Some Specifics for Design Engineering

(i) Existing Practices for Design Engineering; (ii) Comparison of Taguchi Methods (TM) to HPD_Opt

This “Page” is especially important for Design Engineers. Other pages cover other aspects of HPD’s advancements, but here we will first state what are currently being used. Then, for Design Optimization, (a) point out TM’s major problems and (b) how HPD_Opt far supersedes TM. (Note: Pages HPD/Descriptions A, B, & D are also of relevance to Design Engineering. Those, however, do not specifically point to TM’s shortfalls.) The info below is from what we prepared recently for a “User Corporation.”
Existing Engineers' Practices for Addressing Variability
  • For Variability Analysis (e.g., for tolerancing, failure analysis, obtaining Output variability, . . .):
    A few use Monte Carlo (+ variants), ... ; some use RSS (mostly inappropriately) & Worst Case; . . .
  • For Design Optimization:
    Some use Taguchi Methods; many use ad hoc DoEs; some use iterative processes
On Comparing What Exists to HPD’s Capabilities

For Variability Analysis: Much on other pages has covered how HPD_VA leapfrogs over Monte Carlo and far supersedes existing Sensitivity Analysis techniques

Thus below we only need to compare capabilities for Design Optimization, i.e., Taguchi Methods to HPD_Opt (& HPD_OW) (The comparison is given in 2 textboxes below)

Important:
  • TM optimizes for Robustness
  • HPD optimizes for Robustness AND Latitude (latter is much more important; meaning given in HPD’s textbox below)
Some Major Problems with Taguchi Methods
  • If there are Interactions, and those hadn't been pre-identified, the optimal point by using one OA (= Orthogonal Array) can differ from that by using another OA!! - - See Parks' 2001 paper (reference on Announcement page). Mostly, TM results are valid only for problems with no interactions, but then the optimization process could be far more simplified! Basic fallacy exists from using S/N ratios - - See also Parks' paper.
  • TM needs a 2-step process to find the optimal point that meets the Target mean: Parameter Design and using an Adjustment Parameter, all without having properly considered Variability, and certainly not probability distributions of any type. It then uses Tolerance Design (the 3rd step) to meet the stochastic target, typically with too tight tolerances. Thus TM greatly sub-optimizes (to compensate for not quite the optimum and the 3-step process). (This is without user’s realizing it!)
  • Experimentally, it cannot handle Internal Noise, the most important part of meeting a Stochastic target!!
  • It cannot find Operating Windows which is extremely important for attaining Latitude (meaning is given in next textbox) - - even more important than finding the most Robust point!
  • It cannot treat any case where there are > 1 performance characteristic. Engineers use TM only because till now nothing else has existed for Optimizing for Robustness, though they do not fully understand TM and its significant shortfalls. . . . Also, they use smaller OAs to reduce confusion.
HPD’s Stochastic Optimization (SO) Tools: HPD_Opt & HPD_OW
(Note: It is not possible to do justice to HPD's SO in one textbox of info, thus this is skeletal at best)
  • HPD's SO tools: HPD_Opt (for 1 z) and HPD_OW (post-processor for > 1 z)
  • HPD_Opt (uses HPD_VA as compute engine, thus uses Probability Distributions!):
    • Has 36 combos of possible situations in basic subpaths:
      [Target Types] x [FF, Mixed, CC] x [Analytical; Lab (μ & σ); Lab μ] x [σ; Spread**]
      Note: Internal Noise is always covered (!); For Lab cases, External Noise is covered by the Lab (μ & σ) subpath;
      (** For non-Normal distributions, Spread is equivalent to 6σ (or ... ) span of Normal Distribution)
    • The (Robustness) Optimization Criteria are (can choose σ or Spread, or both):
      min σ; max |μ|/σ; min Spread; max |μ|/Spread
    • TM’s capabilities are included in (part of) only 2 of HPD's 36 combos!!
      Also Important: Relative to TM, HPD:
      • Obtains results far more appropriately (in 1 step); thus does not sub-optimize
      • Takes care of interactions (full, partial, or none)
      • Determines the Operating Window (region where target is met!), a larger size indicates having Latitude!
    • Re. Operating Windows (OWs):
      • They are obtained Stochastically, thus are Stochastic OWs, or SOWs
      • A very simple SOW from a sample run:
  • HPD_OW: Very important; many problems have > 1 z. Run HPD_Opt for each, then apply HPD_OW to the set!
  • HPD_VA’s tools & the HPD Methodology can be used to support the SO process, if needed.
  • All results & process are in simple engineering lingo, thus simplifying understanding of their problem & process.