 3 defects are found. What is the DPMO?

• a.500✓
• b.250
• c.600
• d.5,000

DPMO = defects / (units x opportunities) x 1,000,000 = 3 / (1,200 x 5) x 1,000,000 = 3 / 6,000 x 1,000,000 = 500. Forgetting to multiply by opportunities or the scaling factor gives the wrong answer.

Inspecting 250 units with 4 opportunities each, a team finds 15 defects. What is the DPMO?

• a.1,500
• b.60,000
• c.6,000
• d.15,000✓

DPMO = 15 / (250 x 4) x 1,000,000 = 15 / 1,000 x 1,000,000 = 15,000. The total opportunities are 250 x 4 = 1,000, so 15 defects per 1,000 opportunities scales to 15,000 per million.

A process makes 2,000 units, each with 10 opportunities, and produces 50 defects. What is the DPMO?

• a.500
• b.250
• c.1,000
• d.2,500✓

DPMO = 50 / (2,000 x 10) x 1,000,000 = 50 / 20,000 x 1,000,000 = 2,500. Total opportunities are 20,000, and 50/20,000 = 0.0025, which is 2,500 per million.

A batch of 400 units contains 60 total defects (some units have more than one). What is the Defects Per Unit (DPU)?

• a.0.15✓
• b.0.60
• c.1.50
• d.6.67

DPU = total defects / total units = 60 / 400 = 0.15. DPU counts defects (not defectives) per unit and can exceed 1 if units carry multiple defects; here it is 0.15 defects per unit.