For skewed distributions, the median is the preferred measure of central tendency because it is not pulled by extreme values (outliers). Reporting the mean would be misleadingly high due to the few very long processing times, not representing the ‘typical’ customer experience. The mode may not be representative if the data is continuous, and standard deviation is a measure of dispersion, not central tendency.

A significant interaction means the relationship between one factor (e.g., amperage) and the response (weld strength) changes depending on the level of the other factor (wire feed speed). Therefore, you cannot set factors independently; you must find the best combination of settings. Main effects are still relevant but must be interpreted in the context of the interaction.

The I-MR chart is designed for continuous data where samples are individual measurements (n=1). The X-bar chart requires rational subgroups of size n>1. p-charts and c-charts are for attribute data (defectives or defects). Given the constraint of one measurement per batch and normally distributed continuous data, the I-MR chart is the correct choice.

Sustaining gains requires institutionalizing the change. The core activity of the Control phase is to transfer the improved process to the process owners via updated documentation, training, and control plans. While celebration and documentation are good practices, and financials are important for reporting, without proper training and updated standard work, the process is likely to revert to its old state.

If the p-value (0.03) is less than the chosen significance level α (0.05), we reject the null hypothesis. The correct conclusion is that there is statistically significant evidence that the process means are different. It’s important to note that ‘statistical’ difference does not automatically imply a ‘practical’ or meaningful difference, which must be judged based on process knowledge.

In FMEA, the three core ratings are Severity (S), Occurrence (O), and Detection (D). Occurrence (O) specifically estimates the likelihood of the cause happening, leading to the failure mode. It is based on historical data, reliability predictions, or team consensus on frequency. Severity rates the effect, and Detection rates the ability to find the cause/failure before it impacts the customer.

To determine if a observed difference (30 seconds) is statistically significant or likely due to chance, a hypothesis test is the appropriate tool. A 2-sample t-test would compare the means of the ‘before-improvement’ and ‘after-improvement’ data sets. A run chart shows stability but doesn’t formally test for a difference. Pareto charts analyze categories of defects, and Cpk measures performance against specifications, not the significance of a change.

R-squared (R²) is the coefficient of determination. It represents the proportion of the variance in the dependent variable (output) that is predictable from the independent variable(s) (inputs). An R² of 0.85 means 85% of the variation in Y can be explained by the model’s X variables. It is not a measure of prediction accuracy nor the probability of a correct prediction. The Black Belt should provide this correct interpretation to manage expectations.

The Analyze phase is about validating root causes. After brainstorming and narrowing possibilities (via tools like C&E diagrams and voting), the team must move from suspicion to evidence. A designed experiment (DOE) is a powerful, structured method to objectively test which suspected factors, and their interactions, have a statistically significant effect on the response variable. Implementing solutions without validation is premature and inefficient.

For skewed distributions, the median is the preferred measure of central tendency because it is not pulled by extreme values (outliers). Reporting the mean would be misleadingly high due to the few very long processing times, not representing the ‘typical’ customer experience. The mode may not be representative if the data is continuous, and standard deviation is a measure of dispersion, not central tendency.0