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CSSC MBB practice questions

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Question 1Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

In the CSSC Six Sigma Body of Knowledge, which metric expresses process capability relative to specification limits while accounting for process centering?

  1. Cp
  2. Cpk Correct answer.
  3. Pp
  4. DPMO

Explanation

Cpk compares the distance from the process mean to the nearer specification limit against three standard deviations, so it penalizes off-center processes. Cp uses the specification width and ignores centering, which is why Cpk is preferred when the mean is not centered.

Question 2Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt team is chartering a project and must state the business case. Which element belongs in the project charter rather than in the detailed process map?

  1. The problem statement with quantified baseline and goal Correct answer.
  2. The sequence of process steps with decision diamonds
  3. The rework loop frequency at each operation
  4. The value-added classification of each activity

Explanation

The charter defines the business case, problem statement, goal, scope, and team, so a quantified baseline and target belong there. Process maps document flow, decision points, and activity classification, which come later during analysis.

Question 3Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process produces 12,000 units with 4 opportunities for a defect per unit and records 96 defects. What is the approximate DPMO?

  1. 24,000
  2. 2,000 Correct answer.
  3. 96,000
  4. 8,000

Explanation

DPMO equals defects divided by total opportunities times one million. Total opportunities are 12,000 times 4, or 48,000, so 96 divided by 48,000 times 1,000,000 gives 2,000 DPMO.

Question 4Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which statement correctly distinguishes repeatability from reproducibility in a measurement systems analysis?

  1. Repeatability is the bias of the gauge; reproducibility is the linearity of the gauge.
  2. Repeatability is equipment variation under fixed conditions; reproducibility is appraiser or condition variation. Correct answer.
  3. Repeatability is variation between appraisers; reproducibility is variation of one appraiser over time.
  4. Repeatability applies only to attribute data; reproducibility applies only to continuous data.

Explanation

Repeatability is the variation seen when one appraiser measures the same part with the same gauge repeatedly, essentially equipment variation. Reproducibility captures the shift introduced by different appraisers or measurement conditions.

Question 5Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team plots subgroup averages and ranges over time and observes nine consecutive points on one side of the centerline. What does this signal indicate?

  1. The control limits were calculated with too few subgroups
  2. The measurement system has excessive repeatability
  3. The process is in control because all points are inside the limits
  4. A nonrandom shift in the process mean that warrants investigation Correct answer.

Explanation

Run rules detect nonrandom patterns even when points stay inside the control limits. Nine points on one side of the centerline indicate a sustained shift in the process mean, so the team should look for an assignable cause.

Question 6Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which tool is designed to prioritize potential causes by frequency of occurrence after data have been collected?

  1. Pareto chart Correct answer.
  2. Gantt chart
  3. Cause-and-effect diagram
  4. Affinity diagram

Explanation

A Pareto chart orders categories by frequency or impact so the vital few contributors stand out. The cause-and-effect diagram generates candidate causes but does not rank them by observed frequency.

Question 7Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

In a designed experiment, a Black Belt wants to screen six factors efficiently and estimate main effects and two-factor interactions. Which design is most appropriate?

  1. A one-factor-at-a-time experiment
  2. A response surface central composite design with six factors
  3. A fractional factorial resolution IV design Correct answer.
  4. A full factorial at two levels with all 64 runs

Explanation

A resolution IV fractional factorial aliases main effects with three-factor interactions, so main effects are clear of two-factor interactions while requiring far fewer runs than a full factorial. This makes it a standard screening choice for many factors.

Question 8Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A hypothesis test returns a p-value of 0.03 against a significance level of 0.05. What is the correct interpretation?

  1. The test has a 3% probability of a Type II error
  2. There is a 3% chance the null hypothesis is true
  3. The effect size is practically significant
  4. The null hypothesis is rejected because 0.03 is below 0.05 Correct answer.

Explanation

The p-value is compared with the chosen alpha; since 0.03 is below 0.05, the null hypothesis is rejected at that level. The p-value is the probability of data this extreme given the null, not the probability the null is true.

Question 9Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which Lean concept refers to producing only what the downstream customer needs, when it is needed?

  1. Kaizen
  2. Heijunka
  3. Poka-yoke
  4. Just-in-time Correct answer.

Explanation

Just-in-time synchronizes production with downstream demand so items are made in the right quantity at the right time. It reduces inventory and exposes problems that buffers would otherwise hide.

Question 10Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

During the analyze phase, a team finds that defect rate differs across three suppliers. Which test is appropriate for comparing proportions among three independent groups?

  1. Paired t-test
  2. Two-sample F-test for variances
  3. Chi-square test of independence Correct answer.
  4. One-way ANOVA on defect counts

Explanation

The chi-square test of independence evaluates whether two categorical variables, such as supplier and defect outcome, are associated. Comparing proportions across three groups fits this test rather than a means-based procedure.

Question 11Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process has a stable mean of 50 with a standard deviation of 2. The lower specification limit is 44. What is Cpl?

  1. 3.00
  2. 1.00 Correct answer.
  3. 1.50
  4. 0.67

Explanation

Cpl equals the mean minus the lower specification limit divided by three sigma, so 50 minus 44 is 6, and 6 divided by 6 equals 1.00. This indicates the lower side is exactly three sigma from the mean.

Question 12Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which activity best characterizes the control phase of a Six Sigma project?

  1. Brainstorming potential failure modes
  2. Establishing the baseline sigma level
  3. Transferring the improved process to the owner with a monitoring plan Correct answer.
  4. Identifying the critical Xs through regression

Explanation

The control phase standardizes the improved process, hands ownership to the process owner, and installs monitoring such as control charts and response plans. This sustains the gains after the project team disbands.

Question 13Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team uses an FMEA and scores severity 8, occurrence 4, and detection 3. What is the risk priority number and what does it mean?

  1. 15, indicating moderate risk
  2. 32, indicating detection is the dominant concern
  3. 96, indicating a low-priority risk
  4. 96, indicating a higher-priority risk requiring action Correct answer.

Explanation

The RPN is the product of severity, occurrence, and detection, so 8 times 4 times 3 equals 96. Higher RPN values flag failure modes that merit priority for corrective action.

Question 14Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which statement about the central limit theorem is most relevant when constructing an X-bar chart?

  1. Individual measurements are always normally distributed
  2. The process standard deviation decreases as sample size increases
  3. Subgroup averages approach normality as subgroup size increases regardless of the underlying distribution Correct answer.
  4. Control limits must be recalculated for every new subgroup

Explanation

The central limit theorem supports using X-bar charts because subgroup averages tend toward normality even when individual values are skewed. This justifies normal-based control limits on the averages.

Question 15Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

In a multi-vari study, a team suspects variation from three sources: within-piece, piece-to-piece, and time-to-time. What is the primary purpose of this study?

  1. To estimate the cost of poor quality
  2. To establish specification limits
  3. To calculate the process sigma level
  4. To isolate the dominant family of variation before further investigation Correct answer.

Explanation

Multi-vari studies stratify variation by families such as positional, cyclical, and temporal to reveal where the largest variation originates. This guides the team toward the most productive follow-up analysis.

Question 16Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which action is consistent with the Six Sigma principle of reducing variation rather than merely shifting the mean?

  1. Adding a final inspection step
  2. Increasing the specification range
  3. Reducing the standard deviation so specification limits sit farther out in sigma units Correct answer.
  4. Recalibrating the process mean to the target

Explanation

Reducing variation increases the sigma distance between the mean and the specification limits, which lowers defect rates. This is the core capability improvement that Six Sigma pursues.

Question 17Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt wants to test whether the mean cycle time changed after a kaizen event, using the same 15 operators before and after. Which test is most appropriate?

  1. Two-sample t-test assuming equal variances
  2. One-way ANOVA with three levels
  3. Paired t-test Correct answer.
  4. Chi-square goodness-of-fit test

Explanation

The same operators measured before and after create dependent pairs, so a paired t-test on the differences is appropriate. It removes between-operator variability from the comparison.

Question 18Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which statement best describes the role of the champion in a Six Sigma deployment?

  1. Provides sponsorship, removes barriers, and links projects to business strategy Correct answer.
  2. Trains Green Belts in statistical methods
  3. Audits control charts after project closure
  4. Performs the day-to-day statistical analysis for the project

Explanation

The champion is a senior sponsor who secures resources, removes organizational barriers, and ensures projects align with strategic priorities. This role is distinct from the analytical work done by Belts.

Question 19Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A regression model predicting scrap rate from furnace temperature reports R-squared of 0.82 and a p-value of 0.001 for the slope. What is the most defensible conclusion?

  1. Temperature causes 82% of the scrap
  2. The residuals are normally distributed
  3. The model predicts scrap with 82% accuracy per unit
  4. Temperature is a statistically significant predictor associated with scrap rate Correct answer.

Explanation

The significant slope indicates a real association between temperature and scrap rate, and R-squared shows the proportion of variation explained. Causation and per-unit accuracy are stronger claims than regression alone supports.

Question 20Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which condition must hold for a process to be considered in statistical control on a variables control chart?

  1. The sample size for each subgroup is at least 30
  2. The capability index exceeds 1.33
  3. All plotted points fall within the specification limits
  4. Only random variation is present and no run rules are violated Correct answer.

Explanation

Statistical control means the process varies only from common causes, shown by points within control limits and no nonrandom patterns. Specification limits and capability are separate from control status.

Question 21Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team applies 5S and finds that tools are frequently misplaced because storage locations are not marked. Which 5S step addresses this directly?

  1. Shitsuke, or sustain
  2. Seiton, or set in order Correct answer.
  3. Seiso, or shine
  4. Seiketsu, or standardize

Explanation

Seiton means arranging items so each has a designated, marked location that makes retrieval and return obvious. Marked storage directly addresses misplaced tools.

Question 22Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

An experiment shows a significant interaction between factor A and factor B. What does this imply for interpreting the main effects?

  1. The effect of A depends on the level of B, so main effects alone can mislead Correct answer.
  2. Main effects can be interpreted independently of each other
  3. The interaction should be removed to simplify the model
  4. The experiment must be rerun with more replicates

Explanation

A significant interaction means the effect of one factor changes across levels of the other, so a single main-effect average can mask important behavior. Interpretation should focus on the interaction and on simple effects at fixed levels.

Question 23Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which measure is most directly tied to the cost of poor quality in a Six Sigma business case?

  1. Number of kaizen events completed
  2. Scrap and rework costs Correct answer.
  3. Rolled throughput yield
  4. Training hours per Belt

Explanation

Scrap and rework costs are direct financial consequences of defects and translate improvement into money. They make the business case concrete for sponsors.

Question 24Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process is stable with Cp of 1.6 and Cpk of 0.9. What does this pattern indicate?

  1. The process is capable but off-center Correct answer.
  2. The process is centered and highly capable
  3. The process spread is excessive relative to specifications
  4. The measurement system is inadequate

Explanation

A high Cp with a much lower Cpk means the spread is narrow enough for the specifications, but the mean is shifted toward one limit. Recentering the process would raise Cpk substantially.

Question 25Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

Which sampling approach is most appropriate when a process runs continuously and the team wants to detect drift over time?

  1. Simple random sampling of the full day's output
  2. Convenience sampling of the nearest units
  3. Stratified sampling by operator only
  4. Systematic sampling at fixed time intervals with rational subgroups Correct answer.

Explanation

Systematic sampling at fixed intervals with rational subgroups captures time-based variation and supports control charting for drift. Random sampling of a full day can blur the temporal pattern the team needs to see.

Question 26Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt is drafting the project charter for a defect-reduction effort. Which element of the charter establishes the measurable improvement target and the date by which it must be achieved?

  1. The problem statement and business case
  2. The team roster and sponsor signature block
  3. The scope boundaries listing what is in and out
  4. The goal statement with its metric and timeframe Correct answer.

Explanation

The goal statement is the charter element that quantifies the desired improvement in a specific metric and attaches a completion date, making it verifiable at project closure. The problem statement describes the current gap, while scope and team sections define boundaries and resources rather than performance targets.

Question 27Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process owner asks the Black Belt to explain why a project should follow the DMAIC roadmap instead of jumping straight to solutions. Which rationale best fits the Six Sigma body of knowledge?

  1. DMAIC replaces the need for a business case approved by the champion
  2. DMAIC removes the need for a control plan once the fix is implemented
  3. DMAIC guarantees the solution will require no capital investment
  4. DMAIC ensures the root cause is validated with data before resources are committed to a fix Correct answer.

Explanation

DMAIC sequences define, measure, analyze, improve, and control so that causes are statistically verified before solutions are selected, which reduces the risk of fixing the wrong problem. The other phases do not eliminate the need for capital review, control plans, or a champion-approved business case.

Question 28Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

In a measurement systems analysis for a continuous gauge, the team reports repeatability of 0.8 units and reproducibility of 0.3 units. Which interpretation is most defensible?

  1. Appraiser variation dominates, so operator retraining should be the first action
  2. The gauge is unacceptable because reproducibility must exceed repeatability
  3. Equipment variation dominates, so the gauge itself should be investigated first Correct answer.
  4. The study is invalid because both components must be equal

Explanation

Repeatability reflects variation when the same appraiser measures the same part with the same gauge, so a larger repeatability component points to equipment or method issues. Reproducibility reflects differences between appraisers, and nothing in the body of knowledge requires the two components to be equal or ordered in a particular way.

Question 29Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team is building a process map and wants to distinguish steps that transform the product from steps that only add time, motion, or waiting. Which mapping tool is designed specifically to separate value-adding from non-value-adding activity?

  1. Cause-and-effect diagram
  2. Value stream map Correct answer.
  3. Affinity diagram
  4. Deployment flowchart

Explanation

A value stream map explicitly tags each step as value-adding or non-value-adding and quantifies waiting and inventory time, which supports cycle-time reduction. Deployment flowcharts show who does what, while cause-and-effect and affinity diagrams organize causes or ideas rather than classify process steps by value.

Question 30Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt computes a 95% confidence interval for the mean fill volume as 12.02 to 12.18 ounces. The specification is 12.00 to 12.20 ounces. Which conclusion follows?

  1. The process must be shut down because the interval touches the specification limits
  2. The process is centered acceptably but capability still depends on the spread relative to specification width Correct answer.
  3. The process mean is statistically indistinguishable from the specification limits
  4. The process is proven capable because the interval lies inside the specification

Explanation

The confidence interval addresses uncertainty about the mean only; capability requires comparing process spread to the specification width through indices such as Cp and Cpk. A mean inside the limits says nothing about the tails of the distribution, so capability cannot be declared from the interval alone.

Question 31Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt needs to compare the proportion of orders shipped late across four distribution centers using sample sizes of several hundred per center. Which analysis is appropriate?

  1. One-way ANOVA on the late-shipment counts
  2. Paired t-test between the largest and smallest centers
  3. Two-sample t-test on the proportion of late orders
  4. Chi-square test of homogeneity on the counts of late and on-time orders Correct answer.

Explanation

Comparing proportions across more than two groups uses a chi-square test on the contingency table of counts, which tests whether the distribution of outcomes is the same in each group. ANOVA and t-tests require a continuous response rather than counts of categorical outcomes.

Question 32Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt regresses cycle time on three predictor variables and notes that two predictors are highly correlated with each other. What risk does this multicollinearity create?

  1. The sample size requirement is eliminated
  2. The model residuals become perfectly normal
  3. The coefficient of determination is forced to zero
  4. Coefficient estimates become unstable and hard to interpret individually Correct answer.

Explanation

When predictors are strongly correlated, the model cannot separate their individual contributions, so coefficient estimates and their standard errors become unstable and signs may appear counterintuitive. Multicollinearity does not alter the residual normality assumption, force R-squared to zero, or remove sample size requirements.

Question 33Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team wants a quick visual display of the distribution of 200 bearing diameters, including shape, center, and spread, before running formal tests. Which tool is most appropriate?

  1. Scatter diagram
  2. Histogram Correct answer.
  3. Pareto chart
  4. Control chart

Explanation

A histogram bins continuous measurements and shows the shape, center, and spread of the distribution, which is exactly what is needed before selecting formal tests. Pareto charts rank categories, control charts track a statistic over time, and scatter diagrams show relationships between two variables.

Question 34Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

During the improve phase, a team must choose among four solution alternatives with different costs, implementation risks, and expected benefits. Which approach best supports a defensible decision?

  1. Score each alternative against weighted criteria and review the results with the champion Correct answer.
  2. Defer the decision until the control phase
  3. Select the option with the lowest implementation cost
  4. Adopt the option preferred by the most senior team member

Explanation

A weighted decision matrix makes the selection criteria and their relative importance explicit, so the choice can be defended and reviewed with the project champion. Choosing on cost alone, on seniority, or after the fact ignores benefit and risk trade-offs that the body of knowledge requires teams to evaluate.

Question 35Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process is monitored with a p-chart for fraction nonconforming, and the sample size varies from day to day. What is the correct treatment of control limits?

  1. Replace the p-chart with an individuals chart on the daily counts
  2. Use one set of limits computed from the average sample size for all days
  3. Compute limits for each sample size, producing limits that vary with n Correct answer.
  4. Set limits at the specification limits for fraction nonconforming

Explanation

For a p-chart the standard deviation of the plotted proportion depends on the sample size, so limits must be recalculated for each subgroup size and will appear stepped when n varies. Using a single average-sample limit or specification limits misstates the expected variation and produces false signals.

Question 36Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt is planning a study and wants to detect a shift of 1.5 standard deviations in a process mean with 80% power at a 0.05 significance level. What does the power of the test represent?

  1. The probability that the sample is randomly selected from the population
  2. The proportion of total variation explained by the treatment
  3. The probability of failing to reject the null hypothesis when it is true
  4. The probability of rejecting the null hypothesis when the stated shift truly exists Correct answer.

Explanation

Power is the complement of the type II error rate: it is the probability of detecting an effect of the specified size when that effect is real. It is not the type I error rate, a sampling assurance, or a variance-explained measure.

Question 37Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team suspects that defect rates differ by shift and by machine type and wants to know whether the effect of shift depends on machine type. Which analysis directly addresses this question?

  1. A simple linear regression of defect count on shift code
  2. A two-way ANOVA including the shift-by-machine interaction term Correct answer.
  3. A chi-square goodness-of-fit test on overall defect counts
  4. A one-way ANOVA on shift alone

Explanation

A two-way ANOVA partitions variation by two factors and includes an interaction term that tests whether the effect of one factor changes across levels of the other. One-way ANOVA and simple regression omit the second factor, and goodness-of-fit ignores the factor structure entirely.

Question 38Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt examines a control chart and sees one point beyond the upper control limit followed by several points that remain inside the limits. What is the correct interpretation?

  1. The control limits must be widened so the point falls inside
  2. The point should be deleted and the limits recomputed without investigation
  3. The out-of-limit point is a signal of special cause variation and should be investigated Correct answer.
  4. The process is in control because only one point exceeded the limit

Explanation

A point beyond a control limit is the classic special-cause signal, and the body of knowledge requires that assignable causes be investigated before any recalculation. Widening limits or deleting points without investigation masks the very variation the chart is designed to expose.

Question 39Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt applies poka-yoke to a assembly step where a connector can be inserted in two orientations. Which design best reflects the poka-yoke principle?

  1. Requiring operators to sign a checklist before insertion
  2. Adding an inspection step at the end of the line
  3. Adding a visual warning label beside the connector
  4. Redesigning the connector so it physically fits only one way Correct answer.

Explanation

Poka-yoke prevents errors through design so the mistake cannot occur, and a connector that physically fits only one orientation is a prevention device. Labels, downstream inspection, and checklists are warnings or detection controls that still allow the error to be made.

Question 40Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team is standardizing a process after improvement and wants to ensure the new method is sustained. Which control-phase element specifies who monitors the metric, how often, and what action is taken when a signal appears?

  1. The project charter's business case
  2. The stakeholder communication matrix
  3. The lessons-learned document
  4. The response plan within the control plan Correct answer.

Explanation

A control plan pairs each metric with its monitoring frequency, owner, and a documented response when the metric deviates, which is what sustains the gain. Lessons learned, the business case, and communication planning support the project but do not define reaction to process signals.

Question 41Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt uses a run chart to evaluate a process over 40 consecutive days and observes eight points in a row on the same side of the centerline. How should this pattern be treated?

  1. As a signal of a sustained shift in the process Correct answer.
  2. As random noise, because no point exceeds a control limit
  3. As evidence that the centerline was computed incorrectly
  4. As a reason to reduce the sampling frequency

Explanation

Runs rules such as eight consecutive points on one side of the centerline indicate a nonrandom pattern consistent with a sustained shift, even when no single point is extreme. Treating it as noise, blaming the centerline, or reducing sampling would miss the signal.

Question 42Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt wants to reduce setup time on a packaging line and applies the SMED methodology. Which step is central to SMED?

  1. Scheduling all setups at the end of the month
  2. Converting as much internal setup work as possible into external setup work Correct answer.
  3. Adding a buffer inventory in front of the line
  4. Increasing batch size so that fewer setups are needed

Explanation

SMED separates internal setup, which requires the machine to be stopped, from external setup, which can be done while running, and then converts and streamlines internal tasks. Larger batches, buffers, and end-of-month scheduling avoid addressing setup time rather than reducing it.

Question 43Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt is selecting a sample from a production lot for an acceptance sampling plan and wants to state the risk of rejecting a lot that is actually at the acceptable quality level. Which quantity describes that risk?

  1. The consumer's risk, beta
  2. The lot tolerance percent defective
  3. The average outgoing quality limit
  4. The producer's risk, alpha Correct answer.

Explanation

The producer's risk, alpha, is the probability that a lot at the acceptable quality level is rejected by the sampling plan. Consumer's risk concerns accepting a lot at the lot tolerance percent defective, and the other terms describe quality levels rather than the rejection probability.

Question 44Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt must present the financial benefit of a project that reduced rework hours. Which calculation correctly reflects the hard savings from reduced rework?

  1. Use the raw material cost only, ignoring labor
  2. Multiply the eliminated rework hours by the fully loaded labor rate and subtract project costs Correct answer.
  3. Count the number of defects avoided without converting them to money
  4. Report the total sales of the product line as the benefit

Explanation

Hard savings from reduced rework equal the eliminated hours valued at the fully loaded labor rate, net of the cost to achieve the improvement. Counting defects without monetizing them, claiming total sales, or ignoring labor understates or overstates the true benefit.

Question 45Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt is facilitating a team that must generate a large set of possible causes for a chronic defect before any data are collected. Which tool best fits this purpose?

  1. Brainstorming organized with a cause-and-effect diagram Correct answer.
  2. A hypothesis test on the defect rate
  3. A control chart of historical defect counts
  4. A regression model of defect count on shift

Explanation

Brainstorming structured into a cause-and-effect diagram expands the set of candidate causes across categories such as machine, method, material, and people before data collection. The other tools analyze existing data and therefore come after candidate causes have been identified.

Question 46Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A process capability study yields Cp of 1.33 and Cpk of 1.33 for a stable process. What does the equality of the two indices indicate?

  1. The specification limits are statistically derived
  2. The process mean is centered on the specification midpoint Correct answer.
  3. The process is not in statistical control
  4. The process spread exceeds the specification width

Explanation

Cp and Cpk are equal only when the process mean coincides with the midpoint of the specification limits, so no centering penalty is applied. A spread wider than the specification would give Cp below one, and capability indices are meaningful only for a stable process.

Question 47Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt evaluates whether a new supplier's mean tensile strength differs from the current supplier's, with small samples from each and no evidence that the variances are equal. Which test is most appropriate?

  1. Chi-square test of independence
  2. One-proportion test
  3. Paired t-test
  4. Two-sample t-test assuming unequal variances Correct answer.

Explanation

Two independent small samples with unequal variances call for a two-sample t-test using separate variance estimates, often called the Welch procedure. A paired test requires matched observations, and the proportion and chi-square tests apply to categorical data.

Question 48Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A team wants to understand how a response changes when two factors are varied together and suspects the best setting of one factor depends on the level of the other. Which experimental approach is most suitable?

  1. An observational study of historical production records
  2. A single baseline run repeated five times
  3. A one-factor-at-a-time sequence of trials
  4. A full factorial design at two levels for both factors Correct answer.

Explanation

A two-level full factorial varies both factors together and estimates main effects plus the interaction, which is exactly the dependence of one factor's effect on the other's level. One-factor-at-a-time trials cannot reveal interactions, and repeated baselines or historical records do not manipulate the factors systematically.

Question 49Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt is asked to explain why reducing variation can lower cost even when the process mean already meets target. Which explanation is most consistent with Six Sigma thinking?

  1. Variation drives some output beyond specification limits, creating scrap, rework, and warranty cost Correct answer.
  2. Variation only matters for services, not for manufacturing
  3. Variation increases the average, which raises material usage
  4. Variation has no effect on cost once the mean is on target

Explanation

When spread is large, the tails of the distribution cross specification limits and generate scrap, rework, sorting, and warranty claims, so narrowing spread reduces cost even with a centered mean. Variation does not systematically raise the average, and it affects cost in both manufacturing and service processes.

Question 50Six Sigma Body of Knowledge (major sections of the CSSC Six Sigma Black Belt Body of Knowledge)

A Black Belt reviews a project portfolio and finds several projects pursuing similar improvements in the same value stream. Which portfolio-level action best reflects Six Sigma deployment principles?

  1. Prioritize and sequence projects against business impact and resource capacity Correct answer.
  2. Delay all projects until the next fiscal year
  3. Approve all projects so teams stay motivated
  4. Assign each project to a separate champion to avoid conflict

Explanation

Portfolio management prioritizes and sequences projects by business impact and available resources, and it consolidates overlapping efforts so savings are not double-counted. Approving everything, fragmenting ownership, or delaying everything ignores the resource and impact trade-offs deployment requires.