Sigma Flashcards

A police service is running a Sigma project to reduce false alarm call response times. After completing the Measure phase, the team discovers that the measurement system itself contributes 38% of the observed process variation. What is the MOST appropriate next step?

Answer: Halt the project and redesign the measurement system before continuing, as the data cannot reliably distinguish true process variation

When a measurement system analysis (Gage R&R) reveals that measurement error accounts for more than 30% of total observed variation, the data is considered unreliable for distinguishing real process signals from noise. Proceeding to Analyze would risk drawing false conclusions. The team must remediate the measurement system — recalibrating instruments, retraining data collectors, or redefining operational definitions — before collecting valid baseline data. Option A is wrong because 30% is the typical upper limit (not a floor), not a threshold below which 38% is acceptable. Option C is methodologically unsound as post-hoc correction factors cannot recover the fidelity of flawed raw data. Option D is a category error; DMADV applies to new process design, not measurement system failure.

During the Control phase of a Sigma project targeting officer report-completion cycle time, an Individual-Moving Range (I-MR) chart shows a single data point falling outside the upper control limit (UCL) on Day 14. A thorough investigation reveals no assignable cause. What is the statistically correct action?

Answer: Retain the point in the chart, document that no assignable cause was found, and continue monitoring for additional signals

When an out-of-control signal appears but investigation yields no assignable (special) cause, statistical protocol dictates that the point is retained in the control chart. Removing points without a verified, documented reason inflates false confidence in process stability and violates the integrity of the control chart. Widening limits to ±4 sigma defeats the purpose of the control chart by masking genuine future signals. Triggering a new DMAIC project from a single unexplained point is premature — reaction rules (e.g., Western Electric rules) typically require patterns or consecutive signals before escalating. The correct posture is to document, retain, and monitor.

A police service Black Belt is evaluating two Sigma projects for resource prioritization. Project A has a Cp of 1.8 and a Cpk of 0.9. Project B has a Cp of 1.2 and a Cpk of 1.15. Which interpretation is MOST accurate?

Answer: Project B's process is better centered within its specification limits and is currently more capable despite having lower potential capability

Cp (process potential) measures whether the process spread fits within specification limits, assuming the process is perfectly centered. Cpk (process capability) accounts for actual centering. Project A's large gap between Cp (1.8) and Cpk (0.9) reveals a severely off-center process that is actively producing defects even though it theoretically has enough spread to perform well. Project B's Cp and Cpk are close together (1.2 vs. 1.15), indicating it is well-centered and currently performing at a capable level. For resource allocation, the practical (current) capability matters most — Project B is delivering better real-world results. Option D overstates the case; while Project A's Cpk < 1.0 is a concern, it doesn't mean the project should be abandoned — it suggests centering work is needed.

An OACP Sigma team is analyzing civilian complaint processing times. They run a one-way ANOVA and obtain a p-value of 0.03 (α = 0.05), indicating statistically significant differences across three district offices. The practical effect size (eta-squared) is 0.04. What is the MOST defensible conclusion for the project sponsor?

Answer: The result is statistically significant but the effect size suggests the between-district differences explain only 4% of variation — practical impact is likely limited and further investigation is warranted before action

Statistical significance (p < 0.05) only indicates that the observed differences are unlikely due to chance given the sample size — it does not quantify the magnitude or operational importance of those differences. An eta-squared of 0.04 means between-district variation explains only 4% of total complaint processing time variation, which is a small practical effect by conventional benchmarks (Cohen's f² small ≈ 0.02, medium ≈ 0.15). A responsible Sigma practitioner reports both the statistical result and the effect size to the sponsor, cautioning against large resource commitments for a factor explaining so little variation. Option A conflates statistical and practical significance. Option C mischaracterizes what rejecting the null hypothesis means. Option D is incorrect — ANOVA can accommodate unequal group sizes through weighted analysis.

During a Sigma project aimed at reducing wrongful ticket issuance, the team builds a logistic regression model. The model's Hosmer-Lemeshow test returns a p-value of 0.08 and the area under the ROC curve (AUC) is 0.91. Which statement BEST characterizes the model's fitness?

Answer: The model shows acceptable calibration (Hosmer-Lemeshow p > 0.05 means we fail to reject good fit) and excellent discrimination (AUC 0.91), making it suitable for operational use with monitoring

For the Hosmer-Lemeshow goodness-of-fit test, a p-value > 0.05 means we fail to reject the null hypothesis of good calibration — indicating the model's predicted probabilities align well with observed outcomes. A p of 0.08 clears this threshold. An AUC of 0.91 indicates excellent discrimination (the model's ability to distinguish between the two outcomes), well above the commonly cited 0.80 threshold for strong models and approaching the 0.90+ 'outstanding' range. Together, these metrics indicate a well-calibrated, highly discriminating model appropriate for operational deployment with continued monitoring. Option A misreads the Hosmer-Lemeshow interpretation and invents a 0.95 AUC minimum. Option C incorrectly dismisses calibration. Option D incorrectly claims the p-value indicates poor calibration — 0.08 > 0.05 means calibration is NOT rejected.

A police service has successfully completed a Sigma project reducing court disclosure preparation time by 40%. Six months into the Control phase, the process begins drifting back toward the original baseline — a phenomenon the Sigma literature calls 'process reversion.' Which Control phase mechanism MOST directly prevents this from occurring?

Answer: Embedding the improved process steps into standard operating procedures, training materials, and automated workflow systems — and assigning ongoing ownership to a process owner with defined response protocols

Process reversion is the most common cause of Sigma project failure post-implementation, and it occurs primarily because improvements were not institutionalized into the fabric of how work is done. The most effective countermeasure is a combination of structural embedding (SOPs, training, system configuration that makes the old way harder to do) and accountability (a named process owner who monitors the control chart, responds to signals per a documented response plan, and owns sustained performance). Simply publishing reports (Option A) creates no enforcement mechanism. A follow-up DMAIC project (Option C) only addresses reversion after the fact rather than preventing it. Increasing monitoring frequency (Option D) improves detection speed but does nothing to address the root cause of why the process is reverting — the absence of structural controls.