Dynamic Dual-Phase Forecasting Model for New Product Demand Using Machine Learning and Statistical Control

Abstract

Forecasting demand for newly introduced products presents substantial challenges within high-mix, low-volume manufacturing contexts, primarily due to cold-start conditions and unpredictable order behavior. This research proposes the Dynamic Dual-Phase Forecasting Framework (DDPFF) that amalgamates machine learning-based classification, similarity-driven analogous forecasting, ARMA-based residual compensation, and statistical process control for adaptive model refinement. The framework underwent evaluation through five real-world case studies conducted by a Taiwanese semiconductor tray manufacturer, encompassing a variety of scenarios characterized by high volatility, seasonality, and structural drift. The results indicate that DDPFF consistently outperformed conventional ARIMA and analogous forecasting methodologies, yielding an average reduction of 35.7% in mean absolute error and a 41.8% enhancement in residual stability across all examined cases. In one representative instance, the forecast error decreased by 44.9% compared to established benchmarks. These findings underscore the framework’s resilience in cold-start situations and its capacity to adapt to evolving demand patterns, providing a viable solution for data-scarce and dynamic manufacturing environments.

1. Introduction

Accurate demand forecasting remains critical in high-mix, low-volume (HMLV) manufacturing sectors, particularly in semiconductor packaging. Here, product lifecycles are short, market volatility is high, and order behavior is significantly influenced by unpredictable engineering and customer-driven changes. In this context, tray suppliers play a vital role by delivering customized carriers that enable safe transport and facilitate testing of integrated circuits. These tray products must frequently adapt to new chip designs, resulting in fragmented and intermittent demand patterns. Forecasting demand for newly introduced tray models is especially challenging, as it directly impacts production planning, inventory management, and service-level performance. This challenge is an example of the well-known cold-start problem, which occurs when a product is newly launched and lacks historical demand data. In such situations, conventional time-series models are inapplicable due to their reliance on prior observations. While the cold-start issue has been explored in various domains, manufacturing forecasting specifically refers to generating accurate demand estimates based solely on product attributes, such as dimensions, material types, and application categories. Unlike other definitions that may assume access to collaborative data or related product sales history, the cold-start condition addressed in this study assumes no temporal demand data are available at the outset. The DDPFF framework is designed precisely to operate under this constraint, using supervised classification and similarity-based analog forecasting to construct an initial demand profile without direct demand history.

The demand characteristics of such products are typically defined by (i) intermittent zero-order periods, (ii) limited historical data due to cold-start conditions, and (iii) highly dynamic ordering behavior triggered by frequent engineering revisions. These conditions pose significant challenges to traditional forecasting models, both in terms of modeling flexibility and computational efficiency. For example, classical statistical methods such as ARIMA and Holt–Winters exponential smoothing, while favored for their simplicity and interpretability [1,2,3], assume data stationarity and continuity, making them unsuitable for sparse, irregular demand signals [4]. Moreover, ARIMA’s iterative parameter estimation and retraining requirements under changing conditions often result in considerable computational overhead, limiting its scalability in real-time or high-mix applications.

Likewise, analog forecasting methods rely on similarity-based aggregation of historical analogs, which, although intuitive, are sensitive to feature distance metrics and do not support real-time adaptation or error correction. This restricts their utility in volatile demand environments where structural changes may occur post-launch. Hybrid or machine learning–based models, such as Support Vector Regression, Random Forest, or XGBoost, offer improved adaptability and generalization performance in high-dimensional, non-linear contexts [5], but are seldom designed to react autonomously to evolving demand regimes. Deep learning models (e.g., LSTM, GRU) provide long-term sequence modeling capabilities, yet their performance typically deteriorates under cold-start constraints due to their dependency on large volumes of historical data [6,7].

Moreover, demand signals in HMLV settings—particularly in the semiconductor and aerospace sectors—often exhibit abrupt structural changes and intermittent zero orders that few existing models can address [8,9]. In response to these challenges, this study proposes the Dynamic Dual-Phase Forecasting Framework (DDPFF) explicitly designed for forecasting new product demand under high uncertainty. The proposed DDPFF framework integrates three core components: an Initialization Forecasting Module that employs XGBoost-based classification and analogous product selection to generate early predictions; a Residual Compensation Module based on ARMA, which dynamically adjusts forecasts as real demand emerges; and a Model Transfer Module that monitors residual patterns using run-chart-based statistical process control to detect structural drift, triggering reclassification and model retraining.

This research proposes a unified, modular, and adaptive forecasting framework—Dynamic Dual-Phase Forecasting Framework (DDPFF)—to address the unique challenges of cold-start prediction, real-time adjustment, and structural adaptation in volatile manufacturing environments. The framework was empirically validated using five representative product cases from the new semiconductor tray manufacturing industry. Across these varied demand scenarios, DDPFF consistently outperformed conventional ARIMA and analogy-based forecasting models, achieving an average reduction of 35.7% in mean absolute error (MAE) and a 41.8% improvement in residual stability. These findings demonstrate the framework’s robust predictive performance and adaptability, making it a practical and scalable solution for manufacturers navigating sparse data environments, frequent new product introductions, and dynamic demand behaviors.

This paper is structured as follows. Section 2 reviews relevant literature on cold-start forecasting, hybrid prediction models, and structural adaptation in volatile environments. Section 3 outlines the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF), discussing its design rationale, model components, and system integration approach. Section 4 presents a multi-case experimental evaluation comparing DDPFF with baseline models in various real-world scenarios. Section 5 addresses practical implications for manufacturing and supply chain applications. Finally, Section 6 concludes the paper by summarizing key findings, identifying limitations, and outlining directions for future research.

2. Literature Review

Cold-start demand forecasting in high-mix, low-volume (HMLV) manufacturing has emerged as a critical challenge, particularly due to the scarcity of historical data and the volatility of demand across diverse product portfolios. Between 2022 and 2025, a notable shift occurred in academic and industrial research, emphasizing the use of machine learning to address this issue. In particular, attention has turned toward advanced frameworks such as transfer learning, meta-learning, and hybrid forecasting architectures, which offer promising solutions to sparsity and generalization problems. Our study builds upon these developments by proposing a modular, interpretable hybrid framework specifically designed for HMLV contexts.

Transfer learning has been widely explored across sectors to address the cold-start problem. In retail, Lei et al. demonstrated that hierarchical aggregation at the stock-keeping unit (SKU) and category levels improved the prediction of low-frequency items [10]. liu et al. (2024) applied Graph Neural Networks (GNNs) with transfer learning to predict sales at new store locations [11], while Liu et al. (2021) introduced the Weighted Adversarial Network (WANT) to transfer knowledge across cities with domain adaptation [11]. In transportation, Mallick et al. (2020) proposed the Diffusion Convolutional Recurrent Neural Network (TL-DCRNN) for spatial transfer learning across traffic networks [12]. Energy sector applications include Forootani et al.’s (2024) GAN-augmented framework for electric vehicle charging behavior forecasting [13], and Fatemi et al.’s (2023) causal deep learning model for sparse multivariate series [14]. Transfer learning has also improved personalization in digital domains such as recommender systems [15,16] and online advertising [17], offering methodological insights transferable to HMLV product forecasting.

Meta-learning, in contrast, emphasizes rapid model adaptation to new tasks with minimal data. Xu et al. introduced GNN-FOMAML, a first-order meta-learning model for volatile demand spikes, demonstrating over 25% MAE improvement in cold-start settings [18]. Pan et al. (2022) developed a multimodal meta-learning framework using image and text embeddings to improve recommendation quality [19], while Wang and Zhao (2020) and Guan et al. (2023) proposed embedding ensembles and cross-domain optimizers to improve generalization [20,21]. Zawia et al. (2025) reviewed meta-learning techniques across recommender systems, identifying mechanisms also applicable to demand forecasting [22].

Hybrid forecasting architectures have shown growing success by combining traditional time-series models with deep learning. Fawzy et al. (2024) demonstrated that integrating SARIMA with Informer significantly improves web traffic prediction [23]. Mahmoud and Mohammed (2024) showed that TCN-BiLSTM ensembles outperform baselines in air quality prediction [24]. Yemets (2024) and Lim et al. (2021) both leveraged the Temporal Fusion Transformer (TFT) for forecasting sparse, multivariate time series, emphasizing interpretability via gating mechanisms [25,26]. Zhou et al. (2021) further proposed Informer with sparse attention for scalable long-sequence forecasting [27]. He (2023) highlighted that sequential fusion of ARIMA and LSTM adapts well to regime-shift stock forecasting [28]. Our DDPFF framework draws from these innovations while explicitly avoiding deep models to prioritize explainability and retraining efficiency. It hybridizes four core modules—XGBoost classification, analog forecasting, ARMA residual correction, and statistical drift detection—to deliver robust and interpretable forecasts for volatile HMLV environments.

Cross-domain cold-start techniques also provide useful analogies. DeepAR, proposed by Salinas et al. (2019), modeled seasonality and uncertainty under sparse conditions [29], while Vervloet et al. (2022) combined product metadata and image embeddings for new product demand prediction [30]. Hung and Wang developed a dual-phase forecasting pipeline using XGBoost and ARMA, outperforming standalone methods in intermittent demand environments [31]. Aguilar-Palacios et al. (2020) further improved forecast interpretability by merging gradient boosting with contrastive explanations [32]. Multimodal and modular frameworks extend these ideas by leveraging diverse data types. Li et al. built a transformer-based architecture integrating product images, descriptions, and metadata for retail demand prediction [33]. Chauhan et al. (2020) adapted the Dynamic Key-Value Memory Network to improve cold-start regression across SKUs [34]. In healthcare, Tan et al. (2022) proposed MetaCare++, a meta-learning framework with temporal modeling tailored to sparse diagnostic data [35].

Synthesis. Based on this literature review, four key design patterns emerge as best practices:

• Two-stage pipelines: initialization followed by error refinement;
• Residual correction: absorbing short-term deviations using ARIMA or ARMA;
• Multimodal feature fusion: using structured metadata, text, and images;
• Cross-instance knowledge transfer: via transfer or meta-learning.

However, many existing models lack mechanisms for real-time structural drift detection and retraining feedback, critical for adapting to dynamic manufacturing shifts. Our DDPFF framework addresses this gap by integrating a run-chart-based monitoring module, offering a lightweight and actionable tool for practitioners seeking the balance between accuracy, interpretability, and operational usability.

3. Methodology

To tackle the dual challenges of cold-start forecasting during the initial launch phase of new products and the subsequent changes in demand structure, this study proposes an adaptive forecasting architecture known as the Dynamic Dual-Phase Forecasting Framework (DDPFF). This framework is tailored to function effectively when historical demand data are unavailable or extremely sparse. It also enables the dynamic updating and evolution of its forecasting logic as real-world data accumulates. The key innovation lies in DDPFF’s integration of machine learning classification, statistical residual modeling, and structural adjustment mechanisms, creating a closed-loop learning system that aligns prediction models with ongoing market realities.

The architecture comprises three interrelated functional modules. The Initial Forecasting Module is tasked with generating early-stage demand estimates. It employs an XGBoost-based classification model to categorize new products into one of several predefined demand pattern clusters. These clusters are constructed from historical product data using supervised or unsupervised learning techniques. After classification, the framework executes a similarity-weighted regression, selecting the most comparable historical products based on multidimensional feature proximity and aggregating their demand trajectories. This allows the model to integrate macro-level demand trends and micro-level analog characteristics, resulting in a composite initial forecast.

As actual demand data becomes available during the post-launch phase, the Residual Compensation Module is activated. In this stage, the framework continuously monitors the residuals between the predicted and observed demand values. These residuals are modeled using an autoregressive moving average (ARMA) process, which captures autocorrelated error patterns and provides real-time corrections to forecast outputs. A rolling update mechanism ensures that the correction model remains sensitive to short-term fluctuations and responsive to shifting customer behavior. To manage long-term structural changes in demand behavior, the Model Transfer Module conducts residual trend analysis using a run-chart-based statistical process control approach. This tool monitors forecast error sequences for persistent bias or drift. Once non-random deviations are identified, the system interprets this as a signal that the current forecasting model has become misaligned with the true demand dynamics. In response, it automatically initiates a reclassification process, reallocating the product to a more suitable demand cluster and retraining the model using updated data. This ensures the framework’s adaptability to structural shifts throughout the product’s lifecycle.

Together, these three modules form a forecasting system that is both deployable under data-sparse conditions and capable of continuous refinement. The architecture offers a practical solution for demand forecasting in manufacturing environments characterized by frequent new product introductions and volatile demand patterns, such as the semiconductor industry. Figure 1 presents a five-step process diagram outlining the sequential logic of the DDPFF framework to clarify the operational flow. The process starts with extracting and classifying product feature vectors (Step 1), then retrieving historical analogs and generating corresponding forecasts (Step 2). These outputs are integrated through a confidence-weighted ensemble method (Step 3). As actual demand data become available, forecast residuals are corrected using an ARMA-based compensation mechanism (Step 4), and structural changes are monitored via a run-chart-based statistical control procedure. When deviations indicating drift are detected, the system initiates reclassification and model retraining to ensure alignment with evolving demand behavior (Step 5). This closed-loop structure enables adaptive model evolution while maintaining forecasting accuracy throughout the product lifecycle.

3.1. Initial Forecasting Module

During the initial launch phase of a new product, the lack of historical order data makes conventional time-series models ineffective. To overcome this challenge, the Initial Forecasting Module of the proposed DDPFF framework utilizes a hybrid forecasting strategy that combines cluster-based demand modeling with similarity-weighted regression. This module aims to produce an initial demand forecast, denoted as $\widehat{y}$, through a three-step process, as detailed below.

• Stage 1: Product Classification via XGBoost

Let ${\mathrm{x}}_{\mathrm{new} }$ denote a new product’s feature vector, composed of internal design specifications and external market attributes. The feature vector is input to a trained XGBoost classifier $f_{\mathrm{c}\mathrm{l}\mathrm{s}}$, which assigns the product to one of K predefined demand clusters:

$$f_{\mathrm{c}\mathrm{l}\mathrm{s}}: {\mathrm{x}}_{\mathrm{n}\mathrm{e}\mathrm{w} }\to c_k, \hspace{1em}\hspace{1em}k \in \{1, 2,\dots ,K\}$$

(1)

Each cluster $c_k$ represents a canonical demand pattern derived from historical data via unsupervised or semi-supervised clustering techniques. Upon classification, a corresponding cluster-specific regression model $f_{\mathrm{r}\mathrm{e}\mathrm{g}}^{\left(c_k\right)}$ is used to produce the cluster-based forecast:

$${ \widehat{y}}_{\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}}=f_{\mathrm{r}\mathrm{e}\mathrm{g}}^{(c_k)} ({\mathrm{x}}_{\mathrm{n}\mathrm{e}\mathrm{w} })$$

(2)

The purpose of Equation (1) is to assign the incoming product to a demand pattern cluster based on its feature vector. This classification serves as the entry point for all subsequent forecasting logic. Equation (2) then applies the corresponding cluster-level regression model, which captures macro-level demand behaviors learned from historical products. Together, these two equations constitute the initialization phase of the DDPFF framework, enabling cold-start demand prediction before any real data becomes available.

• Step 2: Similarity-Based Analogous Forecasting

To reinforce robustness against potential misclassification, the module incorporates a similarity-based prediction scheme. For each historical product ${\mathrm{x}}_i$, a similarity score $w_i$ is computed using an inverse-distance weighting function:

$$w_i={\displaystyle \frac{1}{∥{\mathrm{x}}_{\mathrm{n}\mathrm{e}\mathrm{w}}-{\mathrm{x}}_i∥+ϵ}}$$

(3)

where $ϵ$ is a smoothing constant to prevent numerical instability.

Let $N$ denote the set of top-$N$ most similar historical items. The analogous forecast ${\hat{y}}_{\mathrm{analog} }$ is then given by a weighted aggregation of predictions from a Random Forest regressor $f_{\mathrm{R}\mathrm{F}}$ trained on historical products:

$${\hat{y}}_{\mathrm{analog}}={\sum }_{i\in N}{\displaystyle \frac{w_i}{{\sum }_{j\in N}{w}_j}}\cdot f_{\mathrm{R}\mathrm{F}}\left({\mathrm{x}}_i\right)$$

(4)

Equation (3) defines how similarity weights are computed for historical analogs based on feature distance, forming the core mechanism behind the analogy-based regression. Equation (4) aggregates the forecasts from these analogs to form a micro-level prediction that is responsive to the nuances of the new product. These equations enhance the framework’s robustness by providing an alternative forecast path when classification confidence is low.

• Step 3: Hybrid Forecast Integration

The final initial forecast ${\hat{y}}_0$ is computed by linearly blending the cluster-based and analogy-based forecasts using a confidence-weighted factor $\alpha \in \left[\mathrm{0,1}\right]$:

$${\hat{y}}_0=\alpha \cdot {\hat{y}}_{\mathrm{cluster}}+(1-\alpha )\cdot {\hat{y}}_{\mathrm{analog}}$$

(5)

The weighting factor $\alpha$ can be dynamically adjusted based on the classifier’s output confidence (e.g., softmax probability of $f_{\mathrm{cls}}$), enhancing forecast flexibility based on contextual certainty. Equation (5) synthesizes the outputs of the classification-based and similarity-based predictions through a confidence-weighted ensemble. This step is crucial in balancing general pattern recognition (via cluster regression) with localized learning (via analogs), and it serves as the final output of the first forecasting module.

This hybrid forecasting strategy allows the model to utilize both macro-level cluster priors and micro-level feature analogies, leading to a strong baseline prediction under cold-start conditions. Once actual demand observations become available, the framework shifts to the residual compensation phase, where forecast errors are modeled and corrected dynamically to uphold predictive accuracy throughout the product’s early life cycle.

To ensure transparency and replicability, the full parameterization process used in this module is detailed as follows. The XGBoost classifier was tuned via grid search across hyperparameters including max_depth, learning_rate, and subsample, with optimal configurations selected based on classification accuracy on a hold-out validation set. Similarly, the Random Forest regressor was tuned by varying the number of trees and maximum depth to balance accuracy and computational efficiency. For the similarity-based module, key parameters including the similarity threshold λ, the blending weight α, and the number of analogs k were treated as hyperparameters and jointly selected through empirical validation These parameters were tuned using grid search to minimize forecast error (MAE) on validation data. Their sensitivity was evaluated through a robustness analysis reported in Section 4.1. Notably, the value of k was not fixed a priori but derived based on forecasting performance across different case studies. This approach ensures the proposed framework remains adaptable across varying cold-start scenarios and product types.

While prior hybrid models, such as the XGBoost+ARMA pipeline proposed by Hung and Wang (2021), have shown promise in structured forecasting tasks, they are typically designed as static, two-stage sequences that lack feedback or adaptation [31]. In contrast, the DDPFF framework proposes a closed-loop architecture in which each module (classification, analogous forecasting, residual correction, and model transfer) is dynamically linked. This design allows for ongoing model self-adjustment based on real-time demand behavior, offering improved responsiveness and robustness. Furthermore, our architecture embeds structural drift detection and automatic model reassignment, enabling practical use in dynamic production settings—a capability not addressed in conventional hybrid designs.

3.2. Residual Compensation Module

While the initial forecast ${\hat{y}}_t^{\left(0\right)}$ provides a baseline estimate during the product’s early stage, actual demand observations often diverge due to market uncertainty and structural irregularities. To address this issue, the Residual Compensation Module serves as the second phase of the DDPFF framework, introducing a time-series-based error correction mechanism. This module utilizes ARMA modeling to identify temporal patterns in forecast residuals and implement real-time corrections, enhancing short-term prediction accuracy.

• Step 1: Residual Extraction and Monitoring

Let $y_t$ denote the observed demand at time $t$ and ${\hat{y}}_t^{\left(0\right)}$ the initial forecast. The residual error $e_t$ is defined as:

$$e_t=y_t-{\hat{y}}_t^{\left(0\right)}$$

(6)

The residual values $e_t$, collected from time step 1 to T, form a time-series sequence used for error modeling. These residuals are continually monitored for temporal correlation and structural deviation, which form the basis for statistical correction. Equation (6) defines the forecast residual, which forms the basis of the real-time correction mechanism in the second module.

• Step 2: ARMA-Based Residual Modeling

The residual sequence is modeled using an autoregressive moving average (ARMA) process, denoted ARMA(p, q), defined as:

$$e_t={\varphi }_1{e}_{t-1}+{\varphi }_2{e}_{t-2}+\cdots +{\varphi }_p{e}_{t-p}+{\theta }_1{\epsilon }_{t-1}+\cdots +{\theta }_q{\epsilon }_{t-q}+{\epsilon }_t$$

(7)

Here, ${\epsilon }_t$ represents a white-noise error term. The model is fitted using rolling residual data, allowing for dynamic adaptation to new error patterns. ${\varphi }_i$ and ${\theta }_j$ represent the coefficients of the autoregressive (AR) and moving average (MA) terms, respectively, and ${\epsilon }_t~N(0,{\sigma }^2)$ is a zero-mean white-noise process. Model parameters are estimated using a rolling window approach to accommodate time-varying error dynamics. This modeling step allows the system to learn and predict systematic deviations in real-time. Equation (7) models the autocorrelated structure of these residuals using an ARMA process, allowing the system to learn temporal patterns in error terms.

Using ARMA over alternative models, such as LSTM or Prophet, constitutes a deliberate design decision grounded in theoretical and practical considerations. In environments where data are scarce, as is often the case in the context of cold-start forecasting, deep learning models, such as LSTM, are susceptible to overfitting and necessitate extensive historical data for reliable training, conditions that are not typically met during the early stages of a product’s launch. While offering enhanced interpretability and suitability for long-range seasonal forecasting, Prophet assumes a smoother periodicity that does not align with the irregular and short-term nature of the residuals in the application domain under consideration. Conversely, ARMA models exhibit low computational complexity, minimal data requirements, and clear interpretability, rendering them especially well suited for real-time forecast correction in operational settings. Furthermore, ARMA supports incremental updating within rolling windows, enabling fast adaptation without the infrastructure burden associated with complex machine learning models.

• Step 3: Forecast Adjustment

Once the next residual ${\hat{e}}_{t+1}$ is predicted via the fitted ARMA model, the corrected forecast for the next time period is computed as:

$${\hat{y}}_{t+1}={\hat{y}}_{t+1}^{\left(0\right)}+{\hat{e}}_{t+1}$$

(8)

This additive correction ensures that the forecasting model accounts for recently learned biases or trends, effectively bridging the gap between initial estimations and actual market responses. Equation (8) then applies the predicted residual correction to refine the forecast. This sequence ensures the framework remains adaptive as actual demand deviates from early estimates.

• Step 4: Residual Stability Monitoring via Run Charts

To ensure the forecasting model’s temporal stability and structural validity, the residual sequence $e_t$ is continuously monitored using a run chart, a non-parametric statistical process control (SPC) method. The primary objective of this monitoring process is to identify non-random patterns in the forecast errors that may indicate a decline in model performance or the emergence of structural shifts in demand behavior. This step is central in bridging Module 2 (residual correction) and Module 3 (model transfer) by determining whether existing corrective mechanisms remain sufficient or if a structural adaptation is required. The centerline of the run chart is computed as the empirical mean of the residuals over a rolling window of size T.

$$\overline{e}={\displaystyle \frac{1}{T}}{\sum }_{t=1}^T{e}_t$$

(9)

The control limits are constructed using the empirical standard deviation ${\hat{\sigma }}_e$ representing the expected variation in residuals under stable conditions:

$$\mathrm{U}\mathrm{C}\mathrm{L}=\overline{e}+3{\hat{\sigma }}_e,\mathrm{L}\mathrm{C}\mathrm{L}=\overline{e}-3{\hat{\sigma }}_e$$

(10)

where UCL and LCL represent the upper and lower control limits, respectively, and the following run-chart rules are employed to signal potential instability or model drift:

• Shift Rule: If $k$ consecutive residuals lie on the same side of the centerline (commonly $k\ge 7$), it indicates a significant shift in prediction bias. If $\mathrm{sign}\left(e_t-\overline{e}\right)=\mathrm{sign}\left(e_{t-1}-\overline{e}\right)=\cdots =\mathrm{sign}\left(e_{t-k+1}-\overline{e}\right)$, then signal alarm.
• Outlier Rule: If any $e_t$ exceeds the control bounds. If $e_t>UCL$ or $e_t<LCL$, then signal alarm.

This residual-based statistical monitoring process is an autonomous trigger mechanism for structural re-evaluation. When either the shift or outlier rule is violated, the system escalates to the Model Transfer Module (Section 3.3), where the forecasting logic undergoes cluster reassignment and model retraining. This ensures the overall forecasting framework can dynamically adapt to demand evolution while maintaining statistical rigor.

3.3. Model Transfer Module

In dynamic and high-variability manufacturing environments, product demand patterns are susceptible to abrupt structural changes driven by market disruptions, misclassification errors, and customer-specific behaviors. These shifts often exceed the scope of traditional residual correction mechanisms and require the forecasting model to undergo structural adaptation. The Model Transfer Module is the structural adjustment component within the DDPFF framework. It monitors long-term residual trends and dynamically triggers reclassification and retraining to preserve forecast alignment and stability.

• Step 1: Residual-Based Structural Drift Detection

This step continues the logic initiated by the residual monitoring phase (Section 3.2), but adds statistical decision rules to determine when structural drift is likely. Specifically, structural drift is detected if residuals exhibit systematic deviation beyond expected stochastic variation. The system applies the following rules:

• Shift Rule: If $k\ge 7$ consecutive residuals $e_t$ lie entirely above or below the residual mean $\overline{e}$:

  $$\mathrm{sign}\left(e_t-\overline{e}\right)=\mathrm{sign}\left(e_{t-1}-\overline{e}\right)=\cdots =\mathrm{sign}\left(e_{t-k+1}-\overline{e}\right)$$

  (11)
• Outlier Rule: If any residual $e_t$ exceeds the 3-sigma control bounds:

  $$e_t>\overline{e}+3{\hat{\sigma }}_e\mathrm{or} e_t<\overline{e}-3{\hat{\sigma }}_e$$

  (12)

These criteria are adapted from statistical process control and are used to detect non-random trends suggestive of model failure. Once triggered, the system initiates reclassification.

• Step 2: Triggering Reclassification via Distance-Based Matching

Upon identifying a structural drift, the system reevaluates the current feature vector ${\mathrm{x}}_{\mathrm{new} }$ against all existing cluster centroids ${\mu }_k$. The assignment is performed via a distance-based classifier:

Upon detection of structural drift, the system re-evaluates the new product’s feature vector ${\mathrm{x}}_{\mathrm{new}}$ against updated cluster centroids ${\mu }_k$. The reassignment uses a distance-based classification function $d(·)$, typically Euclidean or Mahalanobis.

$$c_k^{\prime }=\mathrm{a}\mathrm{r}\mathrm{g} {\mathrm{m}\mathrm{i}\mathrm{n}}_{k}d\left({\mathrm{x}}_{\mathrm{new}},{\mu }_k\right)$$

(13)

Here, $d(·)$ typically denotes Euclidean or Mahalanobis distance. This reassignment function determines whether the product’s behavioral profile has diverged enough to warrant a new cluster. If $c_k^{\prime }\ne c_k$, the system interprets this as a cluster-level misalignment, prompting forecast logic updates.

• Step 3: Model Retraining and Forecast Updating

Following reclassification, the framework conducts a full reinitialization of the predictive path. This involves three coordinated steps:

(1)

Reselecting analogs: Based on the new cluster assignment $c_k^{\prime }$, top-k most similar historical products are re-identified to reflect the updated demand context.

(2)

Recomputing hybrid forecast: The cluster-based and analogy-based forecasts are recalculated using the updated inputs, ensuring alignment with the new behavioral cluster.

(3)

Retraining ARMA: The residual compensation model is retrained using the corrected residual series from the new analog group to capture evolving error dynamics.

The revised forecast is then expressed as:

$${\hat{y}}_{t+1}^{\prime }=f_{\mathrm{reg} }^{\left(c_k^{\prime }\right)}\left({\mathrm{x}}_{\mathrm{new}}\right)+{\hat{e}}_{t+1}^{\left(c_k^{\prime }\right)}$$

(14)

This full retraining ensures that both the trend and error components reflect the latest structure of the demand signal.

The Model Transfer Module provides structural adaptivity within the DDPFF architecture. By dynamically reclassifying products, reselecting historical analogs, and retraining both predictive and compensatory models, it prevents long-term forecast drift and maintains accuracy across volatile, high-mix environments. This mechanism completes a closed-loop learning cycle essential for sustained deployment in real-world industrial contexts.

3.4. Implementation Workflow and System Integration

This section describes the end-to-end implementation process of the DDPFF framework, including model training, parameter tuning, and system integration. The modular framework enables each component to be independently trained, validated, and integrated within existing operational environments. The training begins with constructing demand pattern clusters from historical product-level time series, using unsupervised k-means or hierarchical clustering algorithms. These clusters represent canonical demand trajectories (e.g., stable, intermittent, ramp-up, seasonal) and serve as the target labels for supervised classification. An XGBoost classifier is trained to map product attribute vectors to their corresponding clusters, allowing cold-start classification for new products with no historical demand data. Following classification, the framework performs similarity-based analog forecasting by identifying the top-k historical products with the highest feature similarity to the new item. A Random Forest regressor, trained on analog items, generates the demand forecast within the assigned cluster. The final output is derived as a convex combination of the cluster-based forecast and the similarity-weighted analog forecast, with blending controlled by a dynamic confidence weight α, determined from classifier confidence scores (e.g., softmax probability), as described in Section 3.1.

As real demand data become available post-launch, the Residual Compensation Module is activated. This module models the forecast residuals using an autoregressive moving average (ARMA) process within a rolling window. ARMA parameters are estimated using ordinary least squares or maximum likelihood estimation over the most recent w time steps. This mechanism enables real-time error correction while adapting to short-term fluctuations in demand. To address structural changes, the Model Transfer Module monitors residual patterns using a non-parametric, run-chart-based statistical process control method. Structural drift is detected when predefined rules are triggered (e.g., the seven-point shift or out-of-control signals). In response, the system automatically initiates reclassification using updated feature vectors and cluster centroids, followed by retraining of all relevant model components. This ensures that forecasting logic remains aligned with evolving demand behavior throughout the product lifecycle. All critical hyperparameters, including the similarity threshold (λ), the confidence blending weight (α), and the number of analogs (k), are selected via grid search using a hold-out validation set.

For system integration, each DDPFF module is developed as a standalone component that can be embedded into existing manufacturing execution systems (MES) or enterprise resource planning (ERP) platforms. Data exchange is managed through standard formats such as CSV or JSON, ensuring compatibility with existing data infrastructure. Modules may be deployed via RESTful APIs or batch processes, allowing flexible integration across cloud-based and on-premises environments. This lightweight implementation strategy minimizes the need for high-performance computing or deep learning infrastructure, enabling scalable and cost-effective deployment.

4. Case Study Analysis Results

To evaluate the forecasting performance and adaptability of the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF) in real-world cold-start scenarios, we perform a comparative analysis using two representative benchmark models: (1) the autoregressive integrated moving average (ARIMA) model and (2) the widely used analogous forecasting method. The evaluation concentrates on three key dimensions: initial forecast accuracy, residual correction effectiveness, and adaptability to structural shifts in demand behavior.

The first benchmark, ARIMA, is a conventional time-series model that operates under the assumption of data stationarity and the existence of consistent historical observations. Considering the inherent limitations exhibited by ARIMA in cold-start contexts, the approach adopted involves utilizing the most analogous historical product as a surrogate time series for each novel item. This practice aligns with a conventional approach frequently observed within the industry, favoring proxy data when direct historical data are inaccessible. The second benchmark, analogous forecasting, is widely used for predicting new product demand. It estimates demand by identifying the top-k most similar historical products based on product feature distances, and then generates a weighted average of their demand trajectories:

$${\hat{y}}_t^{\left(new\right)}={\sum }_{i=1}^k{w}_i\cdot y_t^{\left(i\right)}, \mathrm{where} w_i={\displaystyle \frac{1}{d\left({\mathrm{x}}_{new},{\mathrm{x}}_i\right)}}$$

(15)

While this method enables rapid forecasting in the early phase, it has significant limitations: its accuracy largely relies on the quality of similarity selection, and it cannot adjust to emerging patterns or correct systematic errors over time. In contrast, the DDPFF framework integrates classification-driven initialization, analogous forecasting, ARMA-based residual compensation, and a model transfer mechanism to facilitate multi-stage prediction and real-time learning. Thus, this section evaluates DDPFF against both benchmarks based on forecast error metrics, residual correction behavior, and structural learning responsiveness during the early and intermediate stages of new product introduction.

The evaluation dataset was sourced from a semiconductor tray manufacturing company in Taiwan. It comprises five new product cases (NP-01 to NP-05), each paired with historical reference items from a product database containing 576 entries. Feature selection relied on internal (e.g., tray dimensions, materials) and external (e.g., application type) product attributes. The matching analogs served as initialization inputs for the DDPFF framework. To provide further context while complying with confidentiality constraints, we offer a general description of the dataset’s structure. The historical database contains over 60,000 weekly demand entries across diverse tray types. On average, individual product SKUs exhibit highly intermittent demand, with more than 35% of the weeks showing zero demand. The average weekly quantity per SKU ranges from low single digits to around 30 units, with coefficients of variation frequently exceeding 1.0, indicating high volatility. These characteristics reflect the real-world complexity and sparsity typical of high-mix, low-volume (HMLV) manufacturing settings.

A brief overview of the five test cases follows:

• NP-01 (BGA, small package): Matched with 8 × 13.2, 8 × 14.1, and 9 × 12 trays, representing high-frequency demand volatility.
• NP-02 (QFN, medium): Paired with 5 × 5.1, 6 × 6.2, and 5 × 6 trays, exhibiting intermittent but stable replenishment.
• NP-03 (Custom design): Lacking clear analogs, and thus initialized with average cluster-level patterns from the “Custom” category.
• NP-04 (TSOP, elongated): Compared with 10 × 20, 9 × 21, and 10 × 23, seasonal and cyclic demand trends are exhibited.
• NP-05 (CSP, micro): Linked with CSP 4 × 5, 3 × 4, and 5 × 5 trays, representing abrupt and intermittent demand patterns.

For each new product, weekly demand was tracked over a 20-week post-launch horizon. Depending on data availability, matched analog items contributed between 18 and 40 weeks of historical weekly demand. This setup reflects the cold-start and data-sparse conditions frequently encountered in manufacturing environments.

The historical demand for analog products was weighted based on feature similarity and used to initialize the DDPFF prediction pipeline. Together, these five cases capture diverse practical forecasting challenges, including cold-start uncertainty, high volatility, demand intermittency, structural discontinuities, and seasonality.

Table 1. Summary of case study items and forecasting challenges.

Product ID	Package Type	Size	Forecasting Challenge
NP-01	BGA	Small	High-frequency volatility
NP-02	QFN	Medium	Stable intermittent replenishment
NP-03	Custom	Non-standard	No historical analogs
NP-04	TSOP	Elongated	Seasonal cyclical demand
NP-05	CSP	Micro	Intermittent and abrupt fluctuations

provides a summary of the case configurations and forecasting conditions.

4.1. Sensitivity Analysis of Hyperparameters

To ensure the robustness and reproducibility of the proposed DDPFF framework, a comprehensive sensitivity analysis was conducted, with the analysis targeting three critical hyperparameters: the similarity threshold (λ), the confidence blending weight (α), and the number of analogs (k). These parameters, respectively, determine the inclusion criteria for analog selection, the integration balance between cluster-based and analogy-based forecasts, and the level of granularity used in the analogous regression process.

Utilizing the NP-01 dataset as a paradigm, the similarity threshold, designated as λ, was varied from 0.05 to 0.50, and the blending weight, denoted as α, was varied from 0.10 to 0.90 in incremental steps. The number of analogs, k, was also tested across values from 1 to 5 to assess the trade-off between overfitting and generalization in the similarity-based forecast component. For each hyperparameter configuration, the model was re-executed using a fixed validation split, and the mean absolute error (MAE) was recorded as the performance metric.

The experimental results demonstrated that the DDPFF framework exhibited consistent forecasting accuracy across a range of hyperparameter settings. Specifically, variation in the parameter λ resulted in an MAE change of no more than ±13%, while adjustments in the parameter α led to deviations of less than ±10%. In the experimental phase of the study, an increase in the number of analogs from 1 to 5 was observed to provide only a marginal gain in accuracy. However, it was found that k = 3 consistently yielded a robust balance between prediction stability and responsiveness. These findings emphasize the framework’s robustness and reduce the necessity for exhaustive hyperparameter optimization.

It is recommended that the following default settings for deployment be adopted, based on the observations presented: (i) a value for λ ranging from 0.15 to 0.30, (ii) a value for α ranging from 0.50 to 0.70, and (iii) a value for k set at 3. These values offer a practical trade-off between accuracy and computational efficiency, and apply to most cold-start forecasting scenarios. The detailed hyperparameter settings for the classification and regression modules used in the evaluation are also reported to promote transparency. In the context of the classification task, the XGBoost algorithm was selected due to its scalability and effectiveness in processing structured tabular data. The parameters were selected through a grid search on a hold-out validation set. The final configuration was determined as follows: maximum depth was set at 4, the learning rate at 0.1, subsample at 0.8, colsample at 0.8, and the number of estimators at 100. This configuration was designed to strike a balance between model expressiveness and the capacity for generalization in circumstances where data are limited. The analogous forecasting component utilized a Random Forest regressor trained on the top-k historical analogs. The fixed parameters for the regressor were as follows: n_estimators = 100, max_depth = 5, and min_samples_leaf = 2. These choices enabled the model to capture non-linear dependencies in analog features while ensuring runtime efficiency. The ARMA(p, q) model was employed for residual compensation. The orders (p, q) were selected by minimizing the Akaike information criterion (AIC) from the candidate set {0, 1, 2, 3}. Across all case studies, low-order models such as ARMA(1, 1) and ARMA(2, 1) consistently yielded the optimal trade-off between accuracy and processing time. These configurations are computationally lightweight, enabling frequent updates in real-world production settings. All ARMA models were implemented using the statsmodels library provided by the Python (version number: 3.13) programming language to ensure that the training and fitting times remained below 50 milliseconds per update cycle.

4.2. Analysis Results

4.2.1. Cold-Start Performance Evaluation

During the early launch phase of a new product, forecasting models encounter the inherent challenge of operating under cold-start conditions, where no actual order data are yet available. This phase is especially critical, as accurate early-stage forecasts directly influence production planning, inventory decisions, and supply chain responsiveness. To assess the proposed framework’s predictive accuracy and cold-start adaptability, we choose NP-01, a high-volatility, small-form-factor BGA product, as a representative case study. NP-01 shows irregular demand fluctuations during its introduction, making it an ideal example for testing forecasting robustness in high-variability environments. Three forecasting strategies are compared.

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ARIMA Baseline Model: Constructed as a univariate time-series model using the historical demand of the most similar analog product (determined via feature similarity). Model parameters (p, d, q) were selected using the Akaike Information Criterion (AIC) from a candidate set within (0–3). This reflects a conservative, industry-standard approach.

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Analogous Forecasting: Applied Euclidean distance to identify the top-k most similar historical items (k = 3, same as DDPFF), and performed distance-weighted averaging of their weekly demand trajectories. No further adjustments or corrections were applied.

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DDPFF (Proposed Method): Combines supervised classification to assign the new product to a demand pattern cluster, followed by similarity-based analog forecasting. A hybrid forecast is then produced using confidence-weighted integration.

The cold-start forecast performance of each method is evaluated using three standard error metrics:

• Mean Absolute Error (MAE): Measures average absolute deviation from actual values.
• Mean Absolute Percentage Error (MAPE): This method normalizes errors as a percentage of actual values, which is useful for interpretability.
• Mean Absolute Scaled Error (MASE): Scales MAE relative to a naïve forecast; values > 1 indicate underperformance compared to the mean benchmark.

As shown in

Table 2. Cold-start forecast accuracy comparison for NP-01.

Forecasting Method	MAE ± SE	MAPE (%)	MASE
ARIMA	11.27 ± 0.91	42.1	1.13
Analogous Forecast	8.34 ± 0.72	33.9	0.94
DDPFF (Proposed)	6.21 ± 0.58	27.4	0.79

, the ARIMA baseline yields the highest forecast error, reflecting its limitations in adapting to cold-start conditions. Notably, the MASE value of 1.13 indicates that ARIMA performs worse than a naïve mean-based forecast. The analogous forecasting method shows moderate improvement, reducing MAE by approximately 26% compared to ARIMA, though its accuracy remains sensitive to the quality of analog selection and feature matching. In contrast, the proposed DDPFF framework outperforms both benchmarks across all evaluation metrics. Specifically, it achieves a 44.9% reduction in MAE relative to ARIMA and a 25.6% improvement over the analogous forecasting method. The MASE value of 0.79 further supports its effectiveness in data-sparse environments. To validate the statistical significance of these performance gains, we conducted pairwise two-sample t-tests using the MAE values across five forecasting trials. The DDPFF results were significantly better than both ARIMA (p < 0.01) and analogous forecasting (p < 0.05), indicating that the improvements are not due to random variation. This supports the robustness of DDPFF in real-world cold-start forecasting scenarios.

4.2.2. Residual Compensation Effectiveness

While the DDPFF framework provides relatively strong forecasts under cold-start conditions, forecast biases and structural irregularities can still occur as actual order signals start to accumulate. To tackle this, the framework includes the Residual Compensation Module that uses an autoregressive moving average (ARMA) model to capture and adjust the temporal structure of residuals. This module allows for dynamic, real-time corrections, improving forecast stability throughout the mid-term product lifecycle.

To evaluate the effectiveness of this compensation strategy, NP-04 was selected as the test case. NP-04 exhibits seasonal cyclic demand, making it an ideal candidate for assessing error convergence and variance stabilization. To quantify forecast stabilization, we define the Stability Improvement Rate (SIR) as:

$$SIR={\displaystyle \frac{{\sigma }_{before}-{\sigma }_{after}}{{\sigma }_{before}}}\times 100\%$$

The comparison of residual statistics—before and after ARMA-based correction—is summarized in

Table 3. Comparison of forecast residuals before and after ARMA compensation (NP-04 example).

Forecast Phase	MAE	Standard Deviation	SIR
Initial Forecast	7.92	5.14	N/A
After ARMA	4.32	2.17	+57.78%

.

This metric captures the relative reduction in the standard deviation of residuals, reflecting the model’s ability to smooth volatility and enhance consistency over time. For NP-04, the ARMA-corrected forecast resulted in a 45.5% reduction in MAE and a 57.78% reduction in error variance, demonstrating that the Residual Compensation Module significantly improves accuracy and stability.

As seen in Figure 2, the corrected residuals consistently fall within the ±3σ control limits of the run chart, with no signs of abnormal patterns—such as seven consecutive deviations on one side of the centerline. This meets the SPC “seven-point rule” and indicates that the residual process is under statistical control. Such behavior confirms that the ARMA module effectively reduces bias accumulation and prevents drift propagation, enhancing mid-term forecast reliability.

This analysis confirms that the ARMA-based residual correction not only reduces pointwise forecast errors but also plays a pivotal role in variance containment and structural robustness. By smoothing residual fluctuations and ensuring statistical control, this module enhances the DDPFF framework’s responsiveness and dependability during periods of demand evolution.

Section 4.2.3 examines the framework’s behavior under structural model drift conditions, evaluating its reclassification and retraining capabilities for maintaining long-term forecasting alignment.

4.2.3. Model Transfer Mechanism Analysis

While the ARMA-based Residual Compensation Module effectively mitigates short-term forecast deviations, it becomes increasingly limited when significant changes in the demand structure or when the initial classification places the product in an inappropriate cluster. Under such conditions, systematic bias may emerge, manifesting as sustained residual trends. To address this, the proposed DDPFF framework incorporates the Model Transfer Module that monitors structural alignment and initiates dynamic model reclassification and retraining when necessary.

To validate the effectiveness of this mechanism, NP-03 was selected for an in-depth case study analysis. NP-03 is a fully customized tray product designed for irregular optical lens geometries, and it exhibits minimal feature similarity to items in the historical dataset. Consequently, NP-03 was initially classified in Cluster 2, which typically contains standard tray types with moderately stable demand patterns. However, starting in week 3, the forecasted demand consistently underestimated actual orders, leading to sustained positive residuals. The run chart of forecast residuals displayed a statistically significant anomaly: more than seven consecutive data points were on the same side of the centerline, thus violating the “seven-point rule” for randomness under standard SPC principles. This was interpreted as a structural drift event.

The system automatically initiated the model transfer process in response to this anomaly. The feature vector of NP-03 was re-evaluated against all cluster centroids using a distance-based assignment function. Consequently, NP-03 was reassigned to Cluster 3 in week 9, a group associated with high growth and highly variable demand patterns. Simultaneously, the residual correction model was retrained using the behavioral characteristics of the new cluster.

The effect of model transfer on forecasting performance is summarized below:

• MAE decreased from 13.37 to 8.19, representing a 38.7% improvement in average forecast error.
• MASE dropped from 1.46 to 1.01, moving closer to the threshold where performance equals that of a naïve benchmark.
• The run chart of residuals post-transfer showed no further violations of the ±3σ control limits, and residuals fluctuated randomly around the centerline, indicating that the model had returned to statistical control.

This case exemplifies the closed-loop adaptability of the DDPFF framework, where forecast misalignments are detected, interpreted as structural signals, and automatically resolved through a cycle of error detection → reclassification → adaptive retraining. The ability to recover from misclassification and maintain predictive alignment showcases the practical strength of DDPFF in volatile, low-data, and high-customization manufacturing environments.

This mechanism ensures that the forecasting logic continuously evolves alongside the actual demand trajectory, reinforcing the framework’s relevance for real-world industrial applications where uncertainty and structural changes are common.

4.2.4. Overview of Forecasting Accuracy Across Five New Products

To clarify the evaluation stages, we define initial forecasts as the error outcomes produced solely by the first module of the DDPFF framework, which combines classification-based cluster prediction and similarity-based analog forecasting. These forecasts are generated before any actual demand is observed. In contrast, the post-comp results incorporate the additional effects of Modules 2 and 3—namely, residual correction using ARMA and dynamic model transfer via statistical process control. This terminology distinguishes baseline predictions from enhanced forecasts that adapt to post-launch demand signals.

To thoroughly evaluate the adaptability and predictive robustness of the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF), a multi-sample validation was conducted using five representative new products (NP-01 to NP-05). These cases collectively cover a wide range of forecasting challenges observed in semiconductor tray manufacturing, including high volatility under cold-start conditions (NP-01), intermittent replenishment (NP-02), fully customized demand with no historical analogs (NP-03), seasonal cyclicality (NP-04), and sporadic step-change behavior (NP-05).

Each product was initially matched to historical analogs using feature-based similarity measures that considered package type, dimensional specifications, and functional attributes. These analogs provided inputs for the initialization forecasting module. Subsequently, all samples went through the complete DDPFF pipeline, which included (i) hybrid initialization forecasting, (ii) ARMA-based residual compensation, and (iii) model transfer through reclassification when applicable.

Three key evaluation metrics are utilized to quantify model performance: Mean Absolute Error (MAE), Mean Absolute Scaled Error (MASE), and the newly introduced Stability Improvement Rate (SIR), which reflects the convergence of residual variance before and after compensation.

As shown in

Table 4. Forecast accuracy across five new product cases—initial (module 1 only) vs. post-comp (modules 2 and 3 applied).

Product ID	Initial MAE	Post-Comp MAE	Initial MASE	Post-Comp MASE	SIR
NP-01	8.82	5.24	1.12	0.85	+42.2%
NP-02	4.11	2.98	0.91	0.67	+31.2%
NP-03	13.37	8.19	1.46	1.01	+43.3%
NP-04	6.44	4.03	1.08	0.72	+57.8%
NP-05	5.91	3.88	1.03	0.71	+34.3%

, the DDPFF framework consistently outperforms the baseline initialization forecasts across all test cases. On average, post-compensation MAE decreased by 38%, reflecting enhanced predictive accuracy.

• All post-compensation MASE values fell below 1, indicating better-than-naïve performance;
• The average SIR reached 41.8%, demonstrating a substantial reduction in residual variance and improved forecast stability.

Notably, NP-03—despite being a highly customized product with no clear analogs—benefited significantly from the model transfer mechanism. Following the automatic reassignment in week 7, its MAE dropped by 38.7%, and its MASE decreased from 1.46 to 1.01, confirming the framework’s capability to recover from initial misclassifications.

These results demonstrate the generalizability and effectiveness of the full DDPFF framework, with each module contributing distinct improvements in forecasting accuracy and stability. Its dual-phase structure allows it to manage not only high-frequency and intermittent demand signals, but also structural drift and sparse data challenges. The system’s capacity to combine statistical monitoring with adaptive model evolution positions it as a practical and robust forecasting solution for real-world applications in high-mix, low-volume manufacturing environments.

4.3. Case Study Summary

This study utilized five representative new product items (NP-01 to NP-05) as empirical cases to assess the applicability, performance, and robustness of the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF) across diverse demand scenarios. These cases illustrate real-world complexities often encountered in high-mix, low-volume (HMLV) manufacturing environments, such as cold-start uncertainty, demand intermittency, seasonality, and structural drift.

• Initial Forecasting Effectiveness
  During the early-stage (cold-start) period—marked by the lack of product-specific historical data—the DDPFF framework demonstrated the capability to generate accurate initial forecasts. By integrating classification-based cluster modeling with similarity-weighted analogy, the model effectively derived demand patterns from historical analogs. For instance, in the NP-01 case, DDPFF achieved a 27.4% MAPE, surpassing both ARIMA and traditional analogous methods.
• Mid-Term Residual Correction
  In the dynamic correction phase, the ARMA-based residual compensation module was instrumental in reducing forecast volatility and aligning predictions with emerging order signals. Across the five case studies, the average Stability Improvement Rate (SIR) reached 41.8%, indicating a substantial reduction in residual variance. Notably, for NP-04—a product with cyclical seasonal behavior—the standard deviation of residuals decreased from 5.14 to 2.17, reflecting enhanced forecast convergence.
• Long-Term Structural Adaptability
  Beyond short-term correction, the Model Transfer Module equipped the framework with the ability to detect and respond to structural changes in demand behavior. By leveraging run-chart logic and statistical rules (e.g., seven-point shift), the system autonomously triggered model reclassification and retraining. In the case of NP-03, where initial misclassification led to sustained forecast errors, the transfer mechanism reallocated the product to a more appropriate cluster. As a result, MAE decreased from 13.37 to 8.19, and the residual distribution returned to statistical control.

In summary, the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF) consistently demonstrated superior performance across three critical aspects of new product demand forecasting: (i) enhanced initial accuracy in cold-start conditions, (ii) improved forecast stability through dynamic residual compensation, and (iii) structural adaptability facilitated by autonomous model transfer and retraining mechanisms.

These empirical results validate the DDPFF as a practically deployable solution for forecasting in volatile, data-scarce manufacturing environments. Its closed-loop architecture—integrating machine learning, statistical correction, and control-based adaptation—enhances both predictive accuracy and continuous model evolution. The framework provides substantial value for operational decision-making in the semiconductor sector and other high-mix, low-volume (HMLV) industries, where forecasting uncertainty remains a persistent challenge.

5. Practical Implications

The empirical findings of this study provide several actionable insights for operations managers, production planners, and supply chain professionals working in high-mix, low-volume (HMLV) manufacturing environments, especially those marked by frequent new product introductions and unpredictable demand patterns. The following five implications emphasize the practical value of the proposed Dynamic Dual-Phase Forecasting Framework (DDPFF).

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Cold-Start Forecasting with Minimal Data Requirement

One of the most persistent challenges in forecasting occurs during the early stages of a product’s lifecycle, when historical demand data are unavailable. The DDPFF framework tackles this cold-start problem by utilizing attribute-based product classification and similarity-weighted regression. This approach allows for the generation of reliable forecasts based solely on fundamental product attributes (e.g., form factor, material type), thereby decreasing the reliance on extensive historical datasets. This capability is particularly advantageous in fast-paced, innovation-driven environments, where the rapid deployment of forecasting systems is essential.

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Self-Monitoring and Adaptive Learning Capabilities

By incorporating run-chart-based statistical process control (SPC), the framework acquires real-time diagnostic capability. When deviations indicate structural misalignment or shifts in demand regimes, the system automatically initiates model reclassification and retraining, removing the necessity for manual monitoring. This closed-loop adaptation mechanism greatly alleviates the oversight burden on human planners and facilitates faster, more informed decision-making.

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Forecast Stabilization via Residual Compensation

In addition to enhancing initial accuracy, the framework includes an ARMA-based residual correction module that dynamically adjusts for autocorrelated forecast errors. This feature is particularly relevant in industries characterized by inherent demand volatility, as it offers short-term prediction stability and improves alignment between forecasted and actual demand trajectories. Practically, this leads to more accurate materials planning, lot-sizing, and a reduction in last-minute schedule changes.

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Integration Feasibility with Existing ERP/MES Systems

Due to its modular architecture and use of interpretable, lightweight models (e.g., XGBoost, ARMA), the DDPFF framework is designed to be compatible with existing Enterprise Resource Planning (ERP) and Manufacturing Execution Systems (MES). While full integration may require system-specific customization or middleware support, the framework’s low computational requirements and model transparency reduce the technical barriers typically faced by small and medium-sized enterprises (SMEs). This design facilitates practical implementation without the need for deep learning infrastructure or high-end computing resources, making it a viable option in data-scarce, resource-constrained environments.

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Enabler of Demand-Driven Production Strategy

Strategically, DDPFF supports the transition to demand-driven planning by facilitating more accurate and timely forecasts of new product demand. This enhances alignment between capacity planning, inventory allocation, and distribution scheduling, thereby reducing overproduction, minimizing inventory obsolescence, and improving responsiveness to market signals. In dynamic supply chains, such foresight is essential for achieving both agility and cost efficiency.

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Scalable and Resource-Efficient Deployment

The design of DDPFF emphasizes computational efficiency and scalability. Each module functions with near-linear time complexity relative to input size, and the overall forecast cycle, comprising classification, analog retrieval, and ARMA correction, can be executed in under two minutes on standard CPU hardware using a dataset of over 576 historical products. To reduce system load and align with practical constraints, the framework supports configurable update intervals (e.g., weekly or monthly), rather than relying on real-time model retraining. This flexibility ensures that DDPFF remains viable even in computationally constrained environments. Furthermore, lightweight, interpretable models, such as XGBoost and ARMA, have been demonstrated to enhance processing efficiency and facilitate integration in settings with limited IT infrastructure, including SMEs and hybrid on-premises/cloud deployments.

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Interpretability for Operational Decision Support

To enhance trust and transparency in practical operations, DDPFF is designed with interpretability in mind. The use of tree-based models such as XGBoost and Random Forest allows users to examine feature importance rankings, providing clear insights into which product attributes most influence demand classification and analog matching. Additionally, the residual monitoring mechanism based on run charts offers explainable decision logic for detecting structural drift. These characteristics empower operations managers and planners to understand the rationale behind forecasts, verify the appropriateness of model adaptations, and make informed decisions accordingly. Future work may explore integrating SHAP values or visual dashboards to further strengthen interpretability and user acceptance.

6. Conclusions

In light of the increasing complexity and uncertainty in demand forecasting for low-volume, high-variability manufacturing environments, this study proposes the Dynamic Dual-Phase Forecasting Framework (DDPFF) as a novel solution tailored to the forecasting challenges associated with new product introductions. The framework integrates three key components: an initialization forecasting module based on product classification and similarity-weighted regression, a residual compensation module using ARMA modeling for short-term correction, and a model transfer mechanism that monitors structural drift through statistical process control to trigger reclassification and retraining.

Empirical evaluation using five real-world cases from the semiconductor tray industry demonstrates that DDPFF consistently outperforms traditional ARIMA and similarity-based baselines across diverse demand scenarios, including cold-start, seasonality, customization, and structural shifts. On average, the framework achieved a 35.7% reduction in MAE and a 41.8% improvement in residual stability (SIR). In cases of initial misclassification, such as NP-03, the adaptive logic successfully realigned the model, restoring statistical control and predictive accuracy.

Practically, DDPFF offers a modular and lightweight architecture that can be integrated into ERP or MES systems without requiring deep learning infrastructure, making it viable for both small-scale and legacy manufacturing environments. Its ability to generate early forecasts, adjust to short-term deviations, and detect long-term drift supports agile, demand-driven decision-making.

Nonetheless, several limitations merit discussion. First, the framework’s reliance on product features for classification and analogy makes it sensitive to input noise or inconsistent attribute labeling. High-quality, standardized feature data are essential for optimal performance. Second, while the current implementation is computationally efficient, scaling the system to very large product catalogs or high-frequency settings may require improvements such as approximate nearest-neighbor search, parallel model execution, or incremental learning. Third, the rule-based drift detection mechanism, while interpretable and effective, may lack the flexibility to detect subtle or non-linear distributional changes. More advanced probabilistic approaches, such as Bayesian change-point detection, could improve adaptability.

Future work may explore the use of temporal deep learning architectures (e.g., TCNs, LSTM variants) to model long-range dependencies, and reinforcement learning to accelerate policy adaptation. Generalization to other domains—such as electronics, medical components, or service scheduling—would further establish the framework’s cross-industry applicability. Furthermore, extending the DDPFF framework to accommodate multi-echelon supply chains or more hierarchical manufacturing systems (e.g., tiered assembly lines or distributed logistics hubs) is an important research direction. Addressing challenges such as system integration complexity, real-time data latency, and model scalability across nodes will be essential in enabling widespread deployment in complex supply chain networks. Finally, developing an interactive dashboard for visualization and override control would support human-in-the-loop deployment and enhance industrial usability.

Importantly, the modular nature of DDPFF enables seamless integration of these future enhancements. For example, the rule-based SPC component can be replaced with a Bayesian or learning-based drift detection algorithm without altering the upstream forecast logic. Likewise, a temporal deep learning module may be introduced as a drop-in replacement for the analog regression layer in high-data settings. Visualization tools and dashboard interfaces can be added at the decision-support layer without modifying the model core. This design flexibility ensures the long-term extensibility of the framework while preserving interpretability and operational control.