Application of Artificial Intelligence-Integrated Six Sigma Methodology for Multi-Objective Optimization in Injection Molding Processes

Abstract

This study proposes an artificial intelligence-integrated Six Sigma framework for reducing multiple critical defects in plastic injection molding using real industrial production data from a washing-machine control-panel manufacturing line. Predictive models were developed under severe class imbalance conditions and combined with SHAP-based interpretability to identify the most influential process parameters. A multi-objective NSGA-II optimization strategy was then employed to simultaneously minimize major defect types, including gas-trapped burn (GTB), short shot (SS), sink mark (SK), and flash (FL). The proposed framework was validated through on-site continuous trial production of 300 parts after process stabilization, demonstrating substantial and consistent defect reduction. The results indicate that the integration of data-driven modeling, explainable artificial intelligence, and evolutionary multi-objective optimization provides a practical and scalable approach for quality improvement in industrial injection molding processes.

1. Introduction

Gas-trapped burn (GTB) is a surface defect that occurs when trapped gases in the mold cavity cannot be properly vented during melt filling, leading to localized burn marks or surface discoloration. This defect deteriorates both the aesthetic appearance and mechanical integrity of molded parts [1].

In addition to GTB, other common injection-molding defects—such as short shot (incomplete filling), flash, and sink marks—are highly sensitive to the complex interactions among injection pressure, injection speed, temperature, and timing parameters. Notably, some process variables exhibit inverse correlations: a parameter adjustment that eliminates one defect can inadvertently trigger another. For instance, increasing pressure or speed tends to reduce GTB risk but may induce flash formation; conversely, low pressure or speed may cause short shots, whereas excessive values may lead to flash or surface burns. This phenomenon is often referred to in the literature as the “flash–short chase” [2]. Therefore, a traditional single-defect improvement approach often fails to minimize the total scrap rate.

This study proposes a holistic framework for quality optimization in injection molding. The research progresses along two main axes: (1) A predictive model was developed for the most critical defect (GTB) to achieve reliable detection under class-imbalance conditions, focusing on high recall performance and appropriate decision-threshold calibration. (2) A multi-objective optimization approach was implemented to simultaneously minimize the occurrence probabilities of GTB, sink mark, flash, and short shot defects. This enabled the analysis of process trade-offs through Pareto-optimal solutions.

In practice, common operator interventions to reduce GTB—such as delaying the V→P (velocity-to-pressure) switchover, increasing injection pressure/speed in the final fill stage, or raising the pack/hold level—tend to increase flash likelihood along the parting line. Consequently, single-objective GTB minimization has proven unsustainable in field applications. In this study, flash defect was, therefore, modeled as a binding constraint within the optimization framework. Although flash appears less frequently in Pareto solutions, it shares strong control dependencies with GTB and exhibits the fastest marginal increase when process parameters deviate from the optimal range.

The contributions of this study can be summarized as follows: (i) A Precision-Recall AUC (PR-AUC)-based model evaluation strategy was adopted for the imbalanced classification problem, and various resampling techniques were comparatively assessed using this metric. (ii) The causes of GTB defects were robustly identified using Welch’s ANOVA, providing a statistical framework that relaxes classical ANOVA assumptions. (iii) A multi-objective Pareto optimization based on NSGA-II was applied to minimize all critical defect types simultaneously, incorporating Cost of Poor Quality (COPQ) weights to enhance practical decision-making. (iv) SHAP (Shapley Additive Explanations), originally proposed by Lundberg and Lee, was used to interpret the internal logic of the best-performing model, leading to interpretable process parameter settings applicable in real-world production [3]. In the literature, injection-molding process improvements have predominantly relied on single-objective optimization or trial-and-error adjustments targeting isolated quality characteristics. For example, several studies have tuned parameters such as packing time, melt temperature, or mold temperature to minimize warpage or volumetric shrinkage using design-of-experiments or simulation-based techniques. Multi-objective approaches based on NSGA-II have also achieved promising results for simultaneously reducing warpage and shrinkage [4]. Extending this line of research, Tian et al. [5] developed a two-stage Taguchi–RSM–NSGA-II framework that jointly optimized product deformation, dimensional deviation, weight stability, and energy consumption, demonstrating that evolutionary multi-objective search yields more balanced solutions than traditional single-objective methods. Similarly, Li et al. [6] combined Taguchi design, ANOVA, RSM, and NSGA-II to simultaneously minimize warpage, volumetric shrinkage, and residual stress in fiber-reinforced composites, illustrating that interacting molding parameters require a genuine multi-objective strategy rather than one-factor adjustments.

Furthermore, Chen et al. [7] integrated Taguchi methodology, RSM, and hybrid GA–PSO to enhance dimensional stability and reduce molding defects, highlighting the effectiveness of hybrid evolutionary algorithms in complex molding environments. More recently, multi-objective optimization strategies have been proposed to simultaneously minimize competing surface and dimensional quality characteristics in injection molding; for example, Mukras et al. [8] demonstrated that volumetric shrinkage and surface roughness can be jointly optimized using surrogate-assisted multi-objective frameworks.

Building on these findings, Kitayama et al. proposed a multi-objective optimization strategy using conformal cooling channels to simultaneously reduce warpage and cycle time, reinforcing the suitability of NSGA-II for capturing strongly coupled quality–productivity trade-offs in injection-molding operations [9]. Beyond NSGA-II, several evolutionary and soft-computing approaches have been explored, including particle-swarm-based multi-objective optimization of MIMO process conditions [10] and GA-based sink-mark minimization through response-surface modeling [11]. Surrogate-assisted global optimization methods inspired by Efficient Global Optimization (EGO) have also been applied to packing-profile and process-window design, where Gaussian-process-based models guide the exploration of nonlinear quality landscapes [12,13]. In addition, hybrid learning–optimization approaches, such as artificial neural networks coupled with particle swarm optimization, have been shown to provide sustainable and practical improvements in injection molding process performance [14].

Prior research has largely examined geometric or flow-related defects—such as warpage, shrinkage, sink marks, and short shots—without explicitly modeling gas trap burns. For instance, Mathivanan and Parthasarathy demonstrated that sink-mark formation is highly sensitive to packing pressure and cooling conditions [11], while Moayyedian et al. analyzed short shot probability and showed that underfilling arises from complex interactions among melt-flow behavior, gating design, and process-window boundaries [15].

Beyond simulation- and geometry-based studies, recent data-driven research streams have introduced AI-enhanced modeling and multi-objective optimization approaches tailored for real manufacturing systems. In parallel, data-driven frameworks integrating machine-level production data with quality outcomes have been reported for industrial injection molding systems, enabling improved process understanding and production efficiency [16]. Recent application-oriented studies have demonstrated that machine-learning-based defect prediction and process optimization can be effectively implemented in real injection molding environments; for instance, Ardestani et al. applied machine learning models to predict and optimize blush defect formation using industrial injection molding data, reporting significant process improvements under real production constraints [17]. Research in micro-injection molding has shown that simultaneously optimizing part-weight stability and flash formation can significantly improve process robustness under stringent filling conditions [18]. Cost-oriented design-of-experiments approaches integrated with machine learning further demonstrate that AI-assisted parameter tuning can reduce exploratory effort while increasing quality consistency [19]. Bayesian optimization applied to structurally constrained molding problems has revealed that probabilistic surrogate models can efficiently navigate high-dimensional parameter spaces and identify critical process variables [20]. Moreover, transfer-learning-enhanced multi-objective optimization methods have been shown to improve process stability and enable reliable quality prediction even under limited-data conditions, particularly when mold or material systems vary [21].

Complementary studies have broadened data-driven quality control in injection molding, including online monitoring frameworks [22], explainable-AI-based root-cause analysis [23], multi-task encoder–decoder models for quality prediction [24], predictive-maintenance strategies [25], small-sample transfer-learning approaches [26], mold-compliance analyses [27], real-time flow-behavior monitoring [28], and tie-bar-elongation-based process-control methods [29]. Deep-learning approaches combining multi-feature fusion with transfer learning have also demonstrated strong performance in predicting complex quality indicators [30].

Recently, deep-learning-based architectures have also been introduced for injection molding quality prediction. Transformer-based models have demonstrated a strong capability in capturing long-range temporal dependencies in multivariate process data, enabling improved defect prediction under dynamic manufacturing conditions. In parallel, graph neural networks (GNNs) have been applied to model the spatial and structural relationships between mold components, sensor locations, and quality responses, allowing the learning of complex interdependencies that are difficult to capture with conventional machine-learning models. These advances highlight the growing role of deep learning in intelligent molding systems; however, their industrial deployment often requires large labeled datasets and high computational cost, which limits their applicability in many shop-floor environments.

Despite these advances, most prior studies still focus on geometric deformation, shrinkage, or simulation-driven quality metrics rather than the real multi-defect interactions observed in industrial environments. In particular, the simultaneous, data-driven optimization of multiple defect mechanisms—such as gas trap burns, short shots, sink marks, and flash—remains largely unexplored. To the best of our knowledge, no prior study has jointly optimized these four industrially critical defects using real production data while integrating evolutionary optimization and Six-Sigma-based process improvement. This gap forms the central motivation for the present work.

Here, the term “multi-defect synchronous optimization” refers not to the independent elimination of individual defects, but to the identification of a Pareto-based trade-off solution among multiple defects within the same process window.

This study introduces a comprehensive multi-defect, data-driven optimization methodology based on real production data from a washing-machine control-panel injection line (product code: 1402690300). The proposed framework simultaneously minimizes multiple defect types and bridges a critical gap in the integration of AI-driven modeling, evolutionary optimization, and Six-Sigma methodology for scrap reduction and quality enhancement in plastic injection molding.

2. Materials and Methods

2.1. Data and Pre-Processing

The dataset used in this study consists of 1284 injection-molding production cycles collected from a plastic washing-machine control panel manufacturing line. Each observation includes the machine’s process settings—comprising 24 different parameters such as injection pressure and speed stages, holding (packing) pressure and time, melt and mold temperatures, and relevant cycle times—along with binary labels indicating the presence of various defect types in the produced part. A total of 22 distinct defects were originally recorded as binary (0/1) outcomes (e.g., gas mark, sink mark, flash, short shot, color defect, etc.).

Among these, four major defects—gas mark, sink mark, flash, and short shot—were selected as the focus of this work. Their positive sample counts in the dataset are 29, 24, 12, and 31, respectively (96 defective cycles in total), which represent the minimum but sufficient frequency required for training meaningful classification models. Extremely rare defects (e.g., color defect = 3 observations, scratch = 1 observation) were excluded from modeling since incorporating such sparse targets would introduce statistical noise and unnecessarily expand the Pareto search space.

During data pre-processing, the raw Excel file was imported, and all variable names containing Turkish characters were standardized. Measurement units and scales were harmonized across all parameters. Train–test partitioning followed the “split” indicator provided in the data source, resulting in approximately 70% training (899 samples) and 30% testing (385 samples). The split was performed in a setting-wise stratified manner, ensuring that no identical machine setting combination appears in both training and test sets. This prevents the model from memorizing specific setting profiles.

The dataset consisted of 1284 production cycles grouped into eight distinct machine setups. A value-based (setup-based) stratified split was applied, in which approximately 70% of samples from each setup were assigned to the training set and 30% to the test set, while preserving the defective–non-defective ratio across all critical quality characteristics (CTQs). Because production cycles within the same setup share identical machine settings, material conditions, and mold states, they are highly correlated. A random split would, therefore, introduce information leakage by placing nearly identical samples in both training and test sets, leading to overly optimistic performance estimates. The setup-based partitioning ensures that the test set represents unseen but statistically consistent operating conditions, providing a realistic assessment of model generalization for industrial deployment.

Missing or out-of-scope (NA) values were checked; no outliers requiring removal were detected among the continuous variables.

The distributional characteristics of key process parameters are summarized in

Table 1. Summary statistics of selected process parameters (n = 1284). Median and interquartile range (IQR) are reported for each variable.

Process Parameter	Median	IQR
Injection Pressure 1 (bar)	135	25
Injection Pressure 2 (bar)	130	25
Injection Pressure 3 (bar)	122	35
Injection Pressure 4 (bar)	115	25
Injection Pressure 5 (bar)	90	20
Injection Speed 1 (%)	44	22
Injection Speed 2 (%)	22	11
Injection Speed 3 (%)	20	13
Injection Speed 4 (%)	15	15
Injection Speed 5 (%)	9	11
Holding (Packing) Time (s)	6	2

. For example, the injection pressure in the first stage exhibits a median of approximately 135 bar, with 50% of observations falling within the 125–150 bar range (IQR ≈ 25 bar), whereas the fifth-stage pressure has a lower median of around 90 bar. Injection speed similarly decreases across stages, starting from a median of ~44% in the first stage and dropping to ~9% in the final stage. The holding (packing) time shows a median of ~6 s, with most observations lying between 5 and 7 s.

Injection speed is expressed as a percentage of the machine’s maximum programmable screw speed; 100% corresponds to the maximum allowable screw velocity.

2.2. Initial Quality Level

The initial defect distribution in the dataset was examined using a Pareto chart based on the total occurrence count of each defect type (Figure 1). Among the 1284 produced parts, 192 contained at least one defect, corresponding to a long-term defect rate of 14.94%. A total of 195 defects occurred across these 192 parts, with three parts exhibiting two distinct defect types.

In terms of frequency, the short shot (SS) defect ranked first with 31 occurrences, followed by gas trap burn (GTB) with 29, sink mark (SK) with 24, and flash (FL) with 12. These four major defects together accounted for approximately 49% of all 195 defect instances. Pareto analysis revealed that a small number of leading defect types contributed to the majority of total defects: for instance, the top seven defect types cumulatively represented nearly 80% of all defect cases. Accordingly, the selected focus defects—GTB, SS, SK, and FL—constitute the most critical components influencing total scrap, both in frequency and in process interactions.

In Six Sigma methodology, a defect is defined as any outcome that fails to meet a Critical-to-Quality (CTQ) requirement. A quality opportunity corresponds to one CTQ per produced part. Defects per Million Opportunities (DPMO) expresses how many CTQ defects are expected per one million such opportunities, providing a standardized measure of process quality. The sigma level represents the distance of the process from defect-free performance, with higher sigma values indicating lower defect risk. For reference, a Six-Sigma process corresponds to approximately 3.4 defects per million opportunities, whereas lower sigma levels imply substantially higher scrap and rework rates on the shop floor. In this study, SS, GTB, and SK are treated as CTQs because they directly generate scrap or customer-visible defects.

The initial process quality was also quantified using the Six Sigma methodology. The quality objective of this study is to treat short shot (SS), gas trap burn (GTB), and sink mark (SK) as critical-to-quality (CTQ) characteristics. Flash defects, which can be manually trimmed within 3–5 s on-site without generating scrap, were excluded from the initial sigma-level calculation but were included later as a constraint variable in the GTB optimization framework. This approach aligns with real-world manufacturing and customer-risk considerations by reflecting actual cost-of-quality implications.

Sigma Level Calculation:

N = 1284 parts, OPU = 3 (CTQs: SS, GTB, SK). Total CTQ defects D = 84 (SS = 31, GTB = 29, SK = 24).

Formulas:

DPMO = D/(N × OPU) × 10⁶ = 21,807

(1)

Z_lt (long-term) = Φ⁻¹(1 − D/(N × OPU)) ≈ 2.02 σ

(2)

Z_st (short-term) = Z_lt + 1.5 ≈ 3.52 σ

(3)

This DPMO value indicates that the process quality at baseline is relatively low. Based on the long-term performance assumption, the calculated sigma level of approximately 2.02 σ reflects a process that is far from the ideal Six Sigma benchmark. In other words, given OPU = 3, the probability of a part containing at least one CTQ defect is approximately 6.4%.

Table 2. Summary of initial process quality and sigma-level calculation (long-term assumption).

Metric	Formula/Description	Value
Defects per Million Opportunities (DPMO)	D/(N × OPU) × 106	21,807
Long-term Sigma (Z_lt)	Φ−1(1 − D/(N × OPU))	2.02 σ
Short-term Sigma (Z_st)	Z_lt + 1.5	3.52 σ

provides a detailed summary of the initial sigma-level computation.

2.3. Statistical Screening: Welch ANOVA

To identify process variables significantly influencing the occurrence of gas trap burn (GTB) defects, all continuous process parameters were statistically compared between the GTB-absent (0) and GTB-present (1) groups. Since the classical Student’s t-test can be misleading when the homogeneity of variances is violated, Levene’s test was first applied to assess variance equality. For variables with Levene’s p < 0.05, group means were compared using Welch’s ANOVA (assuming unequal variances), whereas for variables with Levene’s p ≥ 0.05, results from the classical t-test/ANOVA were considered valid.

To control the familywise error rate introduced by multiple hypothesis testing, Benjamini–Hochberg False Discovery Rate (FDR) correction was applied to all p-values, producing adjusted q-values. As an effect size measure, Hedges’ g statistic was calculated for each variable (|g| ≈ 0.2 = small, ≈0.5 = medium, ≈0.8 = large). A positive g value indicates that the mean of the variable is higher for non-defective parts (i.e., lower values increase GTB risk), whereas a negative g implies that higher variable values correspond to higher GTB risk.

Welch’s ANOVA was applied as a univariate screening tool to identify candidate variables prior to model-based learning; therefore, interaction terms were not included at this stage. Potential interaction effects among variables were subsequently captured by the machine-learning models and analyzed through SHAP. In addition, multicollinearity among the selected variables was assessed using correlation analysis and variance inflation factors (VIF), and no problematic collinearity was observed.

The analysis identified 11 process variables that showed statistically significant relationships with GTB formation (p < 0.05, FDR-adjusted): Injection Pressure 1–5 (5 variables), Injection Speed 1–5 (5 variables), and Holding Time (1 variable).

Table 3. Process parameters showing significant differences for gas trap burn (GTB) formation (Welch ANOVA results).

Process Parameter	p-Value	q (FDR)	Hedges’ g	Risk Direction
Injection Speed 3 (%)	4.99 × 10−7	4.60 × 10−6	+0.62	↓ (low value → risk ↑)
Injection Pressure 5 (bar)	8.37 × 10−7	4.60 × 10−6	+0.64	↓ (low value → risk ↑)
Injection Speed 2 (%)	1.96 × 10−6	7.19 × 10−6	+0.42	↓ (low value → risk ↑)
Injection Speed 5 (%)	7.18 × 10−6	1.97 × 10−5	+0.62	↓ (low value → risk ↑)
Injection Pressure 1 (bar)	2.62 × 10−5	5.76 × 10−5	+0.98	↓ (low value → risk ↑)
Injection Pressure 4 (bar)	1.32 × 10−4	2.42 × 10−4	+0.72	↓ (low value → risk ↑)
Injection Speed 4 (%)	1.83 × 10−4	2.88 × 10−4	+0.41	↓ (low value → risk ↑)
Injection Pressure 2 (bar)	2.17 × 10−4	2.98 × 10−4	+0.84	↓ (low value → risk ↑)
Injection Pressure 3 (bar)	7.92 × 10−4	9.68 × 10−4	+0.71	↓ (low value → risk ↑)
Injection Speed 1 (%)	1.92 × 10−3	2.11 × 10−3	+0.70	↓ (low value → risk ↑)
Holding Time (s)	2.21 × 10−2	2.21 × 10−2	–0.36	↑ (high value → risk ↑)

Note: p = raw p-value; q = FDR-adjusted p-value; Hedges’ g = effect size; Direction = “↓” indicates that lower variable values increase GTB risk, whereas “↑” indicates that higher values increase GTB risk.

summarizes the statistical test results.

For instance, the mean difference for Injection Pressure 1 was highly significant (p ≈ 2.62 × 10⁻⁵, q ≈ 5.8 × 10⁻⁵) with a large effect size (g ≈ +0.98). The positive sign of g indicates that non-defective parts exhibited much higher Pressure 1 values, meaning that low injection pressure is statistically associated with a higher GTB risk. This trend was consistent across all five pressure stages (g = +0.64–0.98).

Similarly, all injection speed stages exhibited significant differences (p < 0.001) with g values ranging from +0.4 to +0.7, confirming that lower injection speeds correspond to higher GTB probability. Finally, holding (packing) time was also identified as a significant variable (p ≈ 0.022, q ≈ 0.022, g = –0.36). The negative g indicates that GTB-positive parts had longer average holding times, implying that excessively long holding can increase GTB risk—possibly due to material thermal degradation or localized burning from prolonged pressure and heat exposure.

These findings quantitatively demonstrate that maintaining sufficiently high injection pressure and speed while avoiding excessively long holding times is essential to reducing GTB risk. Additionally, the remaining 13 process variables (e.g., cooling time, mold temperature, melt temperature) showed no statistically significant differences (p > 0.05). Hence, process control for GTB prevention should primarily focus on the pressure–speed profile during the filling stage. In subsequent sections, the predictive models and optimization frameworks are developed using these 11 critical variables.

2.4. Modeling and Explainability

Using the statistically screened process variables, several machine learning (ML) classifiers were developed to predict the occurrence of gas trap burn (GTB) defects in injection molding. The main objective was to enable early warning systems for operators or machine control logic by forecasting potential GTB occurrences during production and to use these predictive models for process-parameter optimization.

The following algorithms were evaluated on the training dataset: Logistic Regression (L1 and L2 regularization), Support Vector Machine (SVM) with an RBF kernel (calibrated using Platt scaling), Random Forest (RF), Balanced Random Forest (BRF), and LightGBM gradient boosting. Because the dataset suffered from strong class imbalance (only ~2% GTB-positive samples), several resampling and weighting strategies were applied. For example, Logistic Regression employed class_weight = “balanced” and Random Oversampling (ROS) to increase the weight of the minority class. In addition, SMOTE and SMOTE-Tomek methods were integrated with the RF and LightGBM models to assess their effectiveness under resampled training sets.

For model evaluation, PR-AUC (Area Under the Precision–Recall Curve) was used as the primary performance metric, as it is more informative in highly imbalanced classification problems. As secondary indicators, ROC-AUC, Recall, Precision, F1-score, and Accuracy were also reported for the positive class.

Random Oversampling (ROS) and SMOTE were intentionally selected as imbalance-handling techniques due to their model-agnostic nature, compatibility with SHAP-based explainability, and suitability for practical deployment in real shop-floor environments. While more advanced approaches, such as focal loss or cost-sensitive ensemble models, can further enhance classification performance, they typically require algorithm-specific loss functions or customized training procedures, which may reduce model transparency and complicate industrial implementation. Since this study prioritizes not only predictive performance but also interpretability and operational feasibility within a Six Sigma-oriented decision-making framework, such approaches were deliberately not employed.

A comprehensive comparison revealed that the L2-penalized Logistic Regression model achieved the best overall performance. Specifically, the L2 + ROS (100% oversampling) configuration yielded PR-AUC ≈ 0.15 and ROC-AUC ≈ 0.89 on the test set, outperforming other algorithms. This model successfully detected ~78% of GTB cases (Recall = 0.78) but had relatively low Precision ≈ 0.09 (and F1 ≈ 0.16) due to the low prevalence of the positive class.

In contrast, the SVM-RBF model performed poorly under data imbalance, achieving only PR-AUC ≈ 0.107 even after calibration. At the default threshold, it failed to identify any positive cases (Recall = 0), a result of an overly conservative decision function and the default threshold (0.5) being unsuitable for rare events.

The Random Forest model showed moderate performance (PR-AUC ≈ 0.109, ROC-AUC ≈ 0.87) but tended to ignore the minority class unless resampling was applied. When SMOTE was introduced, RF’s precision improved, though PR-AUC remained unchanged (~0.109). Balanced Random Forest (BRF) produced nearly identical results, maintaining the same recall (78%) and precision (~8.7%). LightGBM achieved a similar PR-AUC (~0.11), indicating comparable discriminative capacity but limited improvement under imbalance.

Although SVM-RBF achieved a high overall accuracy (97.7%), it failed to detect any GTB cases (Recall = 0) at the default decision threshold. This behavior indicates that the model optimized majority-class correctness rather than rare-defect sensitivity, making it unsuitable for an early-warning system where missing a defect is far more costly than raising a false alarm. Similarly, tree-based models such as Random Forest and LightGBM produced reasonable ROC-AUC values but limited PR-AUC, showing that they ranked samples well but did not sufficiently separate the rare GTB class from the majority. In contrast, L2-regularized logistic regression achieved a better precision–recall balance by producing well-calibrated probabilities and smoother decision boundaries, which is critical for rare-event detection and shop-floor risk prioritization.

Under severe class imbalance, complex tree-based models such as LightGBM tend to overfit sparse minority-class patterns and optimize overall accuracy rather than precision–recall trade-offs. In contrast, L2-regularized logistic regression provides a smoother decision boundary, penalizes extreme coefficients, and directly optimizes probability estimates, which leads to more stable and better-calibrated predictions for rare-event classification. This explains why logistic regression achieved superior PR-based performance in the GTB prediction task.

Overall, Logistic Regression emerged as the top model for ranking rare GTB cases. Its high ROC-AUC (0.89) suggests strong ranking ability, yet the low Precision implies many false alarms in practice. This limitation arises because only 9 of 385 test samples (≈2.3%) were GTB-positive. In such rare-event problems, even high-AUC models tend to overpredict positives. The obtained PR-AUC ≈ 0.15 is roughly 6.4× better than random chance, yet still modest in absolute terms. A practical solution is to optimize the decision threshold (e.g., via Top-K or Precision@Recall strategies), rather than fixing it at 0.5. Given the strong ranking performance, one can capture most GTB cases by inspecting only a small subset of the highest-risk parts, which significantly reduces inspection effort and cost.

The comparative performance of the evaluated machine-learning classifiers under different resampling strategies is summarized in

Table 4. Comparative performance of machine-learning classifiers with different resampling techniques (case study: gas trap burn detection in plastic injection molding).

Model	Resampling	PR-AUC	ROC-AUC	Recall(1)	Precision(1)	F1	Accuracy	TP/FP/FN/TN
Logistic Regression (L2)	None	0.149	0.890	0.778	0.088	0.157	0.805	7/73/2/303
Random Forest	None	0.109	0.870	0.778	0.088	0.157	0.805	7/73/2/303
Balanced Random Forest (BRF)	None	0.109	0.870	0.778	0.088	0.157	0.805	7/73/2/303
LightGBM	None	0.109	0.870	0.778	0.088	0.157	0.805	7/73/2/303
Support Vector Machine (RBF)	None	0.107	0.840	0.000	–	0.000	0.977	0/0/9/376
Logistic Regression (L2)	SMOTE	0.109	0.870	0.556	0.143	0.227	0.912	5/30/4/346
Random Forest	SMOTE	0.109	0.870	0.556	0.143	0.227	0.912	5/30/4/346
Balanced Random Forest	SMOTE	0.109	0.870	0.556	0.143	0.227	0.912	5/30/4/346
LightGBM	SMOTE/SMOTE-Tomek	0.109	0.870	0.556	0.143	0.227	0.912	5/30/4/346

.

To interpret model decisions, SHAP (Shapley Additive Explanations) analysis was performed. For the L2-regularized Logistic Regression model, a model-agnostic SHAP Explainer was used to compute global and local feature attributions. The global SHAP beeswarm plot (Figure 2) reveals that injection pressures (especially stages 1–4) and injection speeds dominate the GTB predictions, while holding time plays a secondary but measurable role. The local waterfall plot (Figure 3) for a representative defective sample shows how individual feature contributions lead to a final predicted GTB probability of f(x) = 0.52, as positive and negative SHAP values are aggregated from the baseline.

These explainability results confirm that while pressure, speed, and packing duration modestly influence GTB probability, the model retains good discriminative power (ROC-AUC ≈ 0.89 and PR-AUC ≈ 0.15) and captures the underlying relationships between key process variables and defect risk.

In addition, SHAP patterns indicate that the joint configuration of injection pressure and injection speed plays a decisive role in GTB formation, highlighting strong interaction effects between filling dynamics.

This figure shows the global contribution of each injection-molding process parameter to the prediction of gas trap burn (GTB) defects, based on SHAP (Shapley Additive Explanations) values.

Each point represents one production cycle. The horizontal axis denotes the SHAP value, which indicates the impact of a given feature on the model output (positive values increase GTB risk, negative values decrease it).

Color indicates the actual feature value, ranging from low (blue) to high (red).

The results reveal that injection pressures (especially stages 1–4) and injection speeds are the most influential variables governing GTB formation, whereas holding time plays a secondary but still relevant role.

This figure illustrates how individual process parameters contributed to the GTB prediction for a representative defective part from the test set (sample index 12).

Starting from the baseline model output $E\left[f\right(X\left)\right]$, each feature shifts the prediction either upward (increasing GTB probability, red bars) or downward (reducing GTB probability, blue bars), leading to the final predicted probability $f\left(x\right)=0.521$.

In this defective part, injection pressures and injection speed stages are the dominant contributors to the predicted GTB probability, confirming that GTB formation is governed by the coupled pressure–speed profile rather than by a single parameter alone.

3. Results

3.1. Multi-Objective Optimization Under Field Constraints

Single-objective improvement targeting only the reduction of gas trap burn (GTB) defects was found to potentially increase other defects. Therefore, in the second phase of this study, a multi-objective optimization framework was implemented for the injection molding process. The objective was to adjust process parameters such that the probability vector [P(GTB), P(Sink Mark), P(Flash), P(Short Shot)] would be minimized simultaneously. Here, P(defect) denotes the model-predicted probability of the respective defect. In short, minimizing four distinct defect probabilities was formulated as a Pareto optimization problem.

Three different optimization algorithms were compared:

(i)

NSGA-II: a simultaneous multi-objective evolutionary optimization that generates a Pareto-optimal set of trade-off solutions.

(ii)

Genetic Algorithm (GA): a single-objective optimization using a weighted-sum scalarization of all defect probabilities based on predefined cost weights.

(iii)

Bayesian Optimization (BO/ParEGO): a surrogate-based multi-objective optimization approach.

Each method was executed under the same search budget (approximately 900 evaluations) and initialized with comparable starting conditions to ensure a fair comparison. The search space was defined according to real-world operational constraints observed on the production floor.

All experiments were conducted using Python (version 3.10), with the DEAP library (version 1.3.3) for evolutionary optimization and scikit-learn (version 1.3.0) for machine-learning implementations.

NSGA-II was implemented using the Python DEAP library with binary tournament selection, crossover, and mutation operators. After preliminary trials with population sizes of 100 and generation counts of 100 (10,000 evaluations), the marginal benefit of larger populations was found to be negligible, and the total budget was, therefore, scaled to approximately 900 evaluations.

For the weighted-sum GA approach, the objective function was defined as a linear combination of the four predicted defect probabilities, weighted according to approximate Cost of Poor Quality (COPQ) ratios derived from industrial feedback: gas trap burn (GTB) = 20, short shot (SS) = 20, sink mark (SM) = 20, and flash (FL) = 1. The GA, therefore, evolved to minimize this weighted sum, prioritizing the three critical-to-quality defects (GTB, SS, SM) while keeping flash under control.

In this study, Bayesian Optimization was implemented using the ParEGO (Pareto Efficient Global Optimization) framework, which converts the original multi-objective defect-minimization problem into a sequence of scalar optimization problems via randomly weighted augmented Tchebycheff decompositions. At each iteration, a Random Forest surrogate model was trained on all previously evaluated parameter sets and used to propose new candidate solutions by maximizing an Expected Improvement acquisition function. This strategy enables sample-efficient exploration of the high-dimensional injection-molding process window while preserving Pareto-optimal trade-offs among gas trap burn, sink mark, flash, and short shot defects.

The BO procedure was initialized with 30 random design points and then run for 870 ParEGO-guided iterations, resulting in approximately 900 surrogate-based evaluations within the feasible process window.

As a result, the NSGA-II method produced a Pareto-optimal solution front. Two-dimensional projections of this front are presented in Figure 4. For example, minimizing the gas trap burn probability often led to a relative increase in the short shot probability, while solutions that reduced sink mark probability tended to increase flash. These patterns reflect the inherent trade-offs among the physical defect mechanisms in the injection-molding process. Consequently, each point on the Pareto front represents a feasible process configuration where improving one defect inevitably leads to a slight degradation in another.

Table 5. NSGA-II, GA, and BO: champion parameter settings, predicted defect probabilities, and COPQ values.

Method	Pressure 1–5 (Bar)	Speed 1–5 (%)	Holding Time (s)	P(GTB)	P(SM)	P(FL)	P(SS)	COPQ (20, 20, 1, 20)
NSGA-II	121/132/112/101/96	55/16/41/16/15	7.0	0.027	0.002	0.118	0.014	0.98
BO	111/133/128/98/118	10/59/21/18/11	6.2	0.007	0.030	0.268	0.007	1.15
GA	117/134/135/125/113	12/52/20/13/27	6.9	0.013	0.045	0.139	0.011	1.51

presents the champion parameter settings proposed by the three optimization techniques (NSGA-II, BO, and GA), along with the model-predicted probabilities for the four major defects and the corresponding total Cost of Poor Quality (COPQ). The total quality cost was calculated using the defect weights w = (20, 20, 1, 20) as follows COPQ = 20 × P(Gas Trap Burn) + 20 × P(Sink Mark) + 1 × P(Flash) + 20 × P(Short Shot). All probabilities are expressed in the [0, 1] range.

NSGA-II achieved the best overall performance with the lowest COPQ (=0.98), followed by BO (1.15) and GA (1.51). The superiority of NSGA-II stems from maintaining extremely low probabilities for sink marks and short shots while keeping gas trap burn at an acceptable level. Although BO produced the lowest probabilities for gas trap burn and short shot, it generated higher risks for sink mark and especially flash, thereby increasing the total COPQ. The GA method, on the other hand, exhibited a relatively higher sink mark probability, which primarily drove its higher cost value.

Under the given weighting scheme (gas trap burn, sink mark, and short shot as critical defects, flash as secondary), the NSGA-II champion setting represents the most suitable candidate for production implementation. BO may serve as a viable alternative when gas trap burn is considered more critical and flash has a lower economic impact. GA, under this cost structure, yields a comparatively higher total quality risk.

The ranking may vary depending on the company’s specific economic priorities; for instance, increasing the unit cost weight of flash could improve the relative standing of BO. Therefore, a weight sensitivity analysis is recommended for decision-makers.

3.2. Field Validation (300 Parts)

The 300-part on-site validation was conducted as a continuous production run after mold preheating and process stabilization, and only steady-state cycles were included in the evaluation. To verify the real-world applicability of the optimized parameter sets, each champion configuration was implemented on the production line, and 300 parts were produced under each condition. The resulting defect counts were recorded. In the gas trap burn (GTB) statistical screening (Levene–Welch ANOVA/two-sample tests), 13 process variables with p > 0.05 showed no significant mean difference between defective and non-defective parts and were thus excluded from the critical subset.

These variables were held constant at their Setup-5 levels during implementation. Setup-5 was chosen because, under this configuration, short shot (approximately 20) and sink mark (approximately 5) defects were observed in the same shift, providing a relevant testing ground for GTB–short shot–sink mark interactions. Other defect types (e.g., dimensional deviation, flow marks, burn marks, weld lines, stains, warpage, moisture, color variation, oil marks) were absent, indicating that the process was well-controlled for those modes in the selected window.

In the pilot validation, GA and BO solutions were prioritized first, followed by NSGA-II. Under the GA configuration, no GTB defects were observed, as intended. However, while no short shots occurred (0/300), nine sink marks appeared, and flash defects rose to 43. This outcome demonstrates that maximizing pressure and injection speed successfully eliminated gas entrapment but caused material overflow along mold-parting lines.

Similarly, the BO configuration yielded no GTB or short shot defects. Like GA, BO used high pressure/speed settings that prevented underfilling but resulted in 62 flash defects. Sink mark count decreased to five compared to GA. Because the BO model assigned a low cost weight to flash defects, this elevated flash rate matched expectations (predicted approximately 80, observed 62).

The NSGA-II configuration achieved the best overall quality. Although three GTB defects were recorded (not completely eliminated), both short shots and sink marks were fully prevented (0/300). Flash count (41) was lower than GA and BO. This confirms that NSGA-II’s balanced optimization achieved the lowest total defect count, supporting that tolerating a minimal GTB rate yields a better overall scrap outcome.

The expected and observed defect counts obtained from the 300-part on-site validation are summarized in

Table 6. Expected (Exp) vs. observed (Obs) defect counts (n = 300 per method).

Method	GTB_Exp	GTB_Obs	SK_Exp	SK_Obs	FL_Exp	FL_Obs	SS_Exp	SS_Obs
NSGA-II	8.1	3.0	0.5	0.0	35.4	41.0	4.3	0.0
BO	2.2	0.0	9.0	5.0	80.5	62.0	2.1	0.0
GA	3.8	0.0	13.5	9.0	41.7	43.0	3.3	0.0

Abbreviations: GTB = gas trap burn; SK = sink mark; FL = flash; SS = short shot.

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The expected number of defects was computed as the model-predicted defect probability multiplied by the 300-part on-site trial volume, i.e., Expected Defects = p^{^} × 300.

Because flash can be corrected by trimming excess material, it is often not counted as direct scrap. In this facility, flashed parts can be reworked. If FL is excluded from scrap accounting, NSGA-II becomes markedly superior: NSGA-II shows only three non-flash defects (GTB) versus nine for GA (SK) and five for BO (SK).

3.3. Final Sigma Comparison

The opportunity definition was fixed at OPU = 3 CTQs per part (SS, GTB, SK). At baseline, with D = 84 defects (SS = 31, GTB = 29, SK = 24) and N = 1284 parts, DPMO = 21,807, Z_lt ≈ 2.02, and Z_st ≈ 3.52. Under the NSGA-II pilot with D = 3 (GTB = 3, SS = 0, SK = 0) and N = 300, DPMO = 3333, Z_lt ≈ 2.713, and Z_st ≈ 4.213. A two-proportion comparison on the opportunity scale (84/3852 vs. 3/900) yields z approximately 3.72; p approximately 0.0002 (two-sided), indicating a statistically significant reduction in defect rate. Consistent with the Motorola convention, Z_st = Z_lt + 1.5 is reported; DPMO reflects the long-term equivalent.

The baseline and post-improvement sigma level comparison is summarized in

Table 7. Sigma level comparison (baseline vs. NSGA-II).

Scenario	n (Parts)	OPU (CTQs/Part)	SS	GTB	SK	D Total	DPMO	Z_lt	Z_st (Z_lt + 1.5)
Baseline (initial)	1284	3	31	29	24	84	21,806.9	2.018	3.518
NSGA-II champion	300	3	0	3	0	3	3333.3	2.713	4.213

Formulas: DPMO = D/(n × OPU) × 10⁶; Z_lt = inverse normal of [1 − D/(n × OPU)]; Z_st = Z_lt + 1.5 (Motorola short-term shift). CTQs: SS (short shot), GTB (gas trap burn), SK (sink mark).

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4. Discussion

This study demonstrates that targeting a single defect for improvement may adversely affect other quality indicators. Aggressively minimizing GTB can trigger short shots and flash, increasing total scrap. Traditional process tuning often focuses on one dominant defect, but in complex multi-parameter systems like injection molding, this creates a “balloon effect”—reducing one issue inflates another. The literature also notes this cyclic relationship between flash and short shots in mold optimization.

The balanced multi-objective approach provides a holistic solution. NSGA-II-derived Pareto sets explicitly show trade-offs among defects, allowing decision-makers to evaluate alternatives. For instance, one extreme Pareto point eliminates GTB entirely but increases flash, while another balances minimal GTB with moderate flash. In this study, NSGA-II accepted a minor GTB rate (3/300, approximately 1%) to achieve zero short shots and sink marks, thereby minimizing total scrap. GA and BO, by contrast, achieved zero GTB but did not minimize overall cost due to increases in other defects.

Although the absolute PR-AUC value (0.15) may appear low, it must be interpreted in the context of the extremely imbalanced dataset, where the random baseline corresponds to the GTB prevalence (approximately 29/1284 ≈ 0.02). Thus, the achieved PR-AUC represents more than a six-fold improvement over random ranking, indicating a meaningful discriminative capability for prioritizing high-risk parts within the optimization framework.

Practically, the recommended pressure and speed values were constrained to machine capabilities. Operators verified that suggested ranges remained within physical limits (e.g., Pressure1 lower bounds or Speed5 upper limits), ensuring field feasibility. Thus, the proposed optimization framework serves as a robust, operator-friendly decision-support tool.

Limitations include the single-product dataset (N = 1284), which—while typical—may limit generalization. External factors such as operator behavior, ambient temperature, and material variation were excluded and may explain deviations between predicted and observed outcomes. Additionally, defects outside the optimization scope (e.g., color issues) could increase under different settings, highlighting the need for context-specific cost weighting. The COPQ ratios used were firm-specific and may vary by plant; the method is general, but weight calibration is recommended.

5. Conclusions

This study presented a comprehensive artificial intelligence-integrated framework for defect prediction, interpretability, and multi-objective optimization in plastic injection molding. Statistical screening identified low injection pressure, low injection speed, and long holding time as the primary drivers of gas-trapped burn (GTB). Under severe class imbalance, L2-regularized logistic regression provided stable probability estimates and superior precision–recall performance compared with more complex models.

The proposed NSGA-II-based multi-objective optimization framework simultaneously minimized gas-trapped burn, short shot, sink mark, and flash defects, generating a Pareto-optimal set of process settings that explicitly captures trade-offs among competing quality objectives. On-site validation using a continuous 300-part trial production after process stabilization confirmed the practical effectiveness of the approach, yielding an overall defect reduction of 84.7% relative to baseline production.

From a shop-floor perspective, this improvement corresponds to a substantial reduction in scrap and rework, leading to increased effective production capacity, improved process stability, and lower quality-related costs. Rather than focusing on the complete elimination of a single defect type, the balanced minimization of multiple interacting defects proved to be a more effective strategy for overall quality and yield improvement.

Future work will focus on real-time integration of the proposed framework with machine controllers, the use of transfer learning to enable faster deployment on new products, and adaptive cost-weighted optimization to further enhance economic and operational decision-making in smart manufacturing environments.