### The Beginnings of a Simple Clarifying Intro

This is in Design Engineers' lingo. It is for those who have worked & struggled with Variability. . . . We assume you have viewed the site's main pages, but need a bit more specifics since as users you need more than high level descriptions. But here we just give "the Beginnings;" we stop after the Methodology.

### Introduction

For an electro-mechanical product, HPD enables engineers to **comprehensively **and **coherently **attack the **total **or **piecewise **problem of Design Synthesis, the objective of which is to optimize the Design setpoint (i.e., the combo of nominals of the design and control parameters) and the associated tolerances (of those parameters) that would enable meeting cost & performance specifications where all **Variabilities **that need be addressed are comprehended. In brief, HPD provides **significantly advanced**, yet **user-friendly**, capabilities for tolerancing and for obtaining robustness, operating windows (≡ feasible regions), and latitude for **any **simple-to-complex system.

Yet all this does not require your knowing more than the **very simplest** Probability concepts familiar to everyone (e.g., a probability distribution, the mean, the variance) to start with. And you'll be **amazed **that after using HPD, you will **understand a great deal** about Probability and treating Variability, and know how to **work **stochastically, with ease. You can apply it to any simple problem extremely easily, or you can tackle more complex problems with just a little more effort.

First, a few definitions for clarifications sake (workplace communication can be murky):

- Stochastic and probabilistic are used synonymously (most of the time).
- Optimization process encompasses using all relevant
to enable decision-making on the solution. (Note that in this sense,*concepts, processes, techniques, and tools**tolerancing*is an optimization*process*, and Design Synthesis is essentially Design Optimization.) - An optimization technique is (i) for handling specific local problems, or (ii) a mathematical or computational technique for optimization.
- An optimization tool is a specific software package (or other type of quantitative tool) based on an optimization
**technique**.

### HPD Basics:

HPD consists of** a methodology** and **two software suites (tools)** which enable implementing the methodology. In the sense of the definitions above, HPD is for optimizing (or decision-making on) nominals and tolerances. Very briefly:

-- The HPD Methodology prescribes and guides the work process for dealing with Variability.

-- HPD_VA is a tool for tolerancing (and **much more**, e.g., sensitivity/contribution analysis, computing resulting distributions, . . . ).

-- HPD_Opt is a tool for optimizing the nominals (and **much more**) (with Variabilities and targets accounted for).

### More Specific Descriptions of the 3 Components of HPD:

** The Methodology** (also simply referred to as HPD) guides How To:

- Structure/describe a "
**system**," quasi-hierarchically as necessary (e.g., if needed, from voice of customers downward to ultimately piece parts levels), as a global whole of local problems

*Note on " System":*

*System can have its usual meaning, OR when treating*

**any**particular problem, one may view that problem as a**system**and break it down – if needed - to levels of components that contribute to that total problem.- Of course, if one has a simple problem, e.g., one knows the model
- Segment the problem (as necessary) for local and global treatments
- Stochastically
**Model**(analytically or experimentally; simply or quasi-hierarchically); conduct experiments - Approximate as needed (for models, or for Variability info)
- Analyze effects of Variability (i.e., Tolerance/Latitude/Sensitivity/Contributions/Failure Analysis; resulting distribution)
- Appropriately address probabilistic non-independence of input parameters
- Optimize for Robustness and Latitude
- Address multiple (Stochastic) performance targets and obtain (Stochastic) Operating Windows (to be clarified under HPD_Opt)
- Conduct trade-offs quantitatively (between tolerances, nominals, or nominals and tolerances; intra and inter-entities; and with specs)
- Rigorizes C
_{pk}at any level, and quantitatively deal with C_{pk}s from parts level to system level (a request by management)

**z**= g(

**x**,

_{1}**x**, . . . ,

_{2}**x**

_{N}), there's no need for structuring.

In essence, the Methodology addresses how to specifically and coherently make quantitative decisions on Designs that are driven by Variability. The power of HPD derives from the fact that the HPD software capabilities have expanded what the Methodology could properly deal with, thus significantly advancing the Methodology itself.

"The Beginnings" stops here (we do not go on with describing the other 2 Components of HPD).