For a skewed distribution, the mean is pulled toward the tail and does not represent the ‘typical’ value. The median is a more robust measure of center in such situations as it is the middle value and is not affected by outliers or extreme skew. Reporting the mean could mislead the sponsor about the process’s typical performance.

The primary goal of the Analyze phase is to move from potential causes (hypotheses) to verified root causes. This is done using data and statistical analysis (like hypothesis testing, regression, ANOVA) to ensure the team invests improvement efforts on the true drivers of the problem, not just symptoms or assumptions.

The p-value (0.03) is the probability of observing the data if the null hypothesis (no difference) is true. Since 0.03 < α (0.05), the observed difference is statistically significant at the 5% level. We reject the null hypothesis and conclude there is evidence of a difference. Note: It does not prove the new method is 'better' (that requires looking at the direction of the difference), only that they are not the same.

An Xbar chart (for averages) monitors the process center over time, but it is insensitive to changes within the subgroups. An R (Range) or S (Standard Deviation) chart, used in tandem, monitors process variation. Relying solely on the Xbar chart could miss a significant increase in within-subgroup variation, which is a critical signal of process instability.

Correlation does not imply causation. A strong correlation suggests a relationship but does not prove direction or cause. A lurking (confounding) variable could be influencing both metrics. The team must use further analysis (like stratified analysis or designed experiments) to establish a causal relationship before investing in solutions.

Stratified random sampling divides the population into homogenous subgroups (strata) based on a known characteristic (e.g., shift, machine, product type) and then randomly samples from each stratum. This ensures the sample accurately reflects the population’s structure, providing more precise estimates for each subgroup and preventing a key subgroup from being missed by chance.

While RPN is a useful guide, best practice dictates that failure modes with very high Severity (often 9 or 10), especially those involving safety or regulatory compliance, require immediate action regardless of the Occurrence or Detection scores. The potential consequence of the failure is so severe that even a low probability of occurrence is unacceptable.

Stability (control) means the process variation is consistent and predictable over time (the rifle shots are grouped together). Capability means the process output consistently meets customer specifications (the rifle shots are grouped together AND on the target). A process can be stable but not capable (consistent but off-target), or capable but not stable (on-target on average, but with unpredictable variation that could eventually produce defects).

A key strength of the Pugh Matrix is its use as a creative tool, not just a scoring tool. The logical next step is ‘concept hybridization’—using the high-scoring attributes of Concept B and the positive differentiators of Concept A to synthesize an even better solution (Concept D). This iterative process often yields a more robust final solution than simply selecting the initial front-runner.

For a skewed distribution, the mean is pulled toward the tail and does not represent the ‘typical’ value. The median is a more robust measure of center in such situations as it is the middle value and is not affected by outliers or extreme skew. Reporting the mean could mislead the sponsor about the process’s typical performance.0