4. Fault tree to Bayesian network¶
from hiphopsllm import AgenticReliabilityStudy, load_example, load_outcomes
study = AgenticReliabilityStudy(load_example("parallel_aggregator"))
study.observe(load_outcomes(), profile={"short": 0.3, "medium": 0.5, "long": 0.2})
study.run()
The tables¶
cpts = study.cpts("H2")
print(cpts.summary())
CPT set — FT_H2
variables 15
basic events 8
gates 7 (0 soft, 7 deterministic)
top event TOP
table rows 70
Every node became a variable, in a valid topological order:
cpts.order
# ['CCF_LLM_Qwen_Qwen2_5_Math_1_5B_Instruct', 'BE_aggregator_SELECT',
# 'BE___start___BADREQ', 'BE_cot_agent_NONDET', 'BE_cot_agent_HALLUC', 'E5',
# 'BE_react_agent_NONDET', 'BE_react_agent_HALLUC', 'E3', 'G7', 'G8', 'G6', ...]
cpts.priors
# {'CCF_LLM_…': 0.08, 'BE_aggregator_SELECT': 0.1114, …}
Look at one table:
cpts.to_frame("BE-react_agent-HALLUC")
Variables can be addressed three ways — by variable name, by fault tree node id, or by basic-event id — because those are the names that appear in cut sets, in the FMEA and in evidence dictionaries:
cpts.resolve("BE-react_agent-HALLUC") # 'BE_react_agent_HALLUC'
cpts["BE-react_agent-HALLUC"] is cpts["BE_react_agent_HALLUC"] # True
The network¶
network = study.bayesnet("H2")
print(network.summary())
Bayesian network — agentic workflow — H2
variables 15
basic events 8
gates 7 (0 soft, 7 deterministic)
top event TOP
table rows 70
P(top = Fail) 0.227643
Verify it¶
network.cross_check()
{'exact': 0.2276430…, 'pyagrum': 0.2276430…,
'difference': 1.1e-16, 'relative_difference': 4.9e-16,
'agree': 1.0, 'compared': 1.0}
Two engines that share no code — pyAgrum’s junction tree, and exact enumeration in NumPy — agreeing to machine precision. Run this whenever you change gate semantics; it is the cheapest evidence that the conversion is still right.
Because the second engine exists, pyAgrum is optional:
network.p_fail(engine="exact") # NumPy only
Against the cut sets¶
network.compare_with_cutsets(study.report.analysis("H2"))
{'exact_bayesnet': 0.2276, 'minimal_cut_upper_bound': 0.2322,
'rare_event_sum': 0.2521, 'bound_overestimate': 0.0046}
The bound is loose by 0.0046 because those cut sets share basic events —
CCF-LLM-… appears in several of them, and MCUB treats cut sets as independent.
Exact inference does not. On a coherent tree the overestimate can never be
negative; if it is, the tree and the network have drifted apart, and the test
suite checks that on every hazard of every bundled example.
Diagnosis¶
Condition on what a run showed:
network.posteriors({"BE-aggregator-OWN": "Fail"})
BE-aggregator-OWN 1.0000
BE-aggregator-SELECT 0.1103
BE-react_agent-HALLUC 0.0910
CCF-LLM-Qwen-Qwen2-5-Math-1-5B-Instruct 0.0800
BE-react_agent-NONDET 0.0735
BE-cot_agent-HALLUC 0.0679
States may be written "Fail", 1, or True. Ask about intermediate nodes too:
network.posteriors({"TOP": "Fail"}, basic_events_only=False)
The single most likely joint explanation, given the hazard occurred:
network.most_probable_explanation({"TOP": "Fail"})
{'CCF-LLM-Qwen-Qwen2-5-Math-1-5B-Instruct': 'OK',
'BE-aggregator-SELECT': 'OK',
'BE-__start__-BADREQ': 'OK',
'BE-cot_agent-NONDET': 'OK',
'BE-cot_agent-HALLUC': 'OK',
'BE-react_agent-NONDET': 'OK',
'BE-react_agent-HALLUC': 'OK',
'BE-aggregator-OWN': 'Fail'}
The most probable single story behind a wrong answer is not the agents failing — it is the judge hallucinating its own. That is an order-1 cut set on a component that exists to improve reliability, and it is the kind of thing the structural view alone will not rank for you.
The imprecise pair¶
imprecise = study.imprecise_bayesnet("H2")
imprecise.envelope() # [0.172738, 0.291474]
imprecise.lower.p_fail() # every leaf at its lower bound
imprecise.upper.p_fail() # every leaf at its upper bound
Per-cause envelopes:
imprecise.posterior_envelopes()
BE-aggregator-SELECT [0.073713, 0.151711]
BE-aggregator-OWN [0.073713, 0.151711]
BE-react_agent-HALLUC [0.060891, 0.124137]
BE-react_agent-NONDET [0.049017, 0.100608]
BE-cot_agent-HALLUC [0.039574, 0.097997]
Changing the gate logic¶
The synthesised structure can be right while the logic is not — a two-of-three majority aggregator being the usual case:
network = study.bayesnet("H2", gate_overrides={"G7": ("KOFN", 2)})
Soften every OR to a noisy-OR when propagation is probabilistic rather than certain:
network = study.bayesnet("H2", soft_gates=True, link_probability=0.85, leak=0.02)
network.cpts.notes
# ['OR gates were softened to noisy-OR: the network no longer encodes the same
# Boolean function as the minimal cut sets']
That warning matters. Once gates are soft, the network and the cut sets no longer
describe the same object, and compare_with_cutsets is no longer a bound.
Drawing¶
network.show() # pyAgrum, or matplotlib
network.view(evidence={"BE-aggregator-OWN": "Fail"}).show()
network.view().to_png("bn_h2.png")
network.view().to_svg("bn_h2.svg")
network.view().to_dot() # Graphviz source, no dot binary needed
The backend is chosen by whether the Graphviz dot binary is genuinely callable
— not by whether import pydot succeeds, which proves nothing. Check for
yourself:
from hiphopsllm import graphviz_available
graphviz_available() # varies by environment
network.view().resolved_backend # 'pyagrum' or 'matplotlib'
The matplotlib backend lays the network out in longest-path layers with a
barycentre pass to reduce edge crossings, and draws each node the way pyAgrum’s
showInference does: a titled box holding one bar per state, each bar labelled
with its percentage, over a title strip shaded by the node’s posterior. Evidence
nodes are outlined in green, the caption reports the measured inference time and
says whether Graphviz was absent, and show_probabilities=False collapses the
nodes to compact labelled boxes. Pass annotations=[...] for one or more lines
of explanatory text above the graph. Force either backend with
backend="pyagrum" or backend="matplotlib".
Next¶
Tutorial 5 puts the whole thing together and compares two architectures under the same profile.