Lean Six Sigma Black Belt Free Sample Questions

A Multi-Vari Chart is the correct tool because it is specifically designed to display multiple sources of variation on a single graph. It can effectively show positional (within-piece), cyclical (piece-to-piece), and temporal (time-to-time) variation, making it ideal for pinpointing the largest contributor to overall process variability in this scenario. Box plots are good for comparing distributions but don't show all three types of variation simultaneously. Interaction plots are used after a DOE to visualize interactions, and a Main Effects Plot shows the effect of one factor at a time.

The most critical finding is that the number of distinct categories (ndc) is 3. An ndc of less than 5 indicates that the measurement system cannot adequately distinguish between different parts. This is a primary indicator of an unacceptable system, regardless of other metrics. While a %Tolerance of 25% is borderline acceptable (10-30% may be acceptable based on application), the low ndc value is a definitive failure point. The low Part-to-Part variation %Contribution (18%) also suggests the measurement error is consuming a large portion of the observed variation, reinforcing the conclusion that the system is inadequate.

A D-Optimal custom design is the most appropriate choice. This approach is specifically suited for situations with mixed-level factors (3, 3, and 2 levels) and a strict constraint on the number of runs (15). D-Optimal designs algorithmically select the most informative subset of possible runs to efficiently estimate the desired model terms (main effects, interactions, quadratic terms). A full factorial (3x3x2=18 runs) exceeds the budget. A Box-Behnken design requires factors to have 3 levels and is not directly applicable to the mixed-level scenario. A 2k-p fractional factorial is only for factors with 2 levels.

A control plan must clearly define what is being controlled (the characteristic) and what the acceptable range of performance is (specification limits).

The plan must detail how the characteristic will be measured, how often, and how many samples to take. This ensures consistent monitoring.

A critical component is the reaction or response plan. This pre-defines the steps to take when an out-of-control condition is detected, ensuring a swift and standardized response to problems.

This statement is true. A high Cpk (1.50) indicates excellent potential capability based on short-term, within-subgroup variation. However, a much lower Ppk (0.90) which uses long-term, overall variation, signifies that the process performance degrades over time. This discrepancy is a classic indicator of instability, special cause variation, or shifts and drifts between subgroups.

This is the best goal statement because it follows the SMART (Specific, Measurable, Achievable, Relevant, Time-bound) criteria. It clearly defines the metric ('door-to-doctor' time), specifies the process segment (non-critical patients), provides a measurable baseline (75 mins) and target (45 mins), sets a deadline (end of Q3), and includes a constraint (without impacting outcomes). The other options are too vague, lack metrics, or describe the problem rather than the goal.

The Kruskal-Wallis test is the correct choice. It is the non-parametric equivalent of the One-Way ANOVA and is used to compare the medians of three or more independent groups when the data does not meet the normality assumption. One-Way ANOVA requires normally distributed data. The Mann-Whitney U test is used for comparing only two groups. The Chi-Squared test is used for categorical data, not ordinal rating data.

A U Chart is the most appropriate choice. It is used to monitor the average number of defects per unit (in this case, dropped calls per call) when the sample size (total number of calls) varies over time. A C Chart is used for the number of defects when the sample size is constant. P and NP charts are for tracking the proportion or number of defective units, not the number of defects within a unit or opportunity area.

This interpretation is correct. The coefficient 2.5 indicates that for each one-unit (dollar) increase in Ad Spend, Website Visits increase by 2.5 on average. The p-value of 0.002 is less than the typical alpha level of 0.05, indicating that the relationship is statistically significant. The R-squared value of 0.75 means that 75% of the variation in website visits is explained by the ad spend, suggesting a strong model fit. The other options misinterpret the statistical outputs.

The most appropriate action is to prioritize this failure mode due to its high Severity rating (7), especially since it impacts customer safety. While RPN is a useful tool for prioritization, it should not be used as a rigid, absolute threshold. High Severity ratings, particularly those related to safety or critical regulations, must always be addressed, even if the overall RPN is below a predefined cut-off. Modern FMEA practices (like AIAG-VDA FMEA) emphasize prioritizing high Severity first, then Occurrence, then Detection, rather than relying solely on the RPN.