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Peer Review Article | Open Access | Published 2 July 2026
Beyond Threshold Monitoring: A Bayesian and Time Series Framework for Predictive Contamination Control in Aseptic Manufacturing
Owasu Brown | EJPPS | 3102 (2026) | https://doi.org/10.37521/ejpps31204
Abstract
Contamination control in aseptic pharmaceutical manufacturing environments traditionally relied on predefined thresholds that trigger investigation only after regulatory limits are exceeded. However, recent regulatory findings indicate that such approaches are insufficient for detecting emerging contamination risks in ISO 5 cleanrooms and Restricted Access Barrier Systems (RABS). This study proposes a hybrid analytical framework that integrates time-series classification and Bayesian inference to enable predictive contamination detection and localization. Particle count data are modelled to follow a Poisson process, with heteroscedasticity in low-count regimes addressed using the Freeman–Tukey transformation. Temporal patterns are classified using shapelet-based models implemented in the sktime framework, enabling the identification of contamination mechanisms, including glove breaches, mechanical friction, and HVAC drift. Spatial localization is achieved using Bayesian search theory, updating posterior probabilities of contamination sources based on multi-sensor observations. A simulated case study demonstrates that the proposed framework reduces contamination detection latency by approximately 85% compared with traditional statistical process control (SPC) methods. The findings support a transition from reactive threshold monitoring to proactive, data-driven contamination control strategies aligned with evolving regulatory expectations.
Keywords: time series classification, Bayesian inference, predictive contamination control, sktime, Poisson process, environmental monitoring
Introduction
Aseptic processing for parenteral drugs is regulated to ensure product sterility. Viable and total particles are monitored in ISO 5/Class 100 environments to demonstrate and maintain process control. Despite substantial advances in sensor technology and data acquisition, the prevailing monitoring methods remain fundamentally reactive. Excursions are identified only after exceeding concentration thresholds, at which point a post-hoc investigation is initiated.
Recent regulatory actions issued by the United States Food and Drug Administration (FDA) and the European Medicines Agency (EMA) have documented recurring deficiencies in contamination control programs. These include failure to investigate transient particle excursions, inadequate identification of contamination sources, and systemic overreliance on pass/fail threshold criteria.
Such findings reveal a conceptual limitation: current systems treat contamination as a binary event rather than as a dynamic, spatially evolving signal that can be detected, characterized, and localized before a threshold is breached.
Contamination events in controlled environments are not random anomalies; rather, they are structured signals shaped by airflow dynamics, mechanical vibration profiles, and the physical characteristics of human intervention. Consequently, particle count time series contain latent temporal and spatial information that can be exploited for predictive analysis. The central research problem addressed in this study is the inability of threshold-based systems to interpret these signals before regulatory exceedance.
This study proposes a novel hybrid framework that integrates time-series classification and Bayesian inference to detect and localize contamination events in real time. By transforming raw particle data into discriminative temporal patterns and probabilistic spatial estimates, the framework enables a shift from threshold-triggered reaction to model-driven prediction. The approach is aligned with emerging regulatory expectations for scientifically justified contamination investigations and data integrity, and is designed to augment rather than replace existing environmental monitoring infrastructure.
Literature Review
Time series classification has emerged as a critical domain in machine learning, particularly for applications involving sequential, temporally dependent sensor data. Bagnall et al.¹ wrote a seminal paper titled "Great Time Series Classification Bake-off" that focuses on the challenges of time series. Bagnall et al.¹ demonstrate that no single algorithm consistently outperforms others across all datasets, and emphasize the importance of selecting models whose inductive bias aligns with data structure. This finding directly motivated the multi-archetype approach adopted in the present framework.
The development of the sktime unified interface provides a standardized, reproducible environment for implementing and comparing diverse time-series classifiers ². Shapelet-based methods are particularly relevant for detecting localized, discriminative subsequences within time series, making them well-suited to applications where temporal signatures correspond to underlying physical processes such as the rapid aerosol dispersion following a glove breach or the periodic vibration profile of a failing mechanical component.
In the context of cleanroom monitoring, particles entering the cleanroom follow the Poisson distribution. This assumption is codified in ISO 21501-4 ³ and supported by the Parenteral Drug Association Technical Report No. 13 ⁴, both of which treat particle arrivals as independent events occurring within fixed sampling intervals. A practical consequence of the Poisson assumption is the equality of mean and variance, which introduces heteroscedasticity that can degrade the performance of downstream machine learning models. The Freeman-Tukey variance-stabilizing transformation addresses this issue and is well-established in the count data literature.
Bayesian inference provides a complementary framework for probabilistic reasoning under uncertainty, particularly in spatial search problems. Stone⁵ introduced Bayesian search theory as a method for sequentially updating beliefs about location based on observed evidence, enabling efficient localization in uncertain environments. While widely applied in search-and-rescue operations and fault detection in industrial systems, its application to cleanroom contamination source localization has not previously been formalized. The present study addresses this gap.
Existing EM approaches primarily rely on statistical process control (SPC), which detects deviations from established control limits but does not incorporate temporal pattern recognition or probabilistic spatial reasoning. This limitation, the inability to distinguish mechanism type or infer source location before a breach occurs, motivates the integrated framework proposed in this paper.
Theoretical Framework
Stochastic Modelling of Particle Counts
Airborne particle counts in controlled environments follow the Poisson distribution. The probability of observing k particles within a sampling interval, given an expected rate parameter λ, is:
P(k; λ) = (λᵏ · e⁻λ) / k! (Equation 1)
where λ represents the expected baseline particle count under normal operating conditions. This formulation reflects the discrete, event-driven, and non-negative nature of particle arrivals. A fundamental property of the Poisson distribution is that its variance equals its mean (Var[X] = λ),
introducing heteroscedasticity across different operating regimes that can adversely affect machine learning model performance.
To stabilize variance across low-count regimes, the Freeman-Tukey transformation is applied to the raw count data x:
y = √x + √(x + 1) (Equation 2)
This transformation has the asymptotic property of stabilizing the variance to approximately 1 regardless of the underlying Poisson rate, thereby improving the comparability of time series segments across sensors and sampling windows and enhancing classifier performance.
Time Series Classification
Shapelet-based classifiers identify discriminative subsequences, shapelets, within time series that are maximally predictive of class membership. The dissimilarity between a candidate shapelet S of length l and a time series T of length n is defined as the minimum Euclidean distance over all positions:
D(S, T) = min₁≤t≤n-l+1 √( Σᵢ₌₁ˡ (Sᵢ − T_{t+i-1})² ) (Equation 3)
The ShapeletTransformClassifier, implemented within the sktime framework, identifies the top K shapelets from the training data and transforms each time series into a feature vector of shapelet distances, which is then passed to a downstream classifier (a Random Forest in this implementation). This two-stage pipeline decouples temporal pattern extraction from classification, enabling interpretable feature attribution.
Three contamination archetypes are distinguished by their temporal signatures, each reflecting an underlying physical mechanism:
• Glove breach: characterized by a sharp-onset, exponentially decaying spike corresponding to aerosol dispersal following barrier compromise.
• Mechanical friction: characterized by a periodic oscillatory pattern whose frequency corresponds to equipment RPM (motor or starwheel rotation).
• HVAC drift: characterized by a gradual, monotonic baseline elevation reflecting progressive filter degradation or airflow disruption.
Bayesian Inference for Spatial Localization
The RABS environment is discretized into a set of n spatial cells {C₁, C₂, …, Cₙ}, each representing a candidate contamination source location. Prior probabilities P(Cᵢ) are initialized uniformly or, where available, informed by domain knowledge such as airflow velocity maps or historical excursion records.
Upon receiving a sensor observation D, the posterior probability that cell i is the contamination source is updated via Bayes' theorem:
P(Cᵢ | Data) = P(Data | Cᵢ) · P(Cᵢ) / Σⱼ₌₁ⁿ P(Data | Cⱼ) · P(Cⱼ) (Equation 4)
The likelihood term P(Data | Cᵢ) is computed from the transformed sensor readings, incorporating both positive observations (elevated counts at proximal sensors) and negative evidence (unperturbed baseline counts at distal sensors). This integration of negative search information, akin to Stone's Bayesian search-and-rescue framework, is a key feature of the spatial engine, enabling rapid pruning of the source probability space⁵.
Successive sensor observations progressively concentrate posterior probability mass over the true source location.
Methodology
Synthetic Data Generation
Due to the proprietary and commercially sensitive nature of real-world cleanroom sensor data, a simulated dataset was developed to replicate particle-count behaviour in an aseptic RABS environment. The simulation was implemented in Python using a reproducible random seed (NumPy Generator, seed= 42), and the full workflow is provided as Appendix A. Critically, the simulation was not designed as an abstract exercise; each contamination archetype and its corresponding signal function was informed by published empirical descriptions of real contamination mechanisms reported in cleanroom and aseptic-processing literature. This approach is consistent with established practice in pharmaceutical engineering research when facility-specific data cannot be disclosed, and the fidelity of each archetype to its physical referent is documented with explicit citations to the primary literature.
The simulation models six spatially distributed sensors positioned along a production line. Particle counts are generated as Poisson-distributed random variables with a low baseline rate λ ∈ [1.0, 3.0] particles per sampling interval, consistent with ISO 5 environmental conditions. A total of 180 contamination events were simulated across three equally distributed mechanism classes, yielding 60 replicates per class. Each event comprises 60 time steps, with event onset occurring at a randomly assigned time step within ⁸,¹⁶.
Spatial propagation of contamination was modelled using an exponential distance-decay function:
w(d) = exp(−d / α) (Equation 5)
where d denotes the integer distance (in sensor units) between the source cell and the receiving sensor, and α ∈ [0.7, 1.3] is a per-event airflow decay parameter sampled uniformly to introduce variability. Source strength was additionally modulated by a factor drawn from U(0.9, 1.2).
The three contamination mechanisms were encoded as deterministic signal functions added to the Poisson baseline:
Glove breach: f(t) = 18 · exp(−0.10t), representing rapid aerosol release with exponential decay. This functional form is grounded in empirical studies of personnel-introduced aerosol dispersal in controlled environments. Whyte and Hejab quantified particle emission rates from personnel under differing garment and airflow conditions and demonstrated that motion-induced releases produce sharp, transient spikes followed by exponential recovery under unidirectional airflow. Whyte and Bailey’s garment leakage studies confirm the same spike-and-decay morphology, and the ISO 14644-3 recovery test formalises the observation by mandating measurement of the exponential decay constant following a controlled particle challenge as a standard cleanroom characterisation procedure. The decay constant range of 0.08–0.15 per sampling interval used here is consistent with these empirical characterisations, and the amplitude of 18 particles per interval above baseline was selected to represent a localized particle excursion consistent with the magnitude of near-source particulate increases described in PDA Technical Report No. 13 (Revised) and related cleanroom monitoring literature.
Mechanical friction: f(t) = 6 + 4 sin(2πt/8) + 2 sin(2πt/4), representing a periodic dual-frequency oscillation. The oscillatory morphology reflects the established behaviour of worn or misaligned rotating components in aseptic fill-finish equipment. Stewart’s analysis of particle monitoring locations for fill-finish processes explicitly identifies starwheels, bearings, and seals as recognised cyclic particle-generating components in Grade A environments, and notes that equipment friction is an established contributor to periodic particle generation. Abiyeva et al.’s CFD modelling of equipment-induced airflow perturbations confirms oscillatory fluctuations in particle concentration synchronised with mechanical cycles. Long et al., in their study of robotic gloveless isolators with continuous particle counter monitoring, demonstrated that specific mechanical operations produce distinct and repeatable temporal signatures at frequencies tied to equipment rotation rate. The dual-frequency model captures both the fundamental rotation frequency and its first harmonic, and the amplitude parameters are calibrated to represent sub-threshold, pre-exceedance friction events of the type documented in these studies.
HVAC drift: f(t) = 0.20t, representing a linear baseline ramp. The monotonic, gradual elevation pattern characterising HVAC drift is consistent with published empirical and computational studies of progressive airflow degradation in ISO-classified environments. Li et al. demonstrated that changes in return-air configuration and airflow velocity produce slow, progressive shifts in particle distribution in cleanrooms, and Prado and Dyrness documented baseline elevation using CFD when airflow patterns deteriorate below design performance. Both EN 17141 and ISO 14698 identify HVAC instability as a systemic contamination mechanism with slow-onset characteristics. A linear approximation is appropriate over the 60-step observation window used in this study, as non-linear degradation dynamics operate on timescales of hours to days; within any single monitoring window the local trajectory is well described by a linear ramp. The slope parameter of 0.20 particles per interval was selected to produce a detectable trend prior to SPC threshold exceedance at step 60, consistent with the sub-exceedance drift profiles documented in these studies and in EU GMP Annex 1 contamination investigations. This value was chosen such that cumulative particle elevation remained below the SPC exceedance threshold for a substantial portion of the monitoring window, thereby representing the gradual deterioration scenarios described in Annex 1 contamination investigations.
Freeman-Tukey transformed counts were stored alongside raw particle counts to support direct comparison with threshold-based monitoring (see Appendix A for the full data schema). Taken together, these three archetypes span the principal categories of contamination event documented in regulatory inspection findings and PDA technical guidance: rapid personnel-introduced particulate events, equipment-driven periodic contamination, and environmental control system degradation. The signal functions have been parameterised to produce time-series morphologies that are physically interpretable and consistent with published empirical descriptions of each event type, providing a principled and transparent basis for training and evaluating the proposed classification framework in the absence of disclosable facility data. Future work should validate the framework prospectively against known-cause excursion records in a live cleanroom environment, as noted in the Limitations section.
Simulation validation was performed through face-validity and literature-consistency assessment rather than direct fitting to proprietary manufacturing datasets. The objective was not to reproduce a specific facility or contamination excursion record, but to generate contamination signatures whose temporal morphology, spatial propagation characteristics, and relative magnitudes were consistent with published descriptions of personnel-generated particle releases, equipment-associated particulate generation, and airflow degradation events reported in the cleanroom literature. Accordingly, the synthetic dataset should be interpreted as a mechanistically informed research dataset suitable for proof-of-concept evaluation of the proposed analytical framework rather than as a surrogate for facility-specific environmental monitoring data.
Preprocessing
Raw particle counts were transformed using the Freeman-Tukey transformation (Equation 2) prior to model training and evaluation. This step ensures that low-count fluctuations are preserved without being dominated by high-amplitude excursions and removes the mean-variance relationship inherent to Poisson data. No additional normalization was applied at this stage.
Temporal Classification Model
Time series classification was performed using the ShapeletTransformClassifier from the sktime library (v0.16+), with a Random Forest (100 estimators) as the base learner. The maximum number of candidate shapelets was set to 50, and a one-minute time contract was applied to bound computation during shapelet selection. The classifier was trained on the Freeman-Tukey-transformed sensor traces from the sensor closest to the contamination source, using a stratified 80:20 train-test split.
Spatial Localization Model
Following the temporal classification, Bayesian inference (Equation 4) was applied to estimate the most probable location of the contamination source. The four candidate source positions used in simulation were treated as spatial cells, and prior probabilities were initialized uniformly (P(Cᵢ) = 0.25). Likelihoods were computed from the Freeman-Tukey transformed sensor readings at each time step, conditioned on the expected spatial attenuation profile for each candidate source location.
The posterior distribution was updated sequentially at each time step following event onset, and source identification was declared when the maximum posterior probability exceeded a pre-specified stopping threshold of 0.85.
Baseline Comparison and Evaluation
The proposed framework was benchmarked against a threshold-based SPC approach, which flags an event when any sensor count equals or exceeds a fixed limit of 20 particles per interval, approximately six times the maximum baseline rate, consistent with the proportional scale of a regulatory exceedance in this simulation context.
Performance was evaluated using the following metrics:
Classification accuracy and macro-averaged F1 score (temporal engine).
Detection latency: time steps elapsed from event onset to model alert.
Localization accuracy: rank of the true source cell in the posterior probability distribution at the time of stopping.
Results
Temporal Pattern Classification
Figure 1 illustrates representative Freeman–Tukey-transformed sensor traces for each of the three contamination mechanisms. The distinct temporal morphologies are visually separable: the glove breach trace exhibits a sharp initial peak followed by monotonic exponential decay; the mechanical friction trace presents a regular sinusoidal oscillation; and the HVAC drift trace shows a gradual, sustained ramp with no abrupt onset.
The ShapeletTransformClassifier achieved high classification accuracy across all three contamination classes. Macro-averaged F1 scores exceeded 0.90 across test replications, indicating that the learned shapelets successfully capture the discriminative temporal structure of each mechanism. Of note, the shapelet distance transform (Equation 3) proved particularly effective at distinguishing between glove breach and HVAC drift, two classes that share monotonic directionality but differ substantially in onset sharpness and duration.
Spatial Localization
Figure 2 presents the posterior probability distribution across candidate source cells for a representative glove breach event. Following event onset, the posterior mass rapidly concentrates over the true source location, with all remaining cells assigned negligible probability within ten-time steps. The 0.85 stopping threshold was consistently reached prior to the SPC threshold breach, confirming that Bayesian localization enables actionable source attribution in real time. In simulation, this mechanism reduced the effective search space from the full RABS footprint to a 20 cm target zone within seconds of event onset.
The integration of negative evidence from distal sensors, sensors recording counts consistent with an undisturbed baseline, was critical to posterior concentration. Without this information, posterior updates were dominated solely by the elevated counts at the proximal sensor, slowing convergence. Incorporating unperturbed readings as probabilistic evidence of source absence accelerated localization by approximately 35% in simulated trials⁵.
Detection Performance
Figure 3 presents cumulative detection curves comparing the threshold-based SPC approach with the proposed model-based framework across all 180 simulated events. The SPC baseline detected contamination events exclusively at or after threshold exceedance; for HVAC drift events, where the ramp is gradual, threshold breach occurred late in the observation window or not at all within the 60-step horizon.
By contrast, the proposed framework detected contamination events substantially earlier, achieving a mean detection latency of approximately 2.2 time steps following event onset, compared to a mean of 14.5 steps for SPC. This represents an approximate 85% reduction in detection latency. Detection was consistent across all three contamination classes, including HVAC drift, which the SPC baseline frequently failed to flag within the simulation window.
Table 1. Comparative performance of threshold-based SPC and the proposed hybrid framework.
Metric | SPC Baseline | Proposed Framework |
Mean detection latency (steps) | 14.5 | 2.2 |
Detection latency reduction | — | ~85% |
Macro-averaged F1 score | N/A (binary) | >0.90 |
HVAC drift detection (within 60 steps) | Inconsistent | Consistent |
Source localisation | Not supported | Top-1 rank (>0.85 posterior) |
Discussion
The results demonstrate that threshold-based SPC fails to leverage the rich temporal and spatial information embedded in particle count time series. This is not a deficiency in the sensor technology but in the analytical framework used to interpret the data. The proposed hybrid model treats contamination as a dynamic signal rather than a binary event, enabling earlier detection, mechanism attribution, and spatial localization within a unified pipeline.
The effectiveness of shapelet-based classification indicates that contamination events exhibit consistent and learnable temporal signatures. The ShapeletTransformClassifier's inductive bias toward localized discriminative subsequences aligns naturally with the physical characteristics of contamination mechanisms, brief aerosol bursts, periodic mechanical vibration, and slow HVAC degradation, each producing stereotyped waveforms that are stable across simulation replicates. This consistency suggests that a trained classifier could generalize from a library of known-cause events to novel excursions in production environments.
The Bayesian spatial engine provides an important complementary function. It answers not only what happened but where. The use of negative evidence from unperturbed sensors, formalized through the Bayesian likelihood update in Equation 4, substantially accelerates posterior convergence. This mirrors Stone's optimal search framework, in which the absence of evidence in a searched region is itself informative⁵. In practical terms, this means that even sensors that record normal readings are contributing to source localization, transforming the entire sensor network into an active investigative tool rather than a passive alarm system.
From a regulatory perspective, the proposed framework is well-positioned to support evolving requirements for proactive contamination control and scientifically grounded investigations. The ability to detect and classify events prior to threshold exceedance, and to produce a probabilistic source attribution alongside the classification, provides a documented, reproducible audit trail that is difficult to achieve with conventional SPC approaches. This aligns with the data integrity and investigation quality expectations articulated in EU GMP Annex 1 ⁶ and FDA process validation guidance ⁷.
Several limitations of the present study should be acknowledged. First, although the contamination archetypes were informed by published cleanroom and aseptic-processing literature, the dataset remains synthetic and was not calibrated against proprietary facility-specific environmental monitoring records. Consequently, the reported performance should be interpreted as a proof-of-concept demonstration of the analytical framework rather than a validated estimate of performance in production environments. Prospective evaluation using known-cause excursion records from commercial manufacturing facilities will be required before routine operational deployment.
Conclusion
This study presents a novel hybrid framework for predictive contamination control in aseptic manufacturing, integrating Poisson-based stochastic modelling, Freeman-Tukey variance stabilization, shapelet-based time series classification, and Bayesian spatial inference within a unified analytical pipeline. The simulation results demonstrate that contamination events can be detected and localized substantially earlier than with traditional threshold-based monitoring, achieving an approximately 85% reduction in detection latency and enabling mechanism-specific attribution prior to regulatory exceedance.
The transition from reactive threshold monitoring to predictive contamination intelligence does not require replacing existing sensor infrastructure but rather augmenting it with principled data science. The framework proposed here provides a methodologically rigorous, computationally tractable, and regulatory-aligned foundation for this transition. Implementation priorities for industry should include the construction of facility-specific contamination signature libraries, integration of airflow velocity data into the Bayesian spatial prior, and prospective validation against known-cause excursion records.
References
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2 Löning M, Bagnall A, Ganesh S, Kazakov V, Lines J, Király FJ. sktime: a unified interface for machine learning with time series. arXiv 2019; 1909.07872
3 International Organization for Standardization. ISO 21501-4: determination of particle size distribution light interaction methods Part 4: light scattering airborne particle counter for clean spaces. ISO 2018
4 Parenteral Drug Association. Technical Report No. 13 (Revised): fundamentals of an environmental monitoring program. PDA 2014
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6 European Medicines Agency / European Commission. EU guidelines for good manufacturing practice for medicinal products for human and veterinary use, Annex 1: manufacture of sterile medicinal products. EMA 2022
7 US Food and Drug Administration. Sterile drug products produced by aseptic processing — current good manufacturing practice. FDA 2004
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10 International Organization for Standardization. ISO 14644-3: cleanrooms and associated controlled environments — Part 3: test methods. Recovery test, Section B.5. ISO 2019
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Appendix A: Synthetic Dataset and Reproducible Simulation Workflow
The simulation was implemented in Python 3.11 and generates two output files: synthetic_rabs_particle_dataset.csv (one row per sensor, per time step, per event) and synthetic_rabs_event_summary.csv (one row per event for stratified train/test splitting). The full annotated notebook is provided at the GitHub Repository.
Table A1. Data dictionary for synthetic_rabs_particle_dataset.csv.
Field | Description |
event_id | Unique contamination event identifier (integer, 1–180) |
event_type | Contamination mechanism class: GloveBreach | MechanicalFriction | HVACDrift |
source_location | Simulated source sensor cell (integer, 1–4) |
sensor_id | Sensor identifier (integer, 0–5) |
time_step | Sequential observation index within event (integer, 0–59) |
baseline_lambda | Baseline Poisson rate λ ~ U(1.0, 3.0) |
event_start | Time index of contamination onset ~ U(8, 16) |
airflow_decay | Spatial attenuation parameter α ~ U(0.7, 1.3) |
source_strength | Contamination amplitude modifier ~ U(0.9, 1.2) |
distance_from_source | Integer distance from source to sensor |
spatial_weight | Exponential decay factor w(d) = exp(−d / α) |
particle_count | Observed Poisson-distributed particle count |
freeman_tukey | Variance-stabilised transformed count (Equation 2) |
Author
Corresponding Author: Owasu Brown, National University
Email: o.brown7025@student.nu.edu