Alan N

A confidence interval is used to predict the average value of a random variable, whereas a prediction interval is used to predict an individual value. Since the variation in the average of random variable is less than that of the random variable itself, a confidence interval is narrower than a prediction interval. My golf handicap is calculated based on my average scores over a number of rounds. I will usually shoot close to my handicap, but on any particular day, I could shoot much better, or much worse.

Differences between multiple regression using historical data vs. multiple regression using experimental data (DOE): Data capture: Analysis using historical data may be more representative of the environment (no Hawthorne effect), but such data may be captured in a less controlled and structured manner (levels of factors may not be meticulously set and recorded accurately). Modeling & analysis: No guarantee that historical data includes all the factors and combinations of their levels to allow statistically valid conclusions to be drawn. DOEs can be designed for specific purposes (e.g., screening, optimization) that allow models to be constructed and analyses to be performed in the most economical manner (i.e., in the fewest runs) and yield models

Z scores are useful even when there are other metrics for process performance since it is a uniform metric that can be used for both attribute and variable data. Z scores are especially useful for variable data since it can be used as a predictive, leading indicator (do not have to wait for defects to be produced). Note: Z scores are not always useful for comparisons however, since absolute values are relative to a particular process.

A cause should be considered a root cause when a common solution can be found to prevent or mitigate all lower level causes.

Even though X may be shown to have a statistically significant effect on Y, it may not justify any changes in X if the marginal cost of the change in X exceeds the marginal benefit in Y. Examples include going to higher quality materials that are expensive, but do not result in significant improvements in performance.