### On Design Engineering (DE) of Complex Electro-Mechanical Systems

- HPD components enable practitioners to
handle Variability and reach Design decisions. Since addressing Variability comprises most of DE's work content in many manufacturing industries (especially of Electro-mechanical products), this enables significantly reducing (perhaps by 2/3!)**properly****resources, development time, and # of hardware & prototype builds!** - Our advancements in the following significantly contribute to
**enlightening fundamental concepts and enhancing DE practices:**- Rigorizes Latitude; clarifies distinction between Latitude & Robustness
- Defines C
_{pk}at any level; enables Multi-Level C_{pk}propagation (e.g., parts to system) - Clarifies Analysis, Synthesis, & Optimization, handling simple to complex problems
- Finding Stochastic Operating Windows (≡ Feasible Regions) and the most Robust points within them, comprehending all internal & external noises and performance targets

- As importantly, engineers would understand SO much more technical info about their systems (local or global) with HPD results!

### On All Other Application Areas where Variability Needs to Be Addressed

- For areas such as Material Science, Chemical Engineering, parts manufacturing industries, and
**ALL**technical fields (except computer science) the same HPD software & Methodolodgy capabilities apply as for DE. Importantly, HPD makes it all easier, correct, and comprehensive. - For Operations Research Needs, terminologies differ from DE's, but examples such as Risk Analysis & Stochastic optimization for simple to complex situations are handled just as for DE
- For Miscellaneous Other Areas: Class projects conducted by Univ. of Rochester students who took
**HPD**-based classes covered a wide range of problem types of**their own**choosing. Examples included many that relate to their Master's theses in other disciplines (e.g., "Arsenic in Bangledesh's Ground water" or "Air Induction Rate of an Anti-Swirl Stator Mixing Tank Design") and some to their interests (e.g., to "Variability in Tuba Playing" and "Quality of Calculus Teaching"). All were complex and required FoVs (Flow of Variabilities) as the first step of their structuring a total Stochastic Model.

### On Mathematics, especially Probability, Applied Mathematics, & Statistics

** For specifics, see** Description C. **Here are some major summary points:**

- For
, liberated the concept of "Types" of distributions and proved inadequacy of certain assumptions**Probability** - Liberated
thus enabling Transcendence to the Stochastic Realm (think & work naturally with**Applied Probability****RV**s &**SV**s) - For
, enabled the concept that Deterministic Realm is but a sub-Realm of the Stochastic Realm**Mathematics in general** - Enabled unifying
by providing a comprehensive capability for**Applied Mathematics****SMAO**(Stochastic "Modeling," Analysis, & Optimization) and addressing when are Deterministics & Stochastics appropriate.