Çarpık ve Kirlenmiş Veriler Altında Tekrar Sayısı ve Tahminci Seçiminin İkili Yanıt Yüzeyi Optimizasyonuna Etkisi

Abstract

Deney noktası içindeki tekrar sayısı ve tahminci seçimi, ikili yanıt yüzeyi optimizasyonunda çoğunlukla ayrı ayrı ele alınmaktadır. Bu çalışmada bu iki unsurun temiz, çarpık ve eklemeli olarak kirlenmiş veriler altındaki ortak etkisi, 39 senaryo, 200 Monte Carlo tekrarı ve r ∈ {3,5,8,10} için iç içe örneklemler kullanılarak değerlendirilmiştir. Ana analizde çarpıklığa göre düzeltilmiş bir konum tahmincisi sabit tutulmuş ve altı klasik ve sağlam ölçek tahmincisi karşılaştırılmıştır. Karar kalitesi tam-süreç ve temel-süreç hedeflerine göre değerlendirilmiştir. Tekrar sayısının 3’ten 8’e çıkarılması, tam-süreç için ortalama optimizasyon kaybını temiz veride %66,9, yalnızca çarpık veride %40,5 ve düşük, orta ve yüksek kirlenme olasılıklarında sırasıyla %38,7, %24,6 ve %22,5 azaltmıştır. Ortak konum–ölçek analizinde aynı geçiş, 80 birleşimin 79’unda tam-süreç, tamamında ise temel-süreç kaybını iyileştirmiştir. Hiçbir tahminci bütün koşullarda üstün değildir. Klasik standart sapma temiz veride ve kirlenmenin operasyonel sürecin parçası sayıldığı birçok durumda en iyi performansı göstermiştir. Sağlam yöntemler ise bazı düşük ve orta kirlenme koşullarında, özellikle temel sürecin korunması amaçlandığında daha iyi sonuç vermiştir. Ek tekrarın yararı; tahminci seçimleri, değerlendirme hedefleri, alternatif süreç geometrileri, hafif yanıt yüzeyi yanlış belirlemesi, küçük örneklem kalibrasyonu ve pozitiflik yaklaşımları altında korunmuştur. Baskı süreci örneği ve yarı-sentetik genişletme, temiz ve hafif bozulma koşullarında aynı nitel örüntüyü göstermiştir. Sabit 27 noktalı tasarım içinde en tutarlı etki tekrar sayısından kaynaklanmış; tercih edilen tahminci ise hedefe ve kirlenme yapısına bağlı kalmıştır. Bulgular, ikili yanıt yüzeyi çalışmalarında tekrar sayısının planlanması ve tahminci seçimi için uygulamaya dönük bir temel sunmaktadır.

Keywords

• Sağlam parametre tasarımı
• ikili yanıt yüzeyi metodolojisi
• tekrar sayısı
• ölçek tahmini
• kirlenmiş veri

The Effect of Replication Size and Estimator Choice on Dual Response Surface Optimization under Skewed and Contaminated Data

Abstract

Within-design-point replication and estimator choice are usually examined separately in dual response surface optimization. This study evaluated their joint influence under clean, skewed, and additively contaminated data using 39 scenarios, 200 Monte Carlo replications, and nested samples at r ∈ {3,5,8,10}. The primary analysis fixed a skewness-adjusted location estimator and compared six classical and robust scale estimators. Decision quality was assessed against full-process and baseline-process targets. Increasing r from 3 to 8 reduced mean full-process regret by 66.9% under clean data, 40.5% under skew-only data, and 38.7%, 24.6%, and 22.5% under low, moderate, and high contamination probabilities. In the joint location–scale analysis, the same transition improved full-process regret in 79 of 80 combinations and baseline-process regret in all 80. No estimator was uniformly best. Standard deviation performed best under clean data and often when contamination was treated as part of the operating process. Robust scale estimators performed better in some low- and moderate-contamination settings, especially when preserving the baseline process was the aim. The benefit of additional replication remained consistent across estimator choices, evaluation targets, alternative process geometries, mild response-surface misspecification, finite-sample calibration, and positivity treatments. A printing-process benchmark and a semi-synthetic extension showed the same qualitative pattern under clean and mild-disturbance conditions. Within the fixed 27-point design, replication had the most consistent effect, while the preferred estimator depended on the target and contamination structure. Together, the results provide practical guidance for planning replication and selecting estimators in dual response surface studies.

Keywords

• Robust parameter design
• dual response surface methodology
• replication size
• scale estimation
• contaminated data

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