PriMa-Causa: Causal Prescriptive Maintenance

Felix Saretzky

cs.LGOct 22, 2026

PriMa-Causa: Causal Prescriptive Maintenance

Authors: Felix Saretzky

Abstract

Automated manufacturing requires data-driven decisions under uncertainty and sparse observational records, and unplanned downtime is a dominant cost of getting them wrong. Prescriptive maintenance recommends a maintenance action against an impending failure rather than merely predicting it. Established reference architectures couple predictive models with rule- or optimisation-based recommendation logic. Selecting a corrective action, however, requires an interventional quantity: how the line behaviour would change if the action were set. Manufacturing data is observational, so a model fitted to predict the outcome estimates an associational quantity and may misdirect the choice of action without the prediction error revealing it. Causal estimators target the interventional quantity but require an expert-led causal study per case, for which the bounded decision window of operation leaves no room. This dissertation analyses how causal reasoning can be embedded into prescriptive maintenance so that actions are ranked by their estimated interventional effect. The result is PriMa-Causa, built from three components: a causal reasoning layer that integrates the estimate into the PriMa reference model, a parametric simulator that supplies the interventional ground truth absent from manufacturing data, and a graph-conditioned tabular causal foundation model that, pre-trained once on this synthetic production-line prior, answers interventional queries in a single forward pass. PriMa-Causa attains a lower prescription error than associational baselines, with the largest margin under weak overlap and sparse context, and a partially disclosed causal graph reduces this error further. The causal inductive bias of the synthetic prior and the graph conditioning can thus replace per-case estimator fitting, a step toward automating causal inference for autonomous and self-healing maintenance.

Figures & tables

Symbol	Meaning
Process variables and sets
$\mathbf{V}=\{V_{1},\dots,V_{n}\}$	Endogenous process variables of the production system.
$T\in\mathbf{V}$	Intervention target (the variable set by $\dop(T{=}t)$ ).
$t$	Intervention level assigned to $T$ .
$Y\in\mathbf{V}$	Decision-relevant outcome variable, typically a recovery- or quality-related key performance indicator such as MTTR .
$\mathcal{Y}^{\star}\subseteq\mathrm{range}(Y)$	Desired outcome regime of $Y$ , a set of outcome values.

Table 1

Abbildung 2 : Isometric view of a multi-station high-speed FMCG production line and its sensor layer.

Abbildung 3 : Techno-commercial and technical-scientific objectives of the dissertation.

Abbildung 4 : Simplified causal graph of one station, with context

\{\vartheta,b\}

, corrective action

T

, in-line mediator

h

, and seal-quality outcome

Y

Abbildung 5 : True responses under

\dop(T{=}0)

and

\dop(T{=}1)

(dotted) and their random-forest estimates (solid), on data simulated from the structure of Figure 4 .

RQ	Focus	Research gaps	Design objectives	Addressed in
RQ1	design	RG1, RG4	DO1, DO4	Ch. 4
RQ2	instantiation	RG2, RG3	DO2, DO3	Ch. 5 , Ch. 6
RQ3	evaluation	RG2, RG3	DO2, DO3	Ch. 7 , Ch. 8

Tabelle 1 : Mapping of the research gaps of Chapter 3 and the design objectives of Chapter 4 to the three research questions and the chapters that address them.

Abbildung 6 : Derivation from research gaps to design principles, with the research questions posed from the gaps.

Abbildung 7 : Relation of the three contributions to the research questions and to the four research gaps that jointly motivate them.

Abbildung 2 : Illustration of standard machine learning (left) and structural causal modelling (right) as two representations of a data-generating process.

#	Layer (Formalism)	Activity	Typical Question	PsM Example
1	Association $P(y\mid x)$	Seeing	What is? How does $X$ change the belief in $Y$ ?	Does elevated process temperature predict a higher seal-defect rate?
2	Intervention $P(y\mid\dop(x),z)$	Doing	What if? What happens if $X$ is set?	Will recalibrating the sealing station reduce the seal-defect rate?
3	Counterfactual $P(y_{x}\mid x^{\prime},y^{\prime})$	Imagining	Why? Was it $X$ that caused $Y$ ?	Had the sealing station been recalibrated, would this stop still have occurred?

Tabelle 1 : The three layers of the Pearl causal hierarchy [ 19 ] , adapted from [ 20 ] .

Abbildung 3 : Roles of a process variable relative to an action

T

and an outcome

Y

: (a) confounder, (b) mediator, (c) collider, and (d) unobserved confounder.

Abbildung 2 : Cluster plot of PsM research studies in the PC1–PC2 space, coloured by cluster assignment resulting from the hierarchical clustering on the first three principal components. Adapted from [ 15 ] .

Abbildung 3 : Schematic data-support gap under manufacturing production-line conditions.

Symbol	Meaning
Variables and queries
$\mathbf{V}=\{V_{1},\dots,V_{n}\}$	Endogenous process variables.
$T\in\mathbf{V}$ , $t$	Intervention target and intervention level.
$Y\in\mathbf{V}$ , $\mathcal{Y}^{\star}\subseteq\mathrm{range}(Y)$	Outcome variable (such as MTTR ) and desired outcome regime.
$\mathcal{Y}_{\mathrm{cand}}\subseteq\mathbf{V}\setminus\{T\}$	Mode-2 candidate-outcome set.
$X\subseteq\mathbf{V}\setminus\{T,Y\}$ , $x$	Pre-intervention decision-time context and its observed realisation.

Tabelle 1 : Notation used in Chapter 4 .

Abbildung 2 : Operational PsM structure according to the body of knowledge.

Abbildung 3 : Operational PriMa-Causa structure with the inserted causal reasoning layer.

Abbildung 4 : The translation of a maintenance-related operational challenge into a mathematical formalisation of actions, and the resulting retranslation into a comprehensible operational action.

Type	Description	Manufacturing example
Hard (atomic)	$T_{j}$ is set to a fixed value.	Fix process temperature to $85.0\,^{\circ}\mathrm{C}$ .
Stochastic	$T_{j}$ is drawn from a fixed distribution.	Sample process temperature from $\mathcal{N}(85.0,\,0.5^{2})\,^{\circ}\mathrm{C}$ .
Conditional	$T_{j}$ is set as a function of the observed context.	Set process temperature to $85.0+0.05\,v\;^{\circ}\mathrm{C}$ , where $v$ is line speed.

Tabelle 2 : Intervention types represented by candidate actions

a_{j}=(T_{j},t_{j})

Abbildung 5 : Operational horizon for MTTR reduction through PriMa-Causa.

ID	Source	Design objective
DO1	RG1	Introduce causal inductive bias as a structural component of the prescriptive-maintenance framework rather than as an after-the-fact correction on a predictive output.
DO2	RG2	Provide an end-to-end methodology that connects predictive triggers, causal reasoning, and validated interventional recommendations under explicit identification conditions and across multiple evaluation regimes.
DO3	RG3	Operate under the data and knowledge regimes characteristic of FMCG manufacturing.
DO4	RG4	Integrate root-cause evidence with action selection while preserving the analytical separation between causal diagnosis, candidate-action generation, and prescriptive recommendation.

Tabelle 3 : Design objectives of PriMa-Causa, derived from the research gaps of Chapter 3 .

ID	Source	Meta-requirement
MR1	DO1	Insert a causal reasoning layer between the predictive-analytics layer and the bridge (Figure 3 ) such that the four PriMa layers remain structurally intact.
MR2	DO1, DO2	Classify each case into a decision mode $M\in\{\mathrm{M1},\mathrm{M2},\mathrm{M3},\mathrm{M4}\}$ based on the descriptors $T_{c},Y_{c}\in\mathbf{V}\cup\{\bot\}$ , carrying the structural completeness $\mathcal{K}_{\mathrm{op}}$ forward in the case frame (Subsection 2 ).
MR3	DO1, DO2	Specify each prescriptive query through the tuple $(T,t,X,Y)$ and a decision objective, with $T\in\mathbf{V}$ as the intervention target, $t$ as the intervention level, $X$ as pre-intervention context, and $Y$ as the recovery- or quality-oriented outcome.
MR4	DO1	Justify each recommendation through an interventional quantity of the form $P(Y\mid\dop(T{=}t),X{=}x)$ derived from the mode-specific target $Q_{M}$ , rather than through an associational predictive score.
MR5	DO1, DO3	Operationalise prior knowledge $\mathcal{K}$ through the constraint map $\Phi_{\mathcal{K}}(x)=(\mathcal{G}_{\mathcal{K}},\mathcal{A}_{\mathcal{K}}(x),r_{\mathcal{K}},\mathcal{I}_{\mathcal{K}})$ , with the structural completeness $\mathcal{K}_{\mathrm{op}}\in\{\mathrm{none},\mathrm{ordered},\mathrm{complete}\}$ explicit at decision time.
MR6	DO3	Remain usable under data-sparse manufacturing conditions, including missingness, measurement error, non-stationarity, closed-loop control, and partially observed causal structure (Subsection 4 ).

Tabelle 4 : Meta-requirements for PriMa-Causa, derived from the design objectives of Subsection 1 .

Principle	Specification
DP1. Separate diagnosis from prescription	Aim. Preserve the analytical separation between root-cause identification and action selection. Context. Mode-3 cases that begin with an observed deviation in $Y$ and an unknown intervention target. Mechanism. Diagnostic evidence enters only as a restriction on $\mathcal{A}_{\mathcal{K}}(x)$ . The prescription $\rho_{c}$ is derived from $P(Y\mid\dop(T_{j}{=}t_{j}),X{=}x)$ , not from the diagnostic score directly. Rationale. Conflating diagnosis and prescription leaves recommendations structurally unjustified (DO4). Sources. MR4, MR9, MR10.
DP2. Restrict intervention targets to intervenable variables	Aim. Avoid prescribing on variables that cannot be changed through maintenance, control, or operator action. Context. All modes involving action selection (Modes 1, 2, and 3). Mechanism. The role map $r_{\mathcal{K}}:\mathbf{V}\to\mathcal{R}_{\mathrm{role}}$ assigns each variable an intervention-target, context, outcome, post-intervention-descendant, or excluded label. Only variables labelled as intervention target enter $\mathcal{A}_{\mathcal{K}}(x)$ . Rationale. The operator $\dop(T_{j}{=}t_{j})$ is formally defined irrespective of physical manipulability [ 19 ] . A prescriptive recommendation, however, is executable only if $T_{j}$ corresponds to a controllable degree of freedom. A variable that cannot be set through maintenance, control, or operator action yields a recommendation that cannot be carried out, so non-actuatable variables and observed outcomes are excluded from the candidate target set. Sources. MR3, MR5, MR10.
DP3. Resolve reverse questions through forward intervention logic	Aim. Convert reverse causal questions into actionable forward queries. Context. Mode 3, where the intervention target is unspecified at decision time. Mechanism. The reverse question is reframed as a finite set of forward queries $P(Y\in\mathcal{Y}^{\star}\mid\dop(T_{j}{=}t_{j}),X{=}x)$ over $\mathcal{A}_{\mathcal{K}}(x)$ , with $X$ restricted to pre-intervention decision context. Rationale. Reverse causal questions rarely admit a unique answer [ 89 ] . Forward $\dop$ -queries yield comparable, rank-able fix-condition evidence, trading explanatory completeness about the origin of the deviation for decision-relevant comparability among the available candidate actions. Sources. MR2, MR3, MR4.
DP4. Operationalise prior knowledge	Aim. Move manufacturing knowledge from informal background to machine-usable inductive bias. Context. All decision modes and all CRL blocks, parametrised by the structural completeness $\mathcal{K}_{\mathrm{op}}$ . Mechanism. The constraint map $\Phi_{\mathcal{K}}(x)$ binds graph search, candidate actions, variable-role assignment, and identification constraints into a single object available at each CRL block. Rationale. Knowledge constrains PriMa-Causa only once it is encoded in machine-usable form. Informal expertise alone does not justify causal identification. Sources. MR5.
DP5. Make uncertainty decision-relevant	Aim. Couple recommendation behaviour to the uncertainty of the underlying evidence. Context. The robust recommendation synthesis block of the CRL (Section 5 ), regardless of mode. Mechanism. The recommendation object $\rho_{c}$ carries a recommendation status ( recommend , return alternatives , abstain , escalate ) jointly with the qualified scores $s_{c}$ and their uncertainty diagnostics. Rationale. Uncertainty reported only as an auxiliary statistic does not change the recommended action and therefore does not lower the decision risk. Coupling the recommendation status to the uncertainty of the estimate makes the diagnostic operationally consequential. Sources. MR11.
DP6. Optimise under operational constraints	Aim. Align causal effectiveness with operational feasibility. Context. Ranking within the robust recommendation synthesis block, whenever candidate actions differ in operational cost, feasibility, or risk, including, but not limited to, ties in interventional outcome. Mechanism. The qualified scores $s_{c}$ attached to each candidate action $a_{j}\in\mathcal{A}_{\mathcal{K}}(x)$ combine the interventional estimate $P(Y\mid\dop(T_{j}{=}t_{j}),X{=}x)$ with cost, downtime budget, safety, production-planning, and implementation-latency constraints. Rationale. A causally effective action is not automatically the preferred action under plant constraints. Sources. MR12.

Tabelle 5 : Design principles of PriMa-Causa, specified in the schema [ 18 ] .

Step	Purpose	Standards and guidelines
Detect	Detect deviations in quality-related key performance indicators (such as scrap rate, rework rate, first-pass yield, or OEE ).	ISO 22400-2 [ 94 ] ; ISO 11462 [ 95 ] ; ISO 7870 [ 96 , 97 ]
Contain	Isolate affected products, batches, or process segments to limit immediate impact.	ISO 9001:2026, cl. 8.7 [ 98 ]
Localise	Identify the affected station, machine, product variant, shift, material batch, or process window.	ISO 11462 [ 95 ] ; ISO 7870 [ 96 , 97 ] ; ISA 95 / IEC 62264 [ 99 ]
Diagnose	Identify the failure mode and most plausible root cause of the quality deviation.	IEC 62740 [ 100 ] ; IEC 60812 [ 101 ] ; IEC 61025 [ 102 ]
Decide / Prescribe	Select a corrective intervention based on the diagnosed cause and expected effect on the key performance indicator.	ISO 9001:2026, cl. 10.2 [ 98 ]
Fix and Verify	Implement the corrective action and verify recovery of the quality-related key performance indicator.	DIN 31051 [ 103 ] ; DIN EN 13306 [ 104 ] ; ISO 9001:2026, cl. 10.2 [ 98 ]

Tabelle 6 : Standard-oriented troubleshooting process for quality problems in production lines.

Abbildung 6 : Prescriptive case framing.

Abbildung 7 : Causal study design.

Abbildung 8 : Digital Intervention Experiments.

Abbildung 9 : Estimation.

Abbildung 10 : Intervention hypotheses and in-silico evaluation, adapted from [ 90 , 91 ] .

Abbildung 11 : Robust recommendation synthesis.

Abbildung 12 : Connected pipeline of the Causal Reasoning Layer.

Abbildung 13 : Scope and resolution boundary of PriMa-Causa.

Abbildung 2 : Operating conditions (a) to (f) of observational manufacturing data that constrain causal estimation and its validation.

Abbildung 3 : A sampled CPG instance with

n=20

and

K=3

(top) and its station backbone (bottom).

Abbildung 4 : Spectral-distance contrast

\widehat{D}_{1}

between CPG and density-matched Erdős–Rényi skeletons. Each panel shows the distance computed from one spectrum: the combinatorial-Laplacian spectrum

\lambda^{\mathbf{L}}

, the normalized-Laplacian spectrum

\lambda^{\boldsymbol{\mathcal{L}}}

, and the adjacency spectrum

\lambda^{\mathbf{A}}

Abbildung 5 : Per-index difference

\lambda_{k}^{\mathrm{CPG}}-\lambda_{k}^{\mathrm{ER}}

along the sorted adjacency spectrum (blue, with median and interquartile band) against the within-null band (grey).

Abbildung 6 : Data generation at one CPG node: the mixed-type parents feed the sampled mechanism

m_{i}

, and zero-mean mixture noise

U_{i}

is added.

Abbildung 7 : Observational and interventional samples of three process variables from an illustrative linear SCM .

Abbildung 8 : t-SNE embedding of the profile vectors

\varphi

of CPG and Erdős–Rényi instances and of the real production-line reference.

Abbildung 9 : UMAP embeddings of the sample rows of nine independent generator draws.

Abbildung 10 : Varsortability over

200

sampled SCM instances at

n=98

: naive additive-noise mechanism (left), proposed mechanisms (centre), and Erdős–Rényi reference (right).

Dataset	Domain	$N_{\mathrm{host}}$	$F$	Provenance
AI4I [ 117 ]	discrete manufacturing, predictive maintenance	10,000	6	synthetic
CBM [ 118 ]	naval gas-turbine propulsion, condition monitoring	11,934	14	calibrated simulator
Hydraulic [ 119 ]	hydraulic test rig, condition monitoring	2,205	17	real (test rig)
SECOM [ 120 ]	semiconductor manufacturing, process control	1,567	30	real (production line)
Steel [ 121 ]	steel-plate fault inspection	1,941	25	real (inspection)

Tabelle 1 : The five host datasets and their covariate provenance.

Rung	model.trt	overlap.trt	model.rsp	alignment	te.hetero
R1_easy	linear	full	linear	0.75	none
R2_mild	polynomial	full	linear	0.75	none
R3_hard	polynomial	one-term	exponential	0.25	none
R4_severe	polynomial	one-term	exponential	0.25	high

Tabelle 2 : The difficulty ladder. Each rung fixes a joint setting of the generator parameters of Equations ( 9 ) and ( 10 ).

Abbildung 2 : Illustration of per-task specialist competence (left) and amortised competence across the task prior (right).

Abbildung 3 : The three-valued ancestor encoding of one sampled CPG at the three structural-completeness levels.

Abbildung 4 : Assembly of one pre-training task: a structural causal model sampled from the CPG prior supplies the observational context and, under

\dop(T{=}t)

, the interventional label

y

of the query.

Abbildung 5 : Decision-mode coverage of the PriMa-Causa model.

Source	Architectural realisation
MR3	The treatment token and its role embedding bind each forward pass to the queried treatment-outcome pair $(T,Y)$ and separate the observational from the interventional regime.
MR4	The supervision is drawn under the truncated factorisation, so the output is an interventional distribution rather than an associational score.
MR5, DP4	The three-valued ancestor encoding is consumed as a learned attention bias, the single entry point of the constraint map $\Phi_{\mathcal{K}}(x)$ .
MR6	Amortised pre-training and frozen weights answer a case in one forward pass without per-case fitting.
MR7, DP8	Identifiability and support are gated upstream per tensor cell, and only admissible cells are estimated.
MR7, DP8	Conditioning is restricted to the pre-intervention context, so no descendant of $T$ enters.

Tabelle 1 : Traceability of the model architecture to the meta-requirements and design principles of Chapter 4 .

Abbildung 2 : Integration architecture of the PriMa-Causa framework.

Abbildung 3 : Data input of the PriMa-Causa framework.

Abbildung 4 : Interaction between the operator and the framework at the operator interface.

Abbildung 5 : Log view of the operator console.

Abbildung 6 : Prescription view of the operator console.

Abbildung 7 : Task view of the operator console.

Panel of Figure 54 — Abbildung 8 : Operator-facing troubleshooting application.

Abbildung 9 : Head-mounted variant of the troubleshooting application on Apple Vision Pro.

Principle	Realisation in the demonstrator	Reference
MR2	Automatic framing of the observed deviation into Mode 3 when a case is opened	Fig. 5
DP3	Candidate interventions ranked through forward interventional queries of the pre-trained model	Fig. 6
DP5, MR11	Ranking coupled to the predictive uncertainty through $95\%$ intervals in the forest plot	Fig. 6
DP7	Observed outcomes recorded as interventional evidence that informs subsequent cases	Fig. 7
DP8, MR7	Evidence panel with the adjusted confounder and the excluded mediator of the estimate	Fig. 7
MR13	Per-case audit trail with model checkpoint, knowledge level $\mathcal{K}_{\mathrm{op}}$ , and identification basis	Fig. 7

Tabelle 1 : Realisation of the design principles and meta-requirements of Chapter 4 in the demonstrated artefacts.

EH	Hyp.	RG	MR	DP	Mode / float
EH1	(i)	RG2	MR4, MR8	–	M1 / Fig. 2 , Fig. 3
EH2	–	RG3	MR5	DP4	M1 / Fig. 4 , Tab. 2
EH3	(i)	RG3	MR6	–	M1 / Fig. 5 , Fig. 6
EH4	–	RG3	MR12	DP6	M1 / Fig. 7
EH5	–	RG3	MR6, MR13	DP7	M1 / Fig. 8 , Fig. 9
EH6	(i)	RG3	MR7	DP8	M1 / Fig. 10

Tabelle 1 : Traceability of the evaluation hypotheses to the central hypothesis halves, research gaps, meta-requirements, design principles, decision modes, and the floats that test them.

Abbildung 2 : Normalised prescription error (PEHE) by model under strong overlap and abundant data (left) and under weak overlap and sparse data (right), medians annotated.

Abbildung 3 : Observational error against prescription error, one point per sampled SCM and model, at weak overlap and sparse data.

Abbildung 4 : Normalised PEHE across the structural-knowledge regime

\mathcal{K}_{\mathrm{op}}

on the mediator family, at weak overlap and sparse context.

Mechanism	Structural family	no graph	full graph	reduction	instances improved
nonlinear	mediator (T1)	$0.77$	$0.75$	$2.0\%$	$31/50$
linear	control (T0)	$0.20$	$0.20$	$-0.3\%$	$25/50$
linear	mediator (T1)	$0.42$	$0.32$	$7.0\%$	$28/50$

Tabelle 2 : Median normalised PEHE of PriMa-Causa without and with the complete graph, by mechanism class and structural family, at weak overlap and sparse context. Fifty instances per cell.

Abbildung 5 : Normalised PEHE against the number of context rows

N_{c}

, at weak overlap with confounding (

\theta=6

Abbildung 6 : Normalised PEHE against the number of nodes

n

Abbildung 7 : Median per-query latency (left) and per-context fit time (right) by model against the number of nodes

n

, on logarithmic axes. Shaded bands show the interquartile range.

Abbildung 8 : Normalised PEHE across the difficulty ladder for the CPG -pre-trained model, one marker per host dataset. The dashed line marks the no-effect reference at

1

Abbildung 9 : Normalised PEHE across the difficulty ladder for the model pre-trained on density-matched Erdős–Rényi graphs, otherwise identical to Figure 8 .

Abbildung 10 : Normalised PEHE against the overlap knob

\theta

. Shaded bands span the per-model interquartile range.

Abbildung 11 : Normalised PEHE of PC-ng and PC-wg on a mediator (a) and a selection-collider (b) structure, both at a CPG-scale, weak-overlap regime. The dashed line marks the predict-zero-effect reference.

Abbildung 12 : Median normalised PEHE against the graph density dial for the three structural-knowledge variants of PriMa-Causa: no graph, partially disclosed, and complete. Weak overlap and sparse context. Bands span the

95\%

bootstrap CI of the median over

N_{\mathrm{SCM}}{=}50

structural causal models per level.

Abbildung 13 : Expected net OEE gain against the adjustment budget per ranking policy. Bands span the

95\%

confidence interval over

20

repeated runs.

	Level shift		Dispersion		Masked
Method	$N_{c}{=}50$	$N_{c}{=}500$	$N_{c}{=}50$	$N_{c}{=}500$	$N_{c}{=}50$	$N_{c}{=}500$
PC-wg	$0.70$ / $\mathbf{0.98}$	$0.75$ / $0.99$	$0.72$ / $\mathbf{0.98}$	$0.78$ / $0.99$	$0.16$ / $0.49$	$0.22$ / $0.51$
PC-ng	$0.59$ / $\mathbf{0.98}$	$0.68$ / $0.98$	$0.61$ / $0.97$	$0.73$ / $0.99$	$0.21$ / $\mathbf{0.53}$	$0.19$ / $0.45$
GCM-IDI	$0.67$ / $0.97$	$0.75$ / $0.99$	$0.62$ / $\mathbf{0.98}$	$0.76$ / $0.99$	$0.16$ / $0.42$	$\mathbf{0.24}$ / $0.56$
CF attribution	–	$0.65$ / $0.84$	–	$0.64$ / $0.78$	–	$0.23$ / $\mathbf{0.62}$
Anomaly rank	$0.73$ / $\mathbf{0.98}$	$0.78$ / $0.99$	$0.75$ / $\mathbf{0.98}$	$0.86$ / $0.99$	$0.15$ / $0.49$	$0.16$ / $0.47$

Tabelle 3 : Recall of the injected root cause (Recall@1/Recall@3) at the complete knowledge level, by fault class and context size. Best value per column in bold.

Method	none	ordered	complete	none	ordered	complete
	Level shift			Dispersion
PC-wg	–	$0.51$	$0.75$	–	$0.37$	$0.78$
PC-ng	$0.56$	$0.51$	$0.68$	$0.60$	$0.36$	$0.73$
GCM-IDI	–	$0.54$	$0.75$	–	$0.36$	$0.76$
Anomaly rank	$0.66$	$0.54$	$0.78$	$0.72$	$0.41$	$0.86$
Traversal	–	$0.55$	$0.84$	–	$0.39$	$0.88$

Tabelle 4 : Recall@1 of the injected root cause across the three structural-knowledge levels at

N_{c}{=}500

, observable fault classes. Methods that require structural knowledge are undefined at the none level.

Abbildung 14 : Normalised per-model profiles across six evaluation axes.

Model	Profile area (% of max)
PC-wg	$67\%$
PC-ng	$54\%$
ML-X	$19\%$
ML-S	$16\%$
ML-T	$6\%$
Causal Forest	$0\%$

Tabelle 5 : Polygon area of each model’s normalised six-axis profile in Figure 14 , as a fraction of the area attained by a model at the best-observed value on every axis. Computed over all six models of Figure 14 .

Software artefact	Realisation	Source
Production-line data generator	Causal Process Graph sampler, synthetic SCM pipeline, and semi-synthetic anchoring on real industrial covariates	Ch. 5
Pre-trained PriMa-Causa foundation model	Graph-conditioned interventional estimator, released with implementation, training configuration, and weights	Ch. 6
Line-deployed software demonstrator	Causal reasoning runtime and operator console on the edge gateway, with the troubleshooting application on mobile and head-mounted devices (co-developed with Dropslab Technologies)	Ch. 7

Tabelle 1 : Software artefacts of the dissertation.

Boundary	What lies outside the validated scope	Source
Sensor and process layer	Recovery of latent physical mechanisms (the framework narrows the search space for actionable levers).	Subsec. 2
Static interventional scope	Counterfactual reasoning, time-varying structures, and latent-confounder identification.	Sec. 1
Controlled ground truth	Realised gain of the recommendation policy in closed-loop field operation (accuracy is verified on synthetic and semi-synthetic data with real covariates, Mode 2 is untested, Mode 3 is tested synthetically).	[ 14 , 106 ] , Sec. 5 , 9
Offline prior match	Query-time check of whether a case lies within the pre-training prior (the match is established offline).	Sec. 2 , 6 , [ 138 , 139 ]
Fixed architecture	Lines wider than the $35$ -variable input layout without reduction or retraining.	Subsec. 1

Tabelle 2 : Boundaries of the evidence.

Panel of Figure 77 — Abbildung 2 : Single-station causal graph of Figure 4 with an image-valued outcome. The intervention $\dop(T)$ on the corrective action removes the incoming edge $\vartheta\to T$ by graph surgery.

Abbildung 3 : Rendered inspection images under observation and under three interventions.

Tool or tool class	Provider / Reference	Use in the dissertation
DeepL	https://www.deepl.com	Translation and writing support.
Claude Code	https://claude.ai	Optimisation and debugging of code.
Positron IDE	https://positron.posit.co	Integrated development environment for Python and R code development and analysis.
Python	https://www.python.org	Data generation, model architecture implementation, and empirical evaluation.
R Project	https://www.r-project.org	Statistical computing, benchmark analysis, and synthetic data generation.
Beckhoff TwinCAT	https://www.beckhoff.com	Programmable logic controller (PLC) programming, machine telemetry acquisition, and ADS protocol integration.

Tabelle 1 : Software and AI-based tools used in the dissertation.

Causal Inference

Causal inference studies how interventions and counterfactuals reveal cause-and-effect relationships beyond observed associations.

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Meta-Learning Neural Processes Bayesian Inference Root Cause Analysis

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Root cause analysis (RCA) in complex systems is challenging due to error propagation across multiple variables, the need for structural causal knowledge, and the computational cost of inference at test time. We introduce PRIM (Prior-fitted Root cause Identification with Meta-learning), a causal meta-learning approach that frames RCA as a Bayesian inference task over a synthetic prior of causal models. By marginalising out structural uncertainty, PRIM implicitly identifies changes in the data-generating mechanism between baseline and anomalous periods. In doing so, PRIM infers distributional differences without explicit statistical testing, and implicitly learns causal structure without model fitting at test time. Following the simulation-based meta-learning paradigm of prior-fitted networks, PRIM uses a Model-Averaged Causal Estimation (MACE) transformer neural process that jointly attends over observational and anomalous samples and the causal structure of nodes, enabling zero-shot inference in 17,ms for systems with up to 100 variables. Across synthetic benchmarks and two realistic benchmark datasets, PetShop and CausRCA, PRIM is competitive with methods that are aware of the system's causal graphical structure a priori while outperforming graph-unaware methods on several tasks. Lightweight fine-tuning to specific domains and data dynamics improves performance further.

Abstract

Causal Inference

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