Sandra

Explain the difference between Prediction Interval and Confidence Interval with application based examples. Prediction interval is relative to the individual values and will be larger than the confidence interval (more variation) Confidence Interval is relative to the average values If a we created a regression line model that depicted the probability of failure a) if asked what is the interval of failure on the next unit we would use the prediction interval b) if asked what is the interval of the average failures for tomorrow, we would use the confidence interval c) if asked what is the precise probability of x failure the we would use the regression line as the point estimate

What are the key differences between Multiple Regression using historical data and Multiple Regression based on Experimental Data (DOE)? Using historical data : you can see how the actual data fits the regression line you can see outliers and unusual observations to investigate or collect more data you can confirm if residuals are random and follow normal distribution DOE 1. models a regression line based upon experimental data - may not reflect all influences - noise, environmental, and control factors as in real data 2. models are only as good as the SME /teams that provide insight to the scope, factors, boundaries, and interactions What are the advantages of one over the other, if at all? using DOE can model and understand interactions with smaller runs/ replications ; can screen for critical X's and then evaluate interactions and provide model equation that cover more factors and levels more efficiently and effectively.

How can you check if you have taken enough samples for carrying out a Regression Analysis? using the adjusted r-sq calculator (https://www.danielsoper.com/statcalc/calculator.aspx?id=25) you can assess if the increase in the sample size will bring the observed r-sq to the r-sq (adj) values closer together (leaving predictors alone) Testing larger sample sizes to see if the values get closer is one way to see if you have taken enough (r-sq values s/b within 20% of each other). If the observed r-sq to the r-sq (adj) are very close within 20% then the sample size is sufficient

Z score allows comparison between attribute and variable processes; It is a universal translator It is a score that can be used to either improve and benchmark a process Can be used to assess ST and LT performance

In how many ways can a Process FMEA relate with a Lean Six Sigma DMAIC project DEFINE Within FMEA, Failure modes can relate to the define the stage of generating a project idea and defining project charter problem statement Within FMEA, the operation, step, process function (from pfd) can relate to the define stage of creating a high level map The requirements column informs of the process/customer requirement Potential Failure mode effect helps define the impact to the customer or producer MEASURE Cause segregates the reasons for the failure Within FMEA, the severity, occurrence, and detection rankings (and raw values) can support the measure effort Values can help differentiate which measure is more relevant to address ANALYZE RPN can relate to the analyze stage to prioritize and down select the project RPN values can help differentiate which measure is more relevant to address (SO, S, or O, or D) RPN sets the initial "as is state" of the process to improve from and which causes to mitigate IMPROVE Mitigation tasks and assigned personnel and committed due dates relate to improving the target RPNs Implementation of the change will show if a change (improvement) is realized Reassessment of change (S<O<D) and the RPN will validate if the change was actually an improvement CONTROL Once improvement validated, the living document of FMEA would continue to access if the change is stable Any change in S, O, or D negative would be reflected in new RPN

Share examples when the outcome of a hypothesis test indicates statistical significance with respect to impact of X on Y but does not warrant a change in X Cases where p is close to .05 the sample size may be small - need more data to make the decision A case where the X is at the limit of the specification or a threshold - cannot change X - machine temperature max is 100F - may need to assess other variables like speed or air flow or A case where the cost to make the change to X is too costly versus the benefit of the change - business case not valid

In what other situations can you use AAA to your benefit Evaluate agreement between supplier and customer - reduce NFF type failures Evaluate agreement between end -customer and manufacturer - reduce rejections or NFF failures Understanding (improve) repeatability of appraisers - determine if more training/tool/methods or improvements needed - determine best tools, techniques for appraisers - establish robust training program Understanding accuracy (improve) between appraisers - is the measurement system sufficient to identify defects and only accept good product - am I at risk for escapes or in needed rework in the factory - determine how to minimize Type I and Type II errors

Assuming a standard normal distribution , you can use probability distributions to make predictions for outcomes of business processes by: calculating the area under the curve that does not meet the business limits - defining how far away from the limit the process is (Z value). With known X=0, sd=1, and a limit calculating the probability of the process not achieving or achieving the desired limits (DPMO) With known mean, sd, and limit with known Z value (item 1) can convert to DPMO with known DPMO (item 2) can convert to Z-value Using the information to establish the business case and support the charter of a DMAIC to ensure we exceed the business goals.