KevN

Confidence intervals provides a range for the mean. Prediction intervals provides a range for a single new observation. The prediction interval is wider than the confidence interval because it includes the uncertainty of individual measures, i.e. data scatter. For example, LeBron averaged between 23.7 and 35.3 points per game (ppg) across the 13 years he has been in the playoffs. But he has scored over 30 points in 110 of his 238 playoff games, which illustrates a broader scatter for his points in any individual game.

Multiple regression using historical data is useful for: A1) Assessing correlation A2) Creating a model to predict an output (Y) from input variables (X's) DOE is useful for: B1) Optimizing designs and the specific experiments necessary and sufficient to validate designs B2) Screening/downselecting design options B3) Provides a process to design experiments including the resolution level and number of runs for a set of factors B4) Includes terms based on cross-products of the factors that can be assessed for significance for modeling

Regression analysis sample size sufficiency will depend on the need. For example, if a prediction is needed then a high Rsq and predictive Rsq implies a good predictive regression and assuming that there is not a over fit situation. If the residuals are small, random, and normal, this also indicates sufficient sample size.

Rationale for using Z-score: A. Most importantly, it is a predictive measure B. Secondly, it is a reasonable performance measure to normalize on as a standard because it can be computed from other methods (Yield, DPMO, DPU) and it's scale relates to a standard normal distribution

PFMEA assesses the severity of the most serious effect for a given failure (S), the likelihood of occurrence (O), and the detectability of the failure (D). The resultant Risk Priority Number (RPN) = S x O x D. Action is then taken to reduce the RPN to achieve an acceptable risk. With Six Sigma DMAIC, PFMEA provides a method that could be included in the Analyze phase as appropriate, and it includes actions in the Improve phase (to reduce higher RPNs).

When is a cause a root cause (or causes the root causes)? Here are some explanations: 1. The lowest level cause (or causes) that eliminates the problem. : a. The lowest level cause in the cause and effect logic tree that eliminates the problem. b. Another explanation, is the minimum and sufficient causes that eliminates the problem. 2. It is not a root cause if it is a critical cause or x(n) (at level n in the cause and effect logic tree) that is a function of a lower level critical x(n+1) (level n+1) that can be found that eliminates the problem 3. In practicality, if the cause can be eliminated economically, then the pursuit can be stopped at that point to conserve resources, in favor of prioritizing eliminating the problem and validating that the solution if effective.

Given: X impacts Y. However, it doesn't indicate how X impacts Y. A plausible scenario is that X can only impact Y adversely.

In order to determine other situations (beyond quality checks), let's first breakdown Attribute Agreement Analysis (AAA) into its components. AAA includes assessing repeatability (both within and between) and accuracy (by appraiser and overall compared to a standard). Repeatability and accuracy assessment could be useful in many other situations. A few possible applications are marketing/advertising; communicating/messaging; opinion surveys; knowledge checks/education/process understanding; intelligence/comparison; information assurance/error checking.

The data set follows a normal distribution and therefore can be characterized by the sample mean and standard distribution (S) with an associated confidence interval. The process outcomes will follow this characterized distribution. For example, future data sets of comparable quantity will have a mean in the range of the confidence interval.