Free Lean Six Sigma Black Belt Practice Test 2026

Question 1Define

A call center Black Belt writes the project relationship as Y = f(x). Average handle time is the output, and agent experience, call type, and system response time are suspected drivers. Which statement BEST describes how the team should use this relationship?

Correct answer: C. Find and control the key x's so the Y behaves predictably
The Y is an output, so it improves only when the critical inputs that drive it are identified and controlled. Adjusting the Y directly treats the symptom and ignores the causes.

Question 2Measure

A plant runs one 8-hour shift with two 15-minute breaks. Customer demand is 900 units per shift. What is the takt time?

Correct answer: B. 30 seconds
Available time is 480 - 30 = 450 minutes, or 27,000 seconds, and takt = 27,000 / 900 = 30 seconds. The value 32 seconds forgets to subtract the breaks.

Question 3Analyze

A Black Belt tests whether a new resin changes average tensile strength from the current 50 MPa. What is the null hypothesis?

Correct answer: D. The population mean strength equals 50 MPa
The null hypothesis states no change, so the population mean equals 50 MPa. Hypotheses are always about population parameters, not sample statistics.

Question 4Improve

A regression model for weekly overtime hours at a distribution center is Overtime = 12 + 3.5 x (thousands of orders). What overtime does the model predict for a week with 8 thousand orders?

Correct answer: A. 40.0 hours
Overtime = 12 + 3.5 x 8 = 12 + 28 = 40.0 hours. The value 28.0 leaves out the intercept of 12.

Question 5Control

A chemical plant measures the viscosity of each batch once, and a new batch is made about every four hours. Which control chart is MOST appropriate?

Correct answer: B. I-MR chart
With one continuous measurement per batch and no natural subgroups, an individuals and moving range chart is used. Xbar-R needs several measurements per subgroup.

Question 6Analyze

A team concludes that a new supplier's parts have a different mean diameter, but in truth there is no difference. What error was made?

Correct answer: A. Type I error
A Type I error rejects a true null hypothesis, finding a difference that does not exist. A Type II error fails to detect a difference that really exists.

Question 7Measure

A value stream map for a permit office shows 30 minutes of total value-added time and a total lead time of 10 hours. What is the process cycle efficiency?

Correct answer: D. 5%
PCE = value-added time / lead time = 30 / 600 minutes = 0.05, or 5%. Lead time must be converted to minutes first, which is why 0.5% and 30% are wrong.

Question 8Improve

A regression of delivery time on number of stops has an R-squared of 0.72. What does this mean?

Correct answer: A. 72% of the variation in delivery time is explained by stops
R-squared is the proportion of variation in the response explained by the model. The correlation would be the square root of 0.72, about 0.85, not 0.72.

Question 9Define

A circuit board plant inspected 500 boards. Each board has 10 opportunities for a defect, and inspectors found 25 defects in total. What is the DPMO?

Correct answer: C. 5,000
DPMO = defects / (units x opportunities) x 1,000,000 = 25 / (500 x 10) x 1,000,000 = 5,000. The value 50,000 comes from ignoring opportunities and using 25 / 500.

Question 10Control

A machining cell measures 4 consecutive parts every hour for shaft diameter. Which control chart is MOST appropriate?

Correct answer: A. Xbar-R chart
Small rational subgroups of continuous data, such as 4 parts, suit an Xbar and range chart. Attribute charts like np or u are for counts, not measurements.

Question 11Measure

A claims office has an average of 200 claims in process and completes 40 claims per day. Using Little's Law, what is the average lead time?

Correct answer: D. 5 days
Little's Law states lead time = WIP / throughput = 200 / 40 = 5 days. The value 0.2 days inverts the ratio.

Question 12Analyze

A seal integrity test on a drug packaging line fails to detect a real increase in seal failures, and the team concludes nothing has changed. What error occurred, and what is its main risk?

Correct answer: B. Type II error; a real problem goes unaddressed
Failing to detect a real change is a Type II error, and its risk is that a true problem continues. Acting on a false alarm is the risk of a Type I error.

Question 13Define

A claims process has three sequential steps with first pass yields of 95%, 90%, and 98%. What is the rolled throughput yield?

Correct answer: C. 83.8%
RTY is the product of the step yields: 0.95 x 0.90 x 0.98 = 0.838, or 83.8%. The value 94.3% is the simple average, which overstates the chance a unit passes every step without rework.

Question 14Improve

Adding a fourth predictor to a regression model raises R-squared from 0.810 to 0.812 but lowers adjusted R-squared from 0.795 to 0.788. What does this suggest?

Correct answer: B. The new predictor adds little and should likely be dropped
R-squared never falls when a predictor is added, but adjusted R-squared penalizes terms that do not add real explanatory power. A drop in adjusted R-squared signals the new term is not worth keeping.

Question 15Control

A high-speed filler samples 12 bottles per subgroup for fill volume. Which control chart is BEST for monitoring both center and spread?

Correct answer: D. Xbar-S chart
For larger subgroups, usually above about 10, the standard deviation estimates spread better than the range, so Xbar-S is preferred. The range ignores most of the data in a large subgroup.

Question 16Measure

A glass plant records the number of surface blemishes found on each sheet. What type of data is this?

Correct answer: B. Discrete (count) data
Counts of blemishes take whole number values, so they are discrete count data. Continuous data, such as thickness, can take any value within a range.

Question 17Analyze

A hypothesis test is designed with beta = 0.20. What is the power of the test?

Correct answer: C. 0.80
Power = 1 - beta = 1 - 0.20 = 0.80, the probability of detecting a real difference. The value 0.95 is 1 - alpha for a common alpha, which is a different quantity.

Question 18Define

A hotel chain survey shows guests rarely mention clean towels, yet complaints spike sharply whenever towels are missing. In the Kano model, clean towels are BEST classified as which type of requirement?

Correct answer: A. Basic (must-be) requirement
Basic needs are expected and unspoken, so meeting them earns little credit but missing them causes strong dissatisfaction. A performance need would raise satisfaction steadily as it improves, which is not the pattern here.

Question 19Improve

A plot of residuals versus fitted values shows a funnel shape that widens as the fitted values increase. What does this indicate?

Correct answer: D. The residuals do not have constant variance
A widening funnel shows that error variance grows with the fitted value, which violates the equal variance assumption. A transformation or weighted regression may be needed.

Question 20Control

A mail-order pharmacy tracks the proportion of prescriptions with errors each day, and daily volume varies widely. Which chart fits?

Correct answer: A. p chart
A p chart plots the proportion defective and handles varying sample sizes by adjusting the limits. An np chart needs a constant sample size.

Question 21Measure

A bank's call volume comes from three regions that differ greatly in size and customer mix. The Black Belt wants a sample that represents each region in proportion. Which sampling method is BEST?

Correct answer: C. Stratified random sampling
Stratified sampling divides the population into groups and samples each one, so every region is properly represented. Simple random sampling could under-represent a small region by chance.

Question 22Analyze

Using alpha = 0.05, a 2-sample t-test comparing the mean output of two machines returns p = 0.03. What is the correct conclusion?

Correct answer: D. Reject the null; the means differ significantly
Because p = 0.03 is below alpha = 0.05, the null hypothesis of equal means is rejected. A p-value is not the probability that either hypothesis is true.

Question 23Define

Patients at an outpatient clinic say they want quick service. The Black Belt is building a CTQ tree from this comment. Which item is the BEST CTQ to place at the end of the branch?

Correct answer: D. 95% of patients seen within 15 minutes of check-in
A CTQ must be specific and measurable with a clear target, which turns vague VOC into a requirement the process can be judged against. Adding staff is a solution, not a requirement.

Question 24Improve

In a multiple regression model, two predictors have variance inflation factors of 12 and 14. What is the MOST likely issue?

Correct answer: B. Strong multicollinearity between predictors
VIF values above about 5 to 10 indicate that a predictor is highly correlated with other predictors, which makes coefficients unstable. VIF does not measure residual normality.

Question 25Control

An inspector checks exactly 200 circuit boards per day and records the number of defective boards. Which chart fits?

Correct answer: C. np chart
An np chart plots the number of defective units when the sample size is constant. A c or u chart counts defects, not defective units.

Question 26Measure

Repair times at a service center are strongly right-skewed because a few jobs take several days. Which statistic BEST describes a typical repair time?

Correct answer: D. Median
The median is resistant to extreme values, so it describes the typical case in skewed data. The mean is pulled toward the long tail and overstates a typical repair time.

Question 27Analyze

A Black Belt compares average loan processing time between two independent branches. The data are continuous and roughly normal. Which test is MOST appropriate?

Correct answer: C. 2-sample t-test
A 2-sample t-test compares the means of two independent groups with continuous data. A paired t-test needs matched observations on the same units.

Question 28Define

A Black Belt is drafting the problem statement for a project charter at a regional distribution center. Which statement is MOST appropriate?

Correct answer: B. Picking errors rose from 0.8% to 2.1% in Q2, adding $40K in returns
A good problem statement describes what, where, when, and how big, with data, and avoids assigning causes or solutions. The training statement assumes a root cause before any analysis.

Question 29Improve

A model of cure time was built from data with oven temperatures between 150 and 200 degrees. A manager wants to use it to predict cure time at 260 degrees. What is the main concern?

Correct answer: C. Predictions outside the data range are unreliable
Extrapolating beyond the range of the data assumes the relationship holds where it was never observed. The process may behave very differently at 260 degrees.

Question 30Control

A paper mill counts the number of flaws on each roll, and every roll is the same size. Which chart fits?

Correct answer: A. c chart
A c chart plots the count of defects per unit when the area of opportunity is constant. A p chart tracks the proportion of defective units.

Question 31Measure

Fill weights are normally distributed with a mean of 50 g and a standard deviation of 4 g. The upper specification limit is 58 g. About what percent of packages exceed the upper limit?

Correct answer: B. About 2.3%
z = (58 - 50) / 4 = 2.0, and the area above z = 2 is about 2.3%. The value 5% is the two-tailed area beyond plus or minus 2 sigma, not the area above one limit.

Question 32Analyze

Ten technicians each had their task time measured before and after a training course. Which test BEST compares the two sets of times?

Correct answer: A. Paired t-test
Each technician provides both measurements, so the data are paired and the test should analyze the differences. A 2-sample t-test treats the groups as independent and loses power.

Question 33Define

A Black Belt at an insurance company has a newly approved charter for claims processing delays. Team members disagree about where the process starts and where it ends. Which tool should the Black Belt use FIRST?

Correct answer: C. SIPOC diagram
A SIPOC gives a high-level view of suppliers, inputs, process steps, outputs, and customers and sets the start and stop points of the scope. A detailed swimlane map comes later, once the boundaries are agreed.

Question 34Improve

A Black Belt plans a full factorial experiment with 4 factors at 2 levels each, replicated twice, with no center points. How many runs are required?

Correct answer: D. 32
A 2^4 design has 16 runs, and two replicates give 16 x 2 = 32 runs. The value 16 is a single replicate.

Question 35Control

A hospital tracks patient falls each month, and the number of patient-days varies widely from month to month. Which chart fits?

Correct answer: D. u chart
A u chart divides each count by its exposure, here patient-days, so months of different sizes are compared fairly. A c chart would mislead because busier months naturally have more falls.

Question 36Measure

For a normally distributed process, about what percent of output falls within plus or minus 2 standard deviations of the mean?

Correct answer: A. 95.4%
The empirical rule gives about 68.3% within 1 sigma, 95.4% within 2 sigma, and 99.7% within 3 sigma. So 68.3% applies to plus or minus 1 sigma, not 2.

Question 37Analyze

A plant compares average yield across four production lines. The data are normal with similar variances. Which test is BEST?

Correct answer: B. One-way ANOVA
One-way ANOVA compares three or more means in one test while holding the overall alpha. Running six t-tests inflates the chance of a false positive.

Question 38Define

During stakeholder analysis, a Black Belt finds that the plant operations director has high influence over the project and is currently opposed to it. What is the BEST action?

Correct answer: D. Meet the director to understand concerns and build support
High-influence stakeholders who resist need active, direct engagement so their concerns can be addressed early. A newsletter is suited to low-influence stakeholders and leaves the resistance in place.

Question 39Improve

A Black Belt runs a half fraction of a 5-factor, 2-level design without replication or center points. How many runs are needed?

Correct answer: C. 16
A half fraction of 2^5 is 2^(5-1) = 16 runs. The full factorial would need 32 runs.

Question 40Control

A Black Belt needs to detect small, sustained shifts of about 0.5 sigma in a well-controlled process. Which chart is MOST suitable?

Correct answer: B. EWMA or CUSUM chart
EWMA and CUSUM charts accumulate information over time, which makes them sensitive to small persistent shifts. Standard Shewhart charts are better at catching large, sudden shifts.

Question 41Measure

A gage R&R study on a bore gauge shows the measurement system accounts for 35% of total study variation. What is the BEST conclusion?

Correct answer: C. The system is unacceptable and must be improved before use
Common guidelines treat under 10% as acceptable, 10% to 30% as possibly acceptable, and over 30% as unacceptable. At 35%, the gauge adds too much noise to make reliable decisions.

Question 42Analyze

A Black Belt wants to know if defect type (scratch, dent, or crack) depends on shift (day or night). Which test fits?

Correct answer: A. Chi-square test of independence
Both variables are categorical, so a chi-square test of independence checks whether they are related. ANOVA needs a continuous response.

Question 43Define

An appliance maker pays for technician visits to repair washing machines that are still under warranty. In a cost of poor quality analysis, these costs belong in which category?

Correct answer: B. External failure
External failure costs arise after the product reaches the customer, such as warranty repairs and returns. Internal failure costs, like scrap and rework, occur before shipment.

Question 44Improve

Which statement is true of a Resolution III fractional factorial design?

Correct answer: A. Main effects are aliased with two-factor interactions
In a Resolution III design, main effects are confounded with two-factor interactions, so it is used mainly for screening. Main effects clear of two-factor interactions describes Resolution IV.

Question 45Control

On an Xbar chart, a point falls outside the upper control limit, but every part in that subgroup is within specification. What should the team do?

Correct answer: C. Investigate it as a possible special cause
Control limits show the voice of the process, so a point outside them signals a likely special cause even if parts meet the customer's specs. Ignoring it risks a later drift outside the specs.

Question 46Measure

In a gage R&R study, the measurement system variance is 4 and the total observed variance is 100. What are the percent contribution and the percent study variation for the measurement system?

Correct answer: B. 4% contribution and 20% study variation
Percent contribution uses variances: 4 / 100 = 4%. Percent study variation uses standard deviations: square root of 4 / square root of 100 = 2 / 10 = 20%.

Question 47Analyze

Before comparing the variability of fill volume across three filler heads, the Black Belt finds the data are clearly not normal. Which test of variances is MOST appropriate?

Correct answer: D. Levene's test
Levene's test compares variances of two or more groups and is robust to non-normal data. Bartlett's test assumes normality, and the F-test handles only two groups.

Question 48Define

A furniture plant built 200 chairs last week. Final audit found 40 defects spread across the chairs, and some chairs had more than one defect. What is the defects per unit?

Correct answer: A. 0.20
DPU = total defects / total units = 40 / 200 = 0.20. The value 5.00 inverts the ratio, and 0.80 confuses DPU with a yield figure.

Question 49Improve

Why do analysts often code DOE factor levels as -1 and +1 before fitting a model?

Correct answer: B. It puts all factors on one scale so coefficients compare directly
Coding puts factors with different units on a common scale, so coefficient sizes can be compared and terms are less correlated. It does not replace randomization.

Question 50Control

On a control chart, nine consecutive points fall above the centerline, but all are inside the control limits. What does this MOST likely indicate?

Correct answer: D. A shift in the process mean
A long run on one side of the centerline is very unlikely by chance and signals a shift in the mean, even if no point is beyond the limits. Common cause variation would scatter points on both sides.

Question 51Measure

A gage R&R study reports 2 distinct categories. What does this mean for the measurement system?

Correct answer: D. It can split parts into only about two groups, which is not adequate
The number of distinct categories shows how many groups of parts the system can reliably tell apart, and at least 5 is the usual guideline. With 2, the gauge acts like a go/no-go check.

Question 52Analyze

Customer wait times at two independent stores are heavily skewed, and the samples are small. Which test BEST compares the central tendency of the two stores?

Correct answer: A. Mann-Whitney test
The Mann-Whitney test is a nonparametric test for two independent groups that does not assume normality. A t-test on small, skewed samples can give unreliable p-values.

Question 53Define

A finance team spends six hours a month adding color charts and extra rounding checks to a variance report. Interviews show the only reader looks at a single total on the first page. Which of the 8 wastes does this BEST represent?

Correct answer: C. Overprocessing
Overprocessing is doing more work or adding more features than the customer needs. Overproduction would mean making more output, or making it sooner, than the customer requires.

Question 54Improve

In a 2-level experiment, the average yield is 70% at the high level of temperature and 60% at the low level. What is the main effect of temperature?

Correct answer: A. 10 percentage points
Main effect = average at high level - average at low level = 70 - 60 = 10 points. The value 65 is the overall average, not an effect.

Question 55Control

Two of three consecutive points on an Xbar chart fall between 2 and 3 sigma above the centerline. How should this be treated?

Correct answer: B. As a signal of a likely special cause
Two of three points beyond 2 sigma on the same side is a common sensitizing rule that signals a nonrandom pattern. Waiting for a point outside 3 sigma would miss early warnings.

Question 56Measure

A gage R&R study shows repeatability variation is much larger than reproducibility variation. Where should the team look FIRST?

Correct answer: B. The gauge itself, such as wear, fixturing, or resolution
Repeatability is equipment variation, the spread when one person measures the same part repeatedly. Large reproducibility would point to operator differences instead.

Question 57Analyze

A Black Belt must compare medians across four groups, and the data contain several extreme outliers. Which nonparametric test is MOST robust to the outliers?

Correct answer: C. Mood's median test
Mood's median test only counts values above or below the overall median, so extreme outliers have little effect. Kruskal-Wallis is more powerful in general but is more affected by outliers.

Question 58Define

After removing unneeded items from a maintenance crib, a team outlines each tool on a shadow board and labels every bin with its contents. Which 5S step are they performing?

Correct answer: B. Set in order
Set in order gives every needed item a defined, visible home so it is easy to find and return. Sort was the earlier step of removing items that are not needed.

Question 59Improve

An interaction plot for pressure and line speed shows lines that cross sharply. What does this mean?

Correct answer: D. The effect of pressure depends on the speed level
Non-parallel or crossing lines show an interaction, so one factor's effect changes with the level of the other. Parallel lines would mean no interaction.

Question 60Control

Six consecutive points on an individuals chart steadily increase. What does this pattern MOST likely indicate?

Correct answer: A. A trend, such as tool wear or drift
A steady run of increasing or decreasing points signals a trend, often caused by wear, fatigue, or gradual drift. Overadjustment tends to cause alternating up and down points.

Question 61Measure

An attribute agreement study of loan file reviewers gives a kappa of 0.45 when their ratings are compared with an expert standard. What is the BEST interpretation?

Correct answer: C. Agreement is poor and the review method needs improvement
Kappa above about 0.9 is excellent, 0.7 to 0.9 is often acceptable, and below 0.7 needs improvement. A value of 0.45 shows agreement is not much better than chance would suggest.

Question 62Analyze

An Anderson-Darling normality test on 50 cycle times returns p = 0.01. Using alpha = 0.05, what does this indicate?

Correct answer: A. There is evidence that the data are not normal
The null hypothesis of a normality test is that the data are normal, so a p-value below alpha rejects normality. A high p-value would mean no evidence against normality.

Question 63Define

Which activity in a mortgage approval process is value-added from the customer's point of view?

Correct answer: D. Underwriter evaluates risk and approves the loan
Value-added work changes the product or service in a way the customer cares about and will pay for, done right the first time. Re-keying, rechecking, and waiting add time and cost without adding value.

Question 64Improve

A Black Belt adds center points to a 2^3 factorial experiment. What is the MAIN benefit?

Correct answer: A. Detecting curvature between the low and high levels
Center points test whether the response bends between the low and high settings, which a two-level design alone cannot reveal. They do not change the resolution or add true factor levels.

Question 65Control

A p chart is planned for a process with an average defective rate of 1%, using subgroups of 50 units. Why is this a problem?

Correct answer: C. Each subgroup expects only 0.5 defectives, so the chart is weak
With n x p-bar = 50 x 0.01 = 0.5, most subgroups show zero defectives and the chart cannot detect changes well. Larger subgroups are needed for low defect rates.

Question 66Measure

A technician measures a 10.00 mm reference standard 20 times and gets an average reading of 10.15 mm. What is the bias of the gauge?

Correct answer: D. +0.15 mm
Bias = observed average - reference value = 10.15 - 10.00 = +0.15 mm. The sign is positive because the gauge reads high.

Question 67Analyze

A Black Belt finds a strong correlation (r = 0.85) between hours of overtime and error rate in a records department. What is the BEST conclusion?

Correct answer: D. A strong link exists, but causation needs further proof
Correlation shows association, not cause, and a third factor such as workload may drive both. A designed test or deeper analysis is needed to prove causation.

Question 68Define

Three weeks into a project, team members openly argue about roles and question the Black Belt's approach in meetings. Which team stage is this, and what is the BEST response?

Correct answer: B. Storming; clarify roles and agree on ground rules
Conflict over roles and direction marks the storming stage, and the leader should clarify roles and set ground rules to move the team forward. Stepping back as if the team were norming lets the conflict continue.

Question 69Improve

A DOE needs 16 runs, but only 8 can be done per day, and day-to-day differences are suspected. What should the Black Belt do?

Correct answer: C. Block the design by day
Blocking assigns runs to days so the day effect can be separated from factor effects. Running all high levels on one day would confound the factor with the day.

Question 70Control

Why should a subgroup for an Xbar-R chart usually be made of consecutive parts produced close together in time?

Correct answer: B. To capture short-term variation and let shifts show between subgroups
Rational subgroups keep within-subgroup variation to common causes, so special causes show up as differences between subgroups. Mixing shifts within a subgroup inflates the range and widens limits.

Question 71Measure

A scale reads accurately at 1 kg but reads 0.3 kg high at 20 kg. Which measurement system property is the problem?

Correct answer: C. Linearity
Linearity is a change in bias across the operating range of the gauge. Stability is a change in bias over time, not across the range.

Question 72Analyze

A simple linear regression of delivery time on distance gives an R-squared of 0.64 with a positive slope. What is the correlation coefficient?

Correct answer: B. 0.80
In simple linear regression, r is the square root of R-squared with the sign of the slope: the square root of 0.64 is 0.80, and the slope is positive. The value 0.41 squares R-squared instead of taking the root.

Question 73Define

A supervisor keeps delaying data collection for a Black Belt's project, saying the team is too busy. What should the Black Belt do FIRST?

Correct answer: C. Talk with the supervisor to learn the reason
Resistance often has a real cause, such as workload or fear of blame, so the first step is to understand it directly. Escalating first can harden resistance and damage the working relationship.

Question 74Improve

Why should the runs in a designed experiment be performed in random order?

Correct answer: A. To protect against unknown time-related nuisance effects
Randomization spreads the effects of unknown lurking variables, such as warm-up or drift, across all runs. Without it, a time trend could be mistaken for a factor effect.

Question 75Control

An Xbar-R chart uses subgroups of 5. The grand average is 50.0 and the average range is 4.0. With A2 = 0.577, what is the upper control limit for the Xbar chart?

Correct answer: D. 52.31
UCL = grand average + A2 x R-bar = 50.0 + 0.577 x 4.0 = 50.0 + 2.31 = 52.31. The value 54.00 adds the full average range instead of A2 x R-bar.

Question 76Measure

How should a lab check the stability of a pH meter over time?

Correct answer: A. Measure the same reference buffer regularly and chart the results
Stability is consistency over time, so repeated measurements of a known reference plotted on a control chart reveal drift. A single-day study measures repeatability and reproducibility, not stability.

Question 77Analyze

A multi-vari study of shaft diameter shows small variation within each shaft and between consecutive shafts, but large differences from one hour to the next. Which family of variation dominates?

Correct answer: C. Temporal (time-to-time)
Large differences between time periods point to temporal variation, such as tool wear, temperature, or shift changes. Positional variation would show large differences within each part.

Question 78Define

A Champion has four candidate projects. Which one is the BEST candidate for a Black Belt DMAIC project?

Correct answer: D. Chronic scrap, unknown cause, $400K COPQ, data on hand
DMAIC suits chronic problems with significant cost, an unknown root cause, and data available to analyze. A known fix is a just-do-it item, not a DMAIC project.

Question 79Improve

After screening, a team believes the optimum lies inside the current factor region and the response is curved. Which design is MOST appropriate?

Correct answer: D. Central composite design
A central composite design adds axial and center points to a factorial so a quadratic model can map curvature and locate an optimum. Two-level screening designs cannot model curvature.

Question 80Control

A p chart has an average proportion defective of 0.10 and a constant subgroup size of 100. What are the control limits?

Correct answer: B. UCL 0.19, LCL 0.01
Sigma = square root of (0.10 x 0.90 / 100) = 0.03, so the limits are 0.10 plus or minus 3 x 0.03, giving 0.19 and 0.01. The pair 0.13 and 0.07 uses 1 sigma instead of 3.

Question 81Measure

A machining process has specification limits of 90 and 110, and a within-subgroup standard deviation of 2.5. What is Cp?

Correct answer: B. 1.33
Cp = (USL - LSL) / (6 sigma) = 20 / 15 = 1.33. Cp ignores centering and only compares the tolerance width with the process spread.

Question 82Analyze

A team wants to organize brainstormed causes of late patient discharges into categories such as people, methods, and equipment. Which tool fits BEST?

Correct answer: D. Cause-and-effect diagram
A cause-and-effect, or fishbone, diagram sorts possible causes into categories to guide investigation. A Pareto chart ranks causes after they have been counted.

Question 83Define

Midway through a project on invoice errors, a director asks the team to also fix vendor onboarding delays. What is the BEST way for the Black Belt to handle this request?

Correct answer: C. Review the in and out of scope list with the Champion
Scope changes should be judged against the agreed in and out of scope boundaries and decided with the Champion. Quietly adding work causes scope creep and delays the original goal.

Question 84Improve

A first-order model shows yield rises with both temperature and time, and the optimum appears to be well outside the current test region. What should the team do next?

Correct answer: B. Use steepest ascent to move toward the optimum
The method of steepest ascent moves runs along the direction of greatest improvement until the response stops rising. Fitting curvature makes sense only once the region near the optimum is reached.

Question 85Control

A c chart for scratches per panel has an average count of 9. What are the control limits?

Correct answer: C. UCL 18, LCL 0
For a c chart, sigma = square root of c-bar = 3, so UCL = 9 + 9 = 18 and LCL = 9 - 9 = 0. The pair 12 and 6 uses only 1 sigma.

Question 86Measure

A process has a mean of 104, USL of 110, LSL of 90, and a standard deviation of 2. What is Cpk?

Correct answer: A. 1.00
Cpu = (110 - 104) / 6 = 1.00 and Cpl = (104 - 90) / 6 = 2.33, and Cpk is the smaller value, 1.00. The value 1.67 is Cp, which ignores that the mean is off center.

Question 87Analyze

A team uses 5 Whys on a complex packaging defect with several interacting causes. What is the MAIN limitation of this approach here?

Correct answer: B. It follows one path and can miss multiple causes
5 Whys is simple and useful, but it tends to follow a single chain of causes. Complex problems with interacting causes need tools such as fishbone diagrams and data analysis.

Question 88Define

A hospital team is applying Lean thinking to its patient discharge process. Which step should the team take FIRST?

Correct answer: A. Define value from the patient's point of view
Lean thinking starts by defining value from the customer's view, then mapping the value stream, creating flow, establishing pull, and seeking perfection. Building flow before value is defined risks speeding up the wrong work.

Question 89Improve

In a Pugh matrix, what is the role of the datum?

Correct answer: C. A reference concept others are scored against
Each alternative is rated better, worse, or the same as the datum for each criterion. The datum is a baseline for comparison, not the winning option.

Question 90Control

When should control limits on an established chart be recalculated?

Correct answer: D. After a verified, lasting change to the process
Limits should be recalculated only when the process has truly changed, such as after an improvement, and the new state is stable. Recalculating after every signal hides special causes.

Question 91Measure

A process has Cp = 1.8 and Cpk = 0.9. What is the BEST first improvement action?

Correct answer: D. Center the process mean within the specification limits
A large gap between Cp and Cpk means the spread fits the tolerance but the mean is off center. Shifting the mean toward the target raises Cpk toward Cp.

Question 92Analyze

A Pareto chart shows that 2 of 9 complaint categories account for 78% of all complaints. What should the team do next?

Correct answer: A. Focus root cause work on the two largest categories
The Pareto principle directs effort to the vital few categories that drive most of the problem. Spreading effort across all nine dilutes the impact.

Question 93Define

A warehouse receives most of its weekly orders on Monday, which causes heavy overtime early in the week and idle staff on Thursday and Friday. Which Lean concept BEST describes the underlying problem?

Correct answer: B. Mura (unevenness)
Mura is unevenness in workload or demand, which is the root issue here. The Monday overtime is muri, or overburden, but it is a result of the uneven demand.

Question 94Improve

Why should a Black Belt pilot a new scheduling process in one clinic before rolling it out to all twelve clinics?

Correct answer: D. To confirm results and find problems at low risk
A pilot tests the solution under real conditions on a small scale, so issues can be fixed before full rollout. It does not replace the control plan.

Question 95Control

An operator adjusts the machine after every part, moving the setting up when a part measures high and down when it measures low, even though the process is stable. What is the likely result?

Correct answer: C. Variation increases because of tampering
Adjusting a stable process in response to common cause variation, called tampering, adds variation. A stable process should be left alone unless a special cause appears.

Question 96Measure

What is the key difference between Cp and Pp?

Correct answer: A. Cp uses within-subgroup sigma, while Pp uses overall sigma
Cp reflects short-term potential using within-subgroup variation, while Pp uses the overall long-term standard deviation. Neither index accounts for centering; Cpk and Ppk do.

Question 97Analyze

A Black Belt suggests always using nonparametric tests to avoid checking assumptions. What is the main drawback of this approach?

Correct answer: C. They have less power than parametric tests when the assumptions hold
When data meet parametric assumptions, tests such as the t-test detect real differences with smaller samples than their nonparametric versions. Nonparametric tests do not require normality, so that option is backwards.

Question 98Define

Which responsibility BEST belongs to the project Champion rather than the Black Belt?

Correct answer: A. Removing organizational barriers and securing resources
The Champion is a senior leader who sponsors the project, clears roadblocks, and provides resources. Leading analysis and choosing tests are Black Belt tasks.

Question 99Improve

In a SMED event, a team finds operators search for dies and fetch tools while the press is stopped. What is the FIRST improvement to make?

Correct answer: B. Move these tasks to external setup while the press runs
SMED first separates internal and external tasks, then converts internal work, such as fetching dies, to external work done while the machine runs. Larger batches hide the problem and add inventory.

Question 100Control

Which set of items is MOST essential to include in a control plan for a critical characteristic?

Correct answer: A. Measurement method, sample size, frequency, and reaction plan
A control plan defines how each key characteristic is measured, how often, by whom, and what to do when it goes out of control. Project history documents do not control the process.

Question 101Measure

A Black Belt is asked to report Cpk for a process whose control chart shows several points beyond the control limits. What should happen FIRST?

Correct answer: C. Find and remove the special causes before judging capability
Capability indices predict future performance only if the process is stable. Deleting points hides the problem without removing the special causes.

Question 102Analyze

With 50,000 transactions, a test shows a statistically significant difference of 0.2 seconds in average processing time between two servers. What should the Black Belt consider NEXT?

Correct answer: B. Whether a 0.2 second difference matters to the business
Very large samples can make tiny differences statistically significant, so practical significance must also be judged. Changing alpha to avoid a result is not good practice.

Question 103Define

A plant reports 98% final yield. A Black Belt finds that operators quietly rework about 15% of units before they reach final inspection. Which concept does this illustrate?

Correct answer: D. The hidden factory
The hidden factory is the unrecorded rework and correction that final yield figures do not show. First pass yield or RTY would reveal it, while final yield hides it.

Question 104Improve

A kanban loop has demand of 100 parts per hour, a replenishment lead time of 2 hours, a 10% safety factor, and 20 parts per container. How many kanban cards are needed?

Correct answer: A. 11
Cards = demand x lead time x (1 + safety) / container size = 100 x 2 x 1.1 / 20 = 220 / 20 = 11. The value 10 leaves out the safety factor.

Question 105Control

An operator sees a point beyond the control limit on a critical dimension. According to a good response plan, what should happen FIRST?

Correct answer: B. Contain suspect product and notify the owner per the plan
A response plan tells the operator exactly what to do, usually to contain affected product and escalate. Unplanned adjustments can make things worse.

Question 106Measure

Why do many practitioners add a 1.5 sigma shift when converting short-term capability to long-term defect rates?

Correct answer: A. To allow for drift in the process mean over time
The 1.5 sigma shift is a convention that assumes the process mean wanders over the long term, which raises the long-term defect rate. It is not a correction for measurement error or sample size.

Question 107Analyze

A sample of 100 orders has a mean processing time of 50 minutes and a standard deviation of 10 minutes. What is the approximate 95% confidence interval for the mean?

Correct answer: D. 48.04 to 51.96 minutes
Standard error = 10 / square root of 100 = 1, so the interval is 50 plus or minus 1.96 x 1, or 48.04 to 51.96. The range 30.4 to 69.6 uses the standard deviation instead of the standard error.

Question 108Define

A car maker added rear-view cameras years ago and buyers were delighted. Today, buyers complain if a car lacks one. What does this show about the Kano model?

Correct answer: A. Delighters tend to become basic needs over time
Customer expectations rise, so features that once delighted become expected basics. This is why Kano analysis needs to be repeated as markets change.

Question 109Improve

A line has 120 seconds of total work content spread over 4 stations, and the cycle time is set at 40 seconds. What is the line balance efficiency?

Correct answer: C. 75%
Balance efficiency = total work / (stations x cycle time) = 120 / (4 x 40) = 120 / 160 = 75%. The rest is idle time built into the line.

Question 110Control

Which element is a core part of standard work?

Correct answer: A. Takt time, work sequence, and standard WIP
Standard work defines the takt time, the best known sequence of steps, and the standard amount of work in process. It becomes the baseline for further improvement.

Question 111Measure

A process makes 10% defective parts, and defectives occur independently. If 5 parts are drawn at random, what is the probability that none of them is defective?

Correct answer: D. About 59%
Using the binomial model, P(0 defectives) = 0.90 to the 5th power = 0.590, or about 59%. The value 50% subtracts 5 x 10% from 1, which is not how independent probabilities combine.

Question 112Analyze

A one-way ANOVA comparing five suppliers gives p = 0.002. What should the Black Belt do next to find which suppliers differ?

Correct answer: B. Run a multiple comparison method such as Tukey's
ANOVA only shows that at least one mean differs, so a multiple comparison method identifies which pairs differ while controlling error rates. Ten separate t-tests inflate the overall Type I error.

Question 113Define

A Black Belt's project frees 400 hours of staff time per year, but no headcount, overtime, or spending is reduced. How should finance classify this benefit?

Correct answer: C. Soft savings, such as freed capacity
Hard savings show up as a real reduction in spending on the financial statements. Freed time with no change in spending is capacity or cost avoidance, which is treated as soft savings.

Question 114Improve

A connector is redesigned with an asymmetric shape so it can only be plugged in the correct way. What type of mistake-proofing is this?

Correct answer: B. Contact method, using shape to prevent errors
The contact method uses physical features such as shape or size to detect or block errors. The fixed-value method checks that a set number of actions or parts was completed.

Question 115Control

A plant installs lights above each workstation that turn on when an operator needs help or the line has a problem. What is this visual tool called?

Correct answer: D. Andon
An andon is a visual or audio signal that alerts others to a problem in real time. Kanban signals material replenishment, not problems.

Question 116Measure

Two failure modes have the same RPN of 120. One is rated severity 10, occurrence 3, detection 4. The other is severity 4, occurrence 5, detection 6. What should the team do?

Correct answer: B. Give priority to the failure mode with severity 10
RPN can hide serious risks, so high severity items, especially those that affect safety, should be addressed regardless of RPN. Equal RPNs do not mean equal risk.

Question 117Analyze

In a one-way ANOVA, the mean square between groups is 40 and the mean square within groups is 8. What is the F statistic?

Correct answer: C. 5.0
F = MS between / MS within = 40 / 8 = 5.0. The value 0.2 inverts the ratio.

Question 118Define

In an assembly cell, workers repeatedly walk 10 meters to a shared cabinet to pick up hand tools. Which waste is this?

Correct answer: A. Motion
Motion is unnecessary movement of people, such as walking, reaching, or searching. Transportation is the unnecessary movement of materials or products between steps.

Question 119Improve

Which statement BEST describes a pull system?

Correct answer: D. Upstream steps produce only when downstream signals a need
In a pull system, consumption downstream triggers replenishment upstream, which limits work in process. Producing to a forecast and pushing work forward describes a push system.

Question 120Control

Which control method gives the STRONGEST protection against a recurring assembly error?

Correct answer: A. A fixture that makes wrong assembly impossible
Mistake-proofing that physically prevents the error is the strongest control because it does not rely on memory or attention. Inspection only catches defects after they are made.

Question 121Measure

In a process FMEA, what does a detection rating of 2 usually mean?

Correct answer: C. Current controls are very likely to catch the failure
Detection is scored so that a low number means the failure is likely to be caught. Occurrence and severity are separate ratings.

Question 122Analyze

A pooled 2-sample t-test compares a group of 12 parts with a group of 10 parts. How many degrees of freedom does the test have?

Correct answer: D. 20
For a pooled 2-sample t-test, df = n1 + n2 - 2 = 12 + 10 - 2 = 20. The value 22 forgets to subtract one degree of freedom for each group.

Question 123Define

A project aims to cut average call handle time. Why should the Black Belt also track a secondary metric such as first call resolution?

Correct answer: D. To catch harmful side effects of the main change
A secondary or counterbalancing metric shows whether improving the primary metric causes harm elsewhere, such as rushed calls and repeat contacts. It does not replace the primary metric.

Question 124Improve

A Black Belt is leading a solution brainstorming session for reducing billing delays. Which guideline should be followed during idea generation?

Correct answer: B. Defer judgment and aim for many ideas
Brainstorming works best when criticism is held back so people offer many ideas, which are evaluated later. Judging ideas immediately discourages participation.

Question 125Control

At project handover, what is the MOST important outcome for the process owner?

Correct answer: C. They accept ownership of the control plan and monitoring
Sustaining the gains depends on the process owner taking responsibility for monitoring and responding with the control plan. Relying on the Black Belt after closure is not sustainable.

Question 126Measure

A Black Belt starts a value stream mapping effort at a coffee roasting facility. What should the team do FIRST?

Correct answer: D. Walk the process and draw the current state with real data
The current state map, built from direct observation and real data, is the basis for finding waste. Designing the future state first skips understanding of how the process actually runs.

Question 127Analyze

In a chi-square test of independence, a cell has a row total of 60 and a column total of 50, and the grand total is 200. What is the expected count for that cell?

Correct answer: C. 15
Expected count = row total x column total / grand total = 60 x 50 / 200 = 15. The expected counts are what the table would show if the variables were independent.

Question 128Define

Which tool BEST helps a Black Belt make sure each stakeholder receives the right project updates, in the right format, at the right frequency?

Correct answer: B. Communication plan
A communication plan lists audiences, messages, channels, frequency, and owners. A control plan defines how a process is monitored after improvement, not how stakeholders are updated.

Question 129Improve

Before installing a new automated dispensing system in a pharmacy, what should the team do to anticipate how the new process could fail?

Correct answer: C. Conduct an FMEA on the new process design
An FMEA on the proposed process finds risks before implementation so controls can be built in. Waiting for errors exposes patients to avoidable harm.

Question 130Control

Which activity is typically part of formally closing a Six Sigma project?

Correct answer: A. Validating savings and documenting lessons learned
Closure includes financial validation, documentation, lessons learned, and recognition. Removing control charts would undermine the sustained gains.

Question 131Measure

Which process map is BEST for showing handoffs between sales, credit, and shipping departments in an order process?

Correct answer: B. Swimlane map
A swimlane, or cross-functional, map places each step in the lane of the department that does it, so handoffs are easy to see. A spaghetti diagram shows physical movement, not departmental handoffs.

Question 132Analyze

A supplier claims a new coating reduces corrosion. Management cares only whether corrosion decreases. Which test setup is MOST appropriate?

Correct answer: A. A one-tailed test with the alternative that corrosion decreases
When only one direction matters, a one-tailed test puts all of alpha in that tail and gives more power for that direction. A two-tailed test would also look for an increase that management does not care about.

Question 133Define

A bank plans to launch a brand new mobile lending product. No process for it exists yet. Which approach is MOST appropriate?

Correct answer: C. DMADV, since there is no process to improve
DMADV is used to design a new product or process to meet customer needs. DMAIC improves an existing process with a measurable baseline, which does not exist here.

Question 134Improve

In a 2-level factorial analyzed in coded units, the coefficient for factor A is 4. What is the effect of factor A?

Correct answer: D. 8
In coded units, the effect is twice the coefficient because the factor moves from -1 to +1, a change of 2 units: 2 x 4 = 8. The coefficient alone is half the effect.

Question 135Control

A plant uses short daily audits in which supervisors, managers, and executives each check a few key process steps at different frequencies. What is this practice called?

Correct answer: D. Layered process audits
Layered process audits have several levels of leadership verify that standards are followed, which builds discipline and sustains gains. Gage R&R studies assess measurement systems.

Question 136Measure

A part characteristic has a total tolerance of 0.20 mm. Using the common 10-to-1 rule, what is the coarsest gauge resolution that is acceptable?

Correct answer: A. 0.02 mm
The 10-to-1 rule says resolution should be one tenth of the tolerance or finer: 0.20 / 10 = 0.02 mm. A resolution of 0.002 mm would also work but is finer than required, so it is not the coarsest acceptable value.

Question 137Analyze

A Black Belt lowers alpha from 0.05 to 0.01 while keeping the same sample size. What is the likely effect?

Correct answer: B. Type I risk falls, but beta rises and power falls
With a fixed sample size, lowering alpha makes it harder to reject the null, so the chance of missing a real effect rises. Reducing both risks at once requires a larger sample.

Question 138Define

A team has brainstormed 30 project ideas, but two senior members dominate every discussion. Which technique BEST gives everyone equal input when ranking the ideas?

Correct answer: D. Nominal group technique
Nominal group technique has each member generate and rank ideas individually before the group combines scores, which limits the influence of dominant voices. Open debate lets the same people dominate.

Question 139Improve

A screening experiment with 7 factors is planned. Which principle supports expecting only a few factors to have large effects?

Correct answer: C. Sparsity of effects
The sparsity of effects principle says most systems are driven by a few main effects and low-order interactions. This is why fractional screening designs work well.

Question 140Control

A stable process produces too many defects because its common cause variation is too large. Whose action is MOST needed to reduce it?

Correct answer: B. Management, by changing the system
Common cause variation is built into the system, so reducing it requires changes to equipment, methods, or materials, which management controls. Asking operators to try harder does not change the system.

Question 141Measure

Two shifts report very different on-time delivery rates for the same trucks. One shift counts a delivery as on time within 30 minutes and the other within 2 hours. What is MOST needed?

Correct answer: C. A clear operational definition of on time
An operational definition states exactly how a characteristic is measured so everyone collects data the same way. More data collected under different definitions would still be inconsistent.

Question 142Analyze

After running a one-way ANOVA, which check BEST verifies that its assumptions hold?

Correct answer: A. Examine residuals for normality and equal variance
ANOVA assumes independent, roughly normal residuals with equal variance across groups, and residual plots check this. The p-value shows the test result, not whether its assumptions are met.

Question 143Define

Last quarter a plant scrapped 1,200 units at $15 each and reworked 300 units at $5 each. Ignoring all other costs, what was the internal failure cost?

Correct answer: B. $19,500
Scrap is 1,200 x $15 = $18,000 and rework is 300 x $5 = $1,500, so internal failure cost is $19,500. The value $18,000 counts scrap only and leaves out rework.

Question 144Improve

In a normal probability plot of standardized effects from an unreplicated factorial, how are the important effects identified?

Correct answer: A. They fall well away from the straight line
Unimportant effects behave like random noise and lie along a straight line, while real effects stand out away from it. Effects on the line are consistent with noise.

Question 145Control

What is the main difference between Phase I and Phase II use of control charts?

Correct answer: C. Phase I sets stable limits from history; Phase II monitors new data
In Phase I, historical data are studied to remove special causes and set trial limits. In Phase II, those limits are used to monitor ongoing production.

Question 146Measure

Operators need a simple way to record the type and location of defects on a form as they occur during the shift. Which tool is BEST?

Correct answer: B. Check sheet
A check sheet is a structured form for tallying events by category or location in real time. A Pareto chart is built afterward from data like this.

Question 147Analyze

A team voted that machine age is the top root cause of downtime. What should the Black Belt do before moving to the Improve phase?

Correct answer: D. Verify the cause with data, such as a test or regression
Root causes must be verified with data before solutions are chosen, because team opinion can be wrong. Replacing machines based on a vote risks spending money on the wrong cause.

Question 148Define

After customer interviews, a team has 120 sticky notes with verbatim comments. Which tool should they use to sort these comments into natural themes?

Correct answer: A. Affinity diagram
An affinity diagram groups large amounts of language data into related themes. A Pareto chart ranks categories by frequency but needs the categories to exist first.

Question 149Improve

A team plans to test temperature, then pressure, then time, changing one factor at a time while holding the others fixed. What is the main drawback?

Correct answer: B. It cannot detect interactions and needs more runs
One-factor-at-a-time testing misses interactions between factors and is less efficient than a factorial design. It can lead to a false optimum.

Question 150Control

An I-MR chart has an average of 20.0 and an average moving range of 2.0. What is the upper control limit for the individuals chart?

Correct answer: D. 25.32
UCL = X-bar + 2.66 x MR-bar = 20.0 + 2.66 x 2.0 = 25.32, which equals 20 + 3 x (2.0 / 1.128). The value 26.00 wrongly uses 3 x MR-bar.