Discussion topics for a non-expert interface
With a case study
From screening to optimization: from DSDs to BBDs and SCCDs there are many OMARS:
| #factors | CCD | SCCD | BBD | DSD |
|---|---|---|---|---|
| 3 | 14 (4,6) | 10 (4,6) | 12 (4,8) | 8 (2,4) |
| 4 | 24 (6,8) | 16 (6,8) | 24 (12,20) | 8 (2,4) |
| 5 | 42 (8,10) | 26 (8,10) | 40 (20,36) | 12 (2,4) |
| 6 | 76 (10,12) | 44 (10,12) | 48 (24,32&40) | 12 (2,4) |
| 7 | 142 (12,14) | 78 (12,14) | 56 (32,48) | 16 (2,4) |
And also with 2-level factors and blocking factors we can make similar tables.
The current flow of OMARS designs
Enumeration → Characterization → Pareto selection → Software
| #factors / #runs | 34 | 36 | 38 | 40 |
|---|---|---|---|---|
| 3 | 38 | 64 | 95 | 127 |
| 4 | 651 | 2,157 | 4,420 | 9,688 |
| 5 | 8,564 | 38,368 | 110,380 | 919,100 |
| 6 | 139,985 | 1,926,480 | 15,097,844 | 1,358,312 |
| 7 | 171,785 | 460,191 | 4,365,957 | 1,935,655 |
Context
A practitioner wants to test 7 factors and he suspects the presence of curvature
An optimal design which allows fitting a full second-order requires at least 36 runs, which is unaffordable. Additionally, it is expected that the sparsity principle will hold, this is, just a fraction of the factors being active.
Therefore, a screening experiment that can be used also for optimization is desired. The budget allows for a maximum of 30 runs, and it would be desirable, if possible, to keep some runs for confirmation tests.
Ready? Then push
Questions
Question 1: what are the most common goals for a practitioner?
- Screening
- Knowledge discovery
- Optimization
Are there more?
Another question: How many times have you been involved in a follow-up experiment?
Question 2: comment on DE approach
They have three options:
1. Screening:
2. LE / Characterization: 2FI
3. Optimization: SOE
Question 3: do you think that the following situation occurs in practice?
An engineer wants to study 10 quantitative factors, but only wants to be able to estimate quadratic effects on 6 of them, as the other 4 are known to have little or no impact. In this case, some of the factors are 3-level and some are 2-level (and all quantitative).
Question 4: how bad is not having split-plot or mixture designs?
Question 5: how can we relate the statistical quality of a design with objectives that a practitioner can understand? How do they relate to the
- Quality of estimation (D-,A-efficiencies…)?
- Quality of prediction (I-,G-efficiencies…)?
- Projection capabilities? Power? 4th order correlation?
Question 6: given that we have a positive answer to the previous question, how would you combine the quality indicators?
Question 7: we have implemented the utopia method for design selection, any other way to choose?
Question 8: do you consider replication in screening experiments?
The are OMARS designs with different replicates than the center point. Even for a low number of runs compared to the number of factors.
Question 9: comment on the following guidelines by Coleman and Montgomery1
| item | comments | |
|---|---|---|
| 1 | name, organization, department, title experiment | |
| 2 | responsible for the experiment coordination | |
| 3 | objectives | |
| 4 | relevant background | |
| 5 | response variables | |
| 6 | control variables | |
| 7 | factors to be “held constant” | |
| 8 | nuisance factors | |
| 9 | interactions | |
| 10 | restrictions in factor levels | |
| 11 | restrictions in randomization | |
| 12 | gage R&R study? | |
| 13 | screening experiment? | |
| 14 | follow-up experiment? |
Coleman, D., & Montgomery, D. (1993). A Systematic Approach to Planning for a Designed Industrial Experiment. Technometrics, 35(1), 1-12. doi: 10.2307/1269280 ↩︎
José Núñez Ares
VLAIO Innovation Mandate holder
My research interests include design of experiments, data analysis and optimization