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CSSC Black Belt practice questions

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Question 1Six Sigma Body of Knowledge (major sections)

In a Six Sigma DMAIC project, which phase establishes the baseline process capability and validates the measurement system before improvement work begins?

  1. Measure Correct answer.
  2. Define
  3. Control
  4. Analyze

Explanation

The Measure phase quantifies current performance, including baseline capability indices and measurement system analysis, so later phases compare against a trustworthy starting point. Define scopes the problem and Analyze explains variation sources, so neither produces the validated baseline.

Question 2Six Sigma Body of Knowledge (major sections)

A Belt is selecting a tool to separate the effect of five factors on a response with the fewest runs. Which approach is most appropriate?

  1. A fractional factorial design Correct answer.
  2. A one-sample t-test
  3. A full factorial design
  4. A p-chart

Explanation

A fraction of the full factorial run set estimates main effects and selected interactions at far fewer runs, which suits screening many factors. Full factorial designs estimate everything but require 2^5 runs, and the other tools do not screen multiple factors.

Question 3Six Sigma Body of Knowledge (major sections)

Which metric directly expresses the process spread relative to specification limits?

  1. Rolled throughput yield
  2. Defects per million opportunities
  3. Cycle time
  4. Process capability index Cpk Correct answer.

Explanation

Cpk compares the distance from the process mean to the nearer specification limit against three standard deviations, so it captures spread relative to tolerances. DPMO and yield are defect-based counts, and cycle time measures duration.

Question 4Six Sigma Body of Knowledge (major sections)

A team must reduce variation in a process where output is measured on a continuous scale. Which tool best organizes potential causes into categories of method, machine, material, and people?

  1. Control chart
  2. Cause-and-effect diagram Correct answer.
  3. Scatter diagram
  4. Pareto chart

Explanation

A cause-and-effect (fishbone) diagram groups candidate causes into categories such as method, machine, material, and people to structure brainstorming. Pareto charts prioritize frequency, scatter diagrams test correlation, and control charts monitor stability.

Question 5Six Sigma Body of Knowledge (major sections)

During the Control phase, a Belt charts the proportion of defective units in samples of varying size. Which chart is appropriate?

  1. p-chart Correct answer.
  2. I-MR chart
  3. c-chart
  4. X-bar and R chart

Explanation

A p-chart tracks the proportion defective and adjusts control limits for varying subgroup sizes. X-bar and R charts require continuous measurements, c-charts count defects per constant-size unit, and I-MR charts handle individual continuous values.

Question 6Six Sigma Body of Knowledge (major sections)

Which element of a project charter defines the boundaries of what the team will and will not address?

  1. Scope statement Correct answer.
  2. Business case
  3. Team roster
  4. Milestone schedule

Explanation

The scope statement defines process start and stop points and clarifies what is inside and outside the project. The business case justifies the effort, the schedule lists timing, and the roster names participants.

Question 7Six Sigma Body of Knowledge (major sections)

A Belt needs to quantify the relationship between a single continuous input and a continuous output. Which tool is most direct?

  1. FMEA
  2. Simple linear regression Correct answer.
  3. Chi-square test of independence
  4. Kano model

Explanation

Simple linear regression fits a line relating one continuous predictor to a continuous response and quantifies strength and direction. Chi-square handles categorical association, Kano classifies requirements, and FMEA prioritizes failure risks.

Question 8Six Sigma Body of Knowledge (major sections)

In Lean thinking, which type of activity adds value from the customer's perspective?

  1. Necessary non-value-added work
  2. Value-added work Correct answer.
  3. Pure waste
  4. Rework

Explanation

Value-added work transforms the product in ways the customer pays for and gets right the first time. Necessary non-value-added and pure waste consume resources without customer value, and rework corrects defects.

Question 9Six Sigma Body of Knowledge (major sections)

A process has a mean of 50 and a standard deviation of 2 with specification limits of 44 and 56. What is the approximate Cpk?

  1. 1.00 Correct answer.
  2. 0.67
  3. 2.00
  4. 1.33

Explanation

Cpk equals the distance from the mean to the nearer limit divided by three sigma. Here the nearer distance is 6 and three sigma is 6, so Cpk equals 1.00.

Question 10Six Sigma Body of Knowledge (major sections)

A control chart shows one point beyond the upper control limit and no other anomalies. What is the correct interpretation?

  1. The process is out of control and the cause should be investigated Correct answer.
  2. The specification limits must be too tight
  3. The process is in control because only one point is affected
  4. The control limits should be recalculated immediately

Explanation

A point beyond a control limit is a standard signal of special-cause variation, so the team investigates the assignable cause. Control limits describe the process's natural variation and are not specification limits, and one signal is enough to act.

Question 11Six Sigma Body of Knowledge (major sections)

In a Designed Experiment, a Belt confounds a two-factor interaction with a main effect. What design feature causes this?

  1. Resolution III design Correct answer.
  2. Randomization
  3. Resolution IV design
  4. Replication

Explanation

Resolution III designs alias main effects with two-factor interactions, which is why they are used only for screening. Resolution IV designs keep main effects clear but alias two-factor interactions with each other.

Question 12Six Sigma Body of Knowledge (major sections)

A measurement system study reports repeatability acceptable but reproducibility poor. What is the most likely source?

  1. Parts selected are too similar
  2. The sample size is too large
  3. Operators differ in how they measure Correct answer.
  4. The gauge lacks precision

Explanation

Reproducibility reflects variation between operators or setups, so poor reproducibility points to inconsistent operator technique or training. Repeatability reflects equipment variation for one operator, so a gauge precision issue would show there instead.

Question 13Six Sigma Body of Knowledge (major sections)

Which Lean tool levels production by distributing volume and mix evenly over time?

  1. Kanban
  2. Poka-yoke
  3. Heijunka Correct answer.
  4. Andon

Explanation

Heijunka is production leveling, smoothing both total volume and product mix to reduce peaks. Kanban signals replenishment, poka-yoke prevents errors, and andon signals abnormal conditions.

Question 14Six Sigma Body of Knowledge (major sections)

A team finds that 80 percent of complaints come from 20 percent of defect types. Which principle supports prioritizing those defect types?

  1. Pareto principle Correct answer.
  2. Central limit theorem
  3. Rule of seven
  4. Taguchi loss function

Explanation

The Pareto principle holds that a small number of causes produce most effects, so teams address the vital few first. The Taguchi loss function quantifies deviation cost, the central limit theorem concerns sampling distributions, and the rule of seven detects runs.

Question 15Six Sigma Body of Knowledge (major sections)

A hypothesis test returns a p-value of 0.03 against alpha of 0.05. What is the correct decision?

  1. Accept the null hypothesis as true
  2. Reject the null hypothesis Correct answer.
  3. Increase alpha to 0.10
  4. Fail to reject the null hypothesis

Explanation

When the p-value is below alpha, the observed result is unlikely under the null, so the null is rejected. Failing to reject occurs when p exceeds alpha, and a test never proves the null true.

Question 16Six Sigma Body of Knowledge (major sections)

A Belt computes a 95 percent confidence interval for a mean and finds it includes zero, while the target difference is nonzero. What does this suggest?

  1. The measurement system is invalid
  2. The sample mean equals zero exactly
  3. The observed difference is not statistically significant at that confidence level Correct answer.
  4. The process is out of statistical control

Explanation

A confidence interval containing zero means zero is a plausible value for the effect, so the difference is not significant at the corresponding alpha. It says nothing about measurement validity or process stability.

Question 17Six Sigma Body of Knowledge (major sections)

In FMEA, which combination sets the risk priority number?

  1. Severity, occurrence, and detection Correct answer.
  2. Frequency, cost, and cycle time
  3. Yield, throughput, and uptime
  4. Mean, variance, and range

Explanation

The risk priority number multiplies severity, occurrence, and detection ratings to rank failure modes. The other combinations are performance measures rather than FMEA risk elements.

Question 18Six Sigma Body of Knowledge (major sections)

A Belt wants to compare means across four suppliers to test whether they differ. Which method is appropriate?

  1. Simple linear regression
  2. One-way ANOVA Correct answer.
  3. Paired t-test
  4. Chi-square goodness-of-fit

Explanation

One-way ANOVA tests equality of means across three or more groups using between- and within-group variation. A paired t-test handles two related samples, chi-square handles categorical counts, and regression models relationships.

Question 19Six Sigma Body of Knowledge (major sections)

During Analyze, a Belt finds that two operators record the same part differently, causing apparent variation. This is best classified as which type of variation?

  1. Common-cause process variation
  2. Special-cause process variation
  3. Within-part variation
  4. Measurement system variation Correct answer.

Explanation

Disagreement between operators on the same part is reproducibility error within the measurement system. It is not inherent process variation or part-to-part variation, though it can masquerade as either.

Question 20Six Sigma Body of Knowledge (major sections)

A process operates at 4 sigma with a 1.5 sigma shift assumption. What is the approximate DPMO?

  1. 233
  2. 6210 Correct answer.
  3. 66807
  4. 3.4

Explanation

At 4 sigma with the 1.5 sigma shift, the long-term defect rate is about 6,210 defects per million opportunities. The 3.4 figure corresponds to 6 sigma, while 66,807 corresponds to 3 sigma.

Question 21Six Sigma Body of Knowledge (major sections)

A Belt must choose between a t-test and a z-test for a single mean with unknown population standard deviation and a sample of 15. Which is appropriate and why?

  1. t-test, because it requires no assumptions
  2. z-test, because the sample size exceeds 10
  3. z-test, because means always follow a normal distribution
  4. t-test, because the population standard deviation is unknown and the sample is small Correct answer.

Explanation

The t-test accounts for estimating the standard deviation from the sample and uses heavier tails for small samples. A z-test presumes a known population standard deviation or a large sample.

Question 22Six Sigma Body of Knowledge (major sections)

A Belt runs a two-level design with four factors at resolution IV. Which effects are confounded?

  1. Three-factor interactions are aliased with main effects
  2. Two-factor interactions are aliased with other two-factor interactions Correct answer.
  3. Main effects are aliased with two-factor interactions
  4. Main effects are aliased with each other

Explanation

Resolution IV designs keep main effects clear of two-factor interactions but alias two-factor interactions with each other. Main effects aliased with two-factor interactions define resolution III instead.

Question 23Six Sigma Body of Knowledge (major sections)

A process is in statistical control but produces defects because its spread exceeds the specification width. What is the appropriate conclusion?

  1. The specification limits should be widened
  2. The process is capable of meeting specifications only if variation is reduced Correct answer.
  3. The process is out of control and needs a control chart
  4. The process is capable because it is stable

Explanation

Statistical stability means only common-cause variation is present, but capability requires that variation to fit within specifications. Stability does not guarantee capability, so the spread must be reduced or the process redesigned.

Question 24Six Sigma Body of Knowledge (major sections)

A team reduces variation in a process and the mean shifts toward the target. Which capability index change is most consistent with this improvement?

  1. Ppk becomes irrelevant
  2. Cpk decreases because the mean moved
  3. Cp decreases because the spread is unchanged
  4. Cpk increases as the mean moves away from the nearer specification limit Correct answer.

Explanation

Cpk accounts for both spread and centering, so moving the mean toward the target increases the distance to the nearer limit and raises Cpk. Cp depends only on spread, and Ppk remains a valid long-term measure.

Question 25Six Sigma Body of Knowledge (major sections)

A Belt needs to determine whether two categorical variables, defect type and shift, are associated. Which test is appropriate?

  1. Simple linear regression
  2. Chi-square test of independence Correct answer.
  3. One-way ANOVA
  4. Two-sample t-test

Explanation

The chi-square test of independence compares observed and expected counts in a contingency table of two categorical variables. ANOVA and t-tests require continuous responses, and regression models continuous relationships.

Question 26Six Sigma Body of Knowledge (major sections)

In the Six Sigma DMAIC roadmap, which phase formally verifies that the improvements are sustained and hands the process back to the owner with documented controls?

  1. Define
  2. Measure
  3. Improve
  4. Control Correct answer.

Explanation

The Control phase institutionalizes the gains through control plans, monitoring, response plans, and ownership transfer so the improvement does not decay. Improve generates and pilots solutions, while Measure and Define precede them.

Question 27Six Sigma Body of Knowledge (major sections)

A Belt is drafting a problem statement for a charter and wants it to be defensible. Which formulation is most consistent with Six Sigma charter standards?

  1. The billing process needs a complete system replacement to become world class.
  2. Errors happen because the staff do not care about quality.
  3. Invoices are bad and the finance team is unhappy about it.
  4. Between January and March, invoice error rate on the East region was 8.4 percent against a customer requirement of 2 percent or less. Correct answer.

Explanation

A strong problem statement is measurable, time-bound, baseline-anchored, and compared to a requirement without asserting a cause or a solution. The other options embed blame, a preselected solution, or no quantification.

Question 28Six Sigma Body of Knowledge (major sections)

A Belt uses a process map to distinguish steps that physically change the product toward what the customer pays for from steps that do not. Which classification scheme is being applied?

  1. Value-added, business-value-added, and non-value-added Correct answer.
  2. Controllable and noise factors
  3. Critical-to-quality and critical-to-process
  4. Common cause and special cause

Explanation

Lean process analysis classifies each step as value-added, business-value-added (necessary but not customer-valued), or non-value-added waste. The other pairs describe variation sources, experimental factor roles, and requirement translation.

Question 29Six Sigma Body of Knowledge (major sections)

A call center logs the number of nonconforming calls per audited sample of 50 calls, where a call may fail several checklist items. Which control chart is most appropriate?

  1. c chart
  2. p chart
  3. u chart Correct answer.
  4. X-bar and R chart

Explanation

When the sample size is constant but each unit can carry multiple defects, the u chart plots defects per unit. A p chart tracks the proportion of nonconforming units, and a c chart requires a constant opportunity area with counts per unit.

Question 30Six Sigma Body of Knowledge (major sections)

A Belt wants to display the distribution of cycle times and see whether the shape is bimodal before choosing a capability analysis. Which tool is most direct?

  1. Pareto chart
  2. Affinity diagram
  3. Gantt chart
  4. Histogram Correct answer.

Explanation

A histogram bins continuous data and reveals shape, center, spread, skew, and multiple modes. Pareto charts rank categorical frequencies, affinity diagrams group ideas, and Gantt charts schedule tasks.

Question 31Six Sigma Body of Knowledge (major sections)

A Belt measures the same 10 parts twice with two appraisers and computes the average range of repeated readings. This quantity directly estimates which component of measurement variation?

  1. Linearity
  2. Repeatability Correct answer.
  3. Reproducibility
  4. Stability

Explanation

Repeatability is the variation when one appraiser measures the same part repeatedly with the same instrument, so it is estimated from the within-appraiser range. Reproducibility concerns differences between appraisers, stability concerns drift over time, and linearity concerns bias across the range.

Question 32Six Sigma Body of Knowledge (major sections)

A Belt wants to reduce setup time on a packaging line following the single-minute-exchange-of-die philosophy. Which activity belongs to external setup?

  1. Running first-piece verification after restart
  2. Mounting and aligning the new die on the spindle
  3. Pre-staging the next die and tools on a cart while the line is still running Correct answer.
  4. Removing the current die after the machine has stopped

Explanation

External setup covers work that can be done while the machine is still producing, such as staging tools and preparing the next die. Internal setup is work that requires the machine to be stopped.

Question 33Six Sigma Body of Knowledge (major sections)

A Belt is calculating the rolled throughput yield of a three-step process with first-pass yields of 0.95, 0.90, and 0.98. Which value is correct?

  1. 0.838 Correct answer.
  2. 0.900
  3. 0.943
  4. 0.980

Explanation

Rolled throughput yield is the product of the individual first-pass yields, so 0.95 times 0.90 times 0.98 equals approximately 0.838. It is always lower than the lowest individual step yield.

Question 34Six Sigma Body of Knowledge (major sections)

A Belt needs to convert a process capability of 3 sigma (with the conventional 1.5 sigma shift) to a defect rate. Which value is closest?

  1. 66,807 DPMO Correct answer.
  2. 6,210 DPMO
  3. 233 DPMO
  4. 3.4 DPMO

Explanation

With the 1.5 sigma shift, a 3-sigma process corresponds to a short-term z of 1.5, giving about 66,807 defects per million opportunities. Each additional sigma reduces the DPMO by roughly an order of magnitude.

Question 35Six Sigma Body of Knowledge (major sections)

A Belt is choosing between a full factorial and a fractional factorial for five two-level factors. Which statement correctly describes the trade-off?

  1. A half-fraction reduces runs but aliases effects, whereas the full factorial estimates all effects independently Correct answer.
  2. A half-fraction estimates all effects independently but requires more runs
  3. A full factorial always requires fewer runs than any fraction
  4. Fractional designs are used only when factors cannot be randomized

Explanation

Fractional factorials trade confounding, or aliasing, of higher-order effects for fewer experimental runs. The full factorial resolves every main effect and interaction separately but costs more runs.

Question 36Six Sigma Body of Knowledge (major sections)

An experiment shows a significant interaction between temperature and pressure on yield. What is the correct interpretation?

  1. The effect of temperature on yield depends on the level of pressure Correct answer.
  2. The experiment failed because interactions mask main effects
  3. Temperature has no effect on yield at any pressure
  4. Pressure alone explains all yield variation

Explanation

A significant interaction means the effect of one factor changes across levels of the other, so the factors must be interpreted jointly rather than as separate main effects. Plotting cell means reveals the pattern.

Question 37Six Sigma Body of Knowledge (major sections)

A Belt applies the five whys and reaches a cause that cannot be probed further and can be verified with data. What has been established?

  1. A confirmed solution to implement immediately
  2. A special cause signal on a control chart
  3. A measurement system error
  4. A potential root cause that still requires validation Correct answer.

Explanation

The five whys generates candidate root causes; the final answer must be verified with data or a physical check before it is treated as the root cause. Reaching a stopping point is not itself proof.

Question 38Six Sigma Body of Knowledge (major sections)

A Belt must verify whether the proportion of reworked orders differs between three plants. Which analysis is appropriate?

  1. Chi-square test of homogeneity on the counts Correct answer.
  2. Paired t-test between plant pairs
  3. Simple linear regression of rework on plant
  4. One-way ANOVA on the proportions

Explanation

Comparing proportions of a categorical outcome across three or more groups uses a chi-square test of homogeneity on the count table. ANOVA and t-tests assume a continuous response, and regression on a nominal predictor would not test the equality of proportions directly.

Question 39Six Sigma Body of Knowledge (major sections)

A Belt computes a 95 percent confidence interval for the difference between two means as 1.8 to 6.4 units. What is the correct conclusion at alpha of 0.05?

  1. The difference is statistically significant and plausibly positive Correct answer.
  2. The test is inconclusive because the interval excludes zero
  3. The difference is not significant because the interval is narrow
  4. The difference is significant only if the sample size exceeds 30

Explanation

Because the entire interval lies above zero, zero is not a plausible value for the difference, so the two-sided test at alpha 0.05 rejects equality. The interval also indicates the effect is positive.

Question 40Six Sigma Body of Knowledge (major sections)

A Belt needs to test whether the variance of fill volume from a new filler is greater than the variance from the existing filler. Which test applies?

  1. F-test for equality of two variances Correct answer.
  2. One-proportion z-test
  3. Mood's median test
  4. Two-sample t-test

Explanation

Comparing two population variances uses the F-test, which is the ratio of sample variances under normality. The t-test compares means, the proportion test compares categorical rates, and Mood's median test compares medians.

Question 41Six Sigma Body of Knowledge (major sections)

A Belt must estimate the proportion of defective units in a large shipment using a sample. Which distribution underlies the exact confidence interval for that proportion?

  1. Poisson
  2. Binomial Correct answer.
  3. Exponential
  4. Normal

Explanation

Each sampled unit is defective or not with a constant probability, which is a binomial process, so exact proportion intervals are built from the binomial distribution. The Poisson models counts of events, and the normal is an approximation.

Question 42Six Sigma Body of Knowledge (major sections)

A Belt wants to compare the median call-handling time across four shifts when the data are heavily skewed and the normality assumption fails. Which method is appropriate?

  1. Kruskal-Wallis test Correct answer.
  2. Levene's test
  3. Two-proportion test
  4. One-way ANOVA

Explanation

The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA for comparing three or more independent groups when normality is doubtful. It ranks observations and compares rank sums.

Question 43Six Sigma Body of Knowledge (major sections)

A Belt is interpreting a control chart of subgroup means and observes a run of nine consecutive points on one side of the centerline. What does this pattern indicate?

  1. An isolated outlier that should be ignored
  2. A subgroup size that is too small
  3. A sustained shift in the process mean Correct answer.
  4. Random variation consistent with a stable process

Explanation

A run of nine points on one side of the centerline is a nonrandom pattern indicating a sustained shift in the process mean. Runs rules detect small persistent shifts that single-point rules miss.

Question 44Six Sigma Body of Knowledge (major sections)

A process is stable and normally distributed with a mean of 100 and a standard deviation of 5, and specifications are 90 to 110. What is the approximate Cpk?

  1. 1.00
  2. 1.33
  3. 2.00
  4. 0.67 Correct answer.

Explanation

Cpk is the distance from the mean to the nearer specification divided by three standard deviations, so 10 divided by 15 equals 0.67. The process is centered but its spread is too wide for the specification width.

Question 45Six Sigma Body of Knowledge (major sections)

A Belt is planning a designed experiment and wants to protect against the effect of an uncontrolled nuisance variable that drifts over time. Which technique is most appropriate?

  1. Randomizing the response
  2. Blocking Correct answer.
  3. Replication
  4. Adding a center point

Explanation

Blocking groups experimental runs so that nuisance variation is isolated and removed from the error term. Replication estimates pure error, randomization guards against bias, and center points test curvature.

Question 46Six Sigma Body of Knowledge (major sections)

A Belt reviews a control plan for a critical characteristic and finds only periodic inspection with no reaction plan. What is the most significant deficiency?

  1. The control plan lacks a process map
  2. No documented response when an out-of-control condition occurs Correct answer.
  3. The inspection frequency is too high
  4. No capability study appears in the control plan

Explanation

A control plan must specify the monitoring method, sample size and frequency, and a reaction plan for when the characteristic goes out of control. Without a documented response, operators cannot act consistently.

Question 47Six Sigma Body of Knowledge (major sections)

A Belt applies poka-yoke to a manual assembly station. Which design is the strongest error-proofing approach?

  1. A sign reminding operators to check orientation
  2. A training session on correct orientation
  3. An inspection step at the end of the line
  4. A fixture that physically prevents the part from being inserted in the wrong orientation Correct answer.

Explanation

Error-proofing is strongest when it makes the error physically impossible or immediately obvious at the source. Physical prevention outranks warnings, training, and downstream inspection.

Question 48Six Sigma Body of Knowledge (major sections)

A team maps the flow of patients through a clinic and finds that patients spend 20 minutes in value-added care and 100 minutes waiting. What is the process cycle efficiency?

  1. 20 percent
  2. 50 percent
  3. 83 percent
  4. 17 percent Correct answer.

Explanation

Process cycle efficiency is value-added time divided by total lead time, so 20 divided by 120 equals about 17 percent. The remaining time is non-value-added waiting.

Question 49Six Sigma Body of Knowledge (major sections)

A Belt is preparing a stakeholder analysis and finds a manager with high influence who is currently neutral toward the project. Which action is most appropriate?

  1. Reduce project scope to avoid the manager
  2. Engage the manager early with tailored information to build support Correct answer.
  3. Escalate to leadership to force compliance
  4. Ignore the manager because the stance is not opposed

Explanation

Stakeholders with high influence and neutral or unknown position should be engaged early and kept informed, since their support or resistance strongly affects project success. Ignoring them or forcing compliance creates avoidable risk.

Question 50Six Sigma Body of Knowledge (major sections)

A Belt calculates the cost of poor quality for a process and wants to classify internal failure costs. Which item belongs in that category?

  1. Customer satisfaction survey administration
  2. Incoming inspection of purchased material
  3. Warranty replacement after customer complaint
  4. Scrap generated before the product reaches the customer Correct answer.

Explanation

Internal failure costs are incurred when defects are found before delivery, such as scrap, rework, and downtime. Warranty claims are external failure costs, while inspection and surveys are appraisal costs.