1 Introduksi
1.1 Latar Belakang
Metode Taguchi (Taguchi, 1986; Roy, 2010) adalah pendekatan DOE yang populer di industri Jepang dan manufaktur kualitas total, dengan filosofi robust design — mengoptimalkan rata-rata sekaligus minimasi variansi terhadap noise factors. Taguchi memperkenalkan orthogonal arrays (OA) standar (L4, L8, L9, L16, L18, L27, ...) sebagai screening efisien untuk multi-faktor pada 2 atau 3 levels.
Signal-to-Noise Ratio (SNR) Taguchi mengkuantifikasi robustness: kombinasi tingkat parameter yang memberi SNR maksimum memberikan optimasi mean + variance reduction simultan (Phadke, 1989). Tiga jenis SNR umum: smaller-the-better (defect rate, impurity), larger-the-better (strength, yield), dan nominal-the-best (target spec).
1.2 Tujuan Modul
Modul Taguchi Quick Design di SQalytics ditujukan untuk:
- Membangun Taguchi orthogonal array standar: L4 (3 faktor 2-level), L8 (7 faktor 2-level), L9 (4 faktor 3-level), L16, L18, L27.
- Mendukung 3 SNR formulations: smaller-the-better, larger-the-better, nominal-the-best.
- Menghitung main effect dan SNR effect per faktor.
- Memberikan optimal level recommendation dari maximum SNR per faktor.
- Audiens: praktisi industrial engineering yang familiar Taguchi, R&D yang ingin pendekatan robust design.
1.3 Posisi di Antara Alternatif
Pilih Taguchi Quick Design untuk robust design + SNR optimization. Untuk screening saturated atau fractional design eksplisit, pakai Screening Design Builder. Untuk multi-level RSM, pakai RSM Studio. Untuk full factorial dengan semua interaksi, pakai Factorial Design Builder.
2 Metode
2.1 Dasar Teoretis
Orthogonal array memberikan struktur balanced: tiap level setiap faktor muncul sama frekuensi, dan setiap pasangan level dari dua faktor muncul sama frekuensi (balanced & orthogonal).
L9 (3⁴) array — 4 faktor 3 level, 9 run:
| Run | A | B | C | D |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 2 | 2 |
| 3 | 1 | 3 | 3 | 3 |
| 4 | 2 | 1 | 2 | 3 |
| 5 | 2 | 2 | 3 | 1 |
| 6 | 2 | 3 | 1 | 2 |
| 7 | 3 | 1 | 3 | 2 |
| 8 | 3 | 2 | 1 | 3 |
| 9 | 3 | 3 | 2 | 1 |
Signal-to-Noise Ratio:
Smaller-the-better (defect, kontaminan):
$$ \text{SNR}_{\text{S}} = -10 \log_{10}\!\left(\frac{1}{n} \sum_{i=1}^{n} y_i^2\right) $$Larger-the-better (yield, strength):
Nominal-the-best (target spec $y^* $, mis. moisture target 6%):
$$ \text{SNR}_{\text{N}} = 10 \log_{10}\!\left(\frac{\bar{y}^2}{s^2}\right) $$Tujuan: maximize SNR untuk semua tipe (lebih tinggi = lebih robust).
Main effect SNR per faktor $A$ pada level $i$:
$$ \overline{\text{SNR}}_{A_i} = \frac{1}{n_{A_i}} \sum_{\text{runs with } A = i} \text{SNR}_{\text{run}} $$Optimal level: level dengan $\overline{\text{SNR}}$ tertinggi per faktor (independent assumption).
Predicted SNR optimal combination (Taguchi prediction):
$$ \hat{\eta}_{\text{opt}} = \bar{\eta} + \sum_{j} (\overline{\text{SNR}}_{j,\text{best level}} - \bar{\eta}) $$dengan $\bar{\eta}$ overall SNR mean.
Confirmatory run wajib di kombinasi optimal untuk validasi prediksi.
2.2 Persamaan Inti
SNR smaller: $-10 \log_{10}(\overline{y^2})$
SNR larger: $-10 \log_{10}(\overline{1/y^2})$
SNR nominal: $10 \log_{10}(\bar{y}^2 / s^2)$
Main effect SNR: $\overline{\text{SNR}}_{A_i} = \text{mean SNR runs with } A = i$
Predicted optimal: $\hat{\eta} = \bar{\eta} + \sum_j (\overline{\text{SNR}}_{\text{best},j} - \bar{\eta})$
2.3 Asumsi & Batas Validitas
| Asumsi | Konsekuensi jika dilanggar | Cara cek di SQalytics |
|---|---|---|
| Independent main effects (no interaction) | Optimal prediction bias | Tambahkan column interaksi dalam L8/L16 |
| Linear/monotonic response within levels | 3-level OA fine; 2-level miss curvature | Pakai L9 minimum untuk 3 level |
| SNR sesuai dengan tipe response | Misinterpretasi optimum | Pilih S/L/N tepat |
| Replicate $\geq 2$ untuk variance estimation | $s^2$ tidak teridentifikasi (nominal) | $r \geq 2$ rekomendasi |
| Confirmatory run pada optimal | Predicted optimal tidak tervalidasi | Jadwalkan confirmatory |
3 Cara Kerja
3.1 Step-by-Step di SQalytics
- Buka
Taguchi Quick Designdari domain Desain Eksperimen. - Pilih orthogonal array: L4, L8, L9 (default 3-level), L16, L18, L27.
- Daftarkan faktor (sesuai capacity OA): nama, level values.
- Pilih SNR type: smaller / larger / nominal.
- Klik
Generate Design. - Setelah eksekusi, input hasil di tabel response.
- Klik
Run SNR Analysis. - Tinjau hasil:
- TabMain Effect Plot— SNR per level per factor.
- TabOptimal Level Table— recommendation per factor.
- TabPredicted SNR— di optimal combination.
- TabConfirmatory— checklist untuk run validasi. - Opsional: klik
📰 Open in Publication Graph Studiountuk meneruskan Taguchi level map ke workflow publikasi cetak.
3.2 Template Tabel Input + Contoh Data Sintetis
Setup L9 untuk optimasi extraction yield (4 faktor 3 level, SNR larger-the-better):
| Factor | Nama | Level 1 | Level 2 | Level 3 |
|---|---|---|---|---|
| A | T (°C) | 50 | 65 | 80 |
| B | Time (min) | 15 | 30 | 45 |
| C | Solvent ratio | 5 | 12.5 | 20 |
| D | Ethanol (%) | 50 | 70 | 90 |
3.3 Contoh Luaran
L9 with response (mg/g yield, n = 3 replicates per run):
| Run | A | B | C | D | $y_1$ | $y_2$ | $y_3$ | SNR_L |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 8.5 | 8.2 | 8.7 | 18.5 |
| 2 | 1 | 2 | 2 | 2 | 12.4 | 12.8 | 12.2 | 21.9 |
| 3 | 1 | 3 | 3 | 3 | 15.8 | 15.5 | 16.0 | 23.9 |
| 4 | 2 | 1 | 2 | 3 | 14.2 | 14.5 | 14.0 | 23.0 |
| 5 | 2 | 2 | 3 | 1 | 18.5 | 18.8 | 18.2 | 25.4 |
| 6 | 2 | 3 | 1 | 2 | 16.8 | 16.5 | 17.0 | 24.5 |
| 7 | 3 | 1 | 3 | 2 | 19.5 | 19.8 | 19.2 | 25.8 |
| 8 | 3 | 2 | 1 | 3 | 17.2 | 17.5 | 17.0 | 24.7 |
| 9 | 3 | 3 | 2 | 1 | 22.5 | 22.8 | 22.2 | 27.0 |
Main effect SNR plot:
| Level | A (T) | B (Time) | C (Ratio) | D (Ethanol) |
|---|---|---|---|---|
| 1 | 21.4 | 22.4 | 22.6 | 23.6 |
| 2 | 24.3 | 24.0 | 23.9 | 24.1 |
| 3 | 25.8 | 25.1 | 25.0 | 23.9 |
| Range | 4.4 | 2.7 | 2.4 | 0.5 |
Optimal level: A₃ B₃ C₃ D₂ (rank by range: A > B > C > D — A dominant).
Predicted SNR at optimal:
$$ \hat{\eta}_{\text{opt}} = 23.8 + (25.8 - 23.8) + (25.1 - 23.8) + (25.0 - 23.8) + (24.1 - 23.8) = 28.6 $$
4 Kesimpulan
4.1 Relevansi Real-World
- Robust manufacturing — minimize defect rate, target nominal dengan low variance.
- Process optimization Toyota-style — 4 process variables, fast screening.
- Formulasi multi-faktor untuk pangan, farmasi, kosmetik.
- Robust design untuk noise factors (humidity, ambient T tidak kontrol).
- Six Sigma DMAIC — Taguchi populer di Improve phase.
4.2 Where to Go from Here
⚙ Troubleshooting Cepat
i Riwayat Revisi
| Tanggal | Revisi | Penulis |
|---|---|---|
| 2026-05-13 | Tambah catatan Step 4 → Step 5 PGS live untuk Taguchi level map | Codex |
| 2026-05-12 | Migrasi MD v2 → HTML final dengan figure publikasi + caption Elsevier-style (W1 batch malam 12 Mei) | Claude |
| 2026-05-12 | Draft v2 publikasi (KaTeX SNR S/L/N + L9 OA + APA Taguchi/Phadke/Roy) | Claude |
4 Referensi
- Taguchi, G. (1986). Introduction to quality engineering: Designing quality into products and processes. Asian Productivity Organization.
- Phadke, M. S. (1989). Quality engineering using robust design. Prentice Hall.
- Roy, R. K. (2010). A primer on the Taguchi method (2nd ed.). Society of Manufacturing Engineers.
- Ross, P. J. (1996). Taguchi techniques for quality engineering (2nd ed.). McGraw-Hill.
- Montgomery, D. C. (2017). Design and analysis of experiments (9th ed.). John Wiley & Sons.