Statistics in Engineering: Summary (Part 8 of 8)

Preface
This series is aimed at providing tools for an electrical engineer to gain confidence in the performance and reliability of their design. The focus is on applying statistical analysis to empirical results (i.e. measurements, data sets).

Introduction
We've covered the basic methods of applying statistics to your design and verification environment. Now let's present them all together and discuss what method is most suited for a particular circumstance.

If you are not familiar with statistics or need a brush up I recommend Schaum's Statistics. It provides a good overview of material without a lot of time spent on proofs and lots of examples.

Procedure
First, how to approach analyzing your data. Here is what I do. It's probably inadequate or susceptible to corner cases but I think it's a good start:

1. Test if application is suitable for particular data. Is your data actually Gaussian? If it matters then test to find out.
2. Is the sample size small? Then adjust your approach for small sample sizes.
3. Find the coefficients. If your method is good then apply it.
4. Apply the particular method to find your result (values on a line, a statistic, etc).
5. Finding confidence intervals. Now that you have your result find out how certain you are of it.
6. Hypothesis Testing If you are comparing more than one data set then use a hypothesis test.

Methodology
Which method to use?

• Is this in a manufacturing environment or during the design phase?
  • Factory: SPC is probably appropriate here. However if you are debugging a problem as opposed to just monitoring a process then one of the other methods is more appropriate.
  • Design Environment: As required (see below).
• Do you have 1 variable, 2 variables or more than two?
  • 1 variable: Gaussian Distribution estimate, Linear Regression
  • 2 variable: Correlation, Hypothesis Testing
  • Multi variable: ANOVA

Summary
I covered every aspect of design and verification I could think of when coverage or quantity becomes an issue knowing the right call for your design. In short I hope these methods will be useful in increasing your confidence and certainty in your design and verification.