Supplier Reliability Evidence Aggregator

The static reliability_score seeds the prior as pseudocounts:

α₀ = reliability_score × 10
β₀ = (1 − reliability_score) × 10

Step-by-Step Execution

Step 1: Retrieve the Beta-Binomial update formula from the knowledge base

search_knowledge_base(
    query="Bayesian parameter learning binary distribution Beta prior posterior pseudocounts update",
    k=3
)

What to extract from the result:

• Beta posterior update rule (Ch.4 §4.2.1, eq. 4.26): posterior = Beta(α + n, β + m − n) where n = successes, m = total trials
• Beta mean formula (eq. 4.27): mean = α / (α + β)
• Pseudocount interpretation: prior α₀, β₀ behave like observed counts

Step 2: Expand linked concepts for prior seeding and evidence weighting

expand_graph_by_ids(
    ids=[<ids from step 1>]
)

What to extract from the result:

• How to choose a prior from expert knowledge (Ch.4 §4.2.1): encode reliability_score as pseudocounts α₀ = score × 10, β₀ = (1−score) × 10
• How prior importance diminishes with more data: large m makes prior negligible

Step 3: Fetch supplier metadata

GET /api/v1/smart-query/procurement/suppliers/{supplier_id}

Fields to extract: reliability_score, region, name

Seed the Beta prior:

α₀ = reliability_score × 10
β₀ = (1 − reliability_score) × 10

Step 4: Fetch completed purchase orders for the supplier

GET /api/v1/smart-query/procurement/purchase-orders
    ?supplier_id=<supplier_id>
    &status_in=received,partial

Fields to extract per PO: id, expected_at, status

Step 5: Fetch shipment arrival data per PO

For each PO returned in Step 4:

GET /api/v1/smart-query/procurement/purchase-orders/{purchase_order_id}

Classify each PO:

on_time = (arrived_at <= expected_at)   →  success (s += 1)
late    = (arrived_at >  expected_at)   →  failure (f += 1)

Apply exponential recency decay (λ = 0.05/day) so older deliveries contribute less than recent ones:

weight_i = exp(−λ × days_since_delivery)
s_effective = Σ weight_i  for on-time deliveries
f_effective = Σ weight_i  for late deliveries

Step 6: Compute Beta posterior

Using the formula from Step 1:

α_post = α₀ + s_effective
β_post = β₀ + f_effective

posterior_mean     = α_post / (α_post + β_post)          # eq. 4.27
n_effective        = s_effective + f_effective

# Lower credible bound (90th percentile) — conservative risk estimate
# Use Beta distribution quantile: credible_lower_90 = Beta.ppf(0.10, α_post, β_post)

Evidence weight classification:

n_effective >= 20  →  "strong"
n_effective >= 5   →  "moderate"
n_effective <  5   →  "weak"   (posterior dominated by prior — treat with caution)

Step 7: Fetch pipeline summary for context

GET /api/v1/smart-query/procurement/pipeline-summary
    ?supplier_id=<supplier_id>
    &status_in=open,pending

Fields to extract: open_po_count, total_remaining, next_expected_at_min

Use this to flag if the supplier has many open unresolved commitments that haven't yet generated delivery evidence.

Step 8: Return result

Failure Modes

Example Walkthrough

User query: "Is SupplierX reliable enough to handle our Q4 critical component orders?"

<thinking>
The static reliability_score may be stale. I need to update it with
real delivery evidence using Beta-Binomial Bayesian learning.
</thinking>

Step 1 — search_knowledge_base("Bayesian parameter learning binary Beta prior posterior pseudocounts")
→ Retrieved eq. 4.26–4.27: posterior = Beta(α+n, β+m−n), mean = α/(α+β)

Step 2 — expand_graph_by_ids([doc_id_1, doc_id_2])
→ Confirmed: seed prior from expert knowledge as pseudocounts

Step 3 — GET /suppliers/supplier-uuid-xyz
→ reliability_score=0.82, name="SupplierX"
→ α₀ = 8.2,  β₀ = 1.8

Step 4 — GET /purchase-orders?supplier_id=supplier-uuid-xyz&status_in=received,partial
→ 23 completed POs returned

Step 5 — Classify deliveries with recency decay:
→ 17 on-time (s_effective = 14.3 after decay)
→  6 late    (f_effective =  5.1 after decay)

Step 6 — Compute posterior:
    α_post = 8.2 + 14.3 = 22.5
    β_post = 1.8 +  5.1 =  6.9
    posterior_mean  = 22.5 / (22.5 + 6.9) = 0.765
    credible_lower_90 = Beta.ppf(0.10, 22.5, 6.9) = 0.634
    evidence_weight = "strong"  (n_effective=19.4)

Step 7 — GET /pipeline-summary?supplier_id=supplier-uuid-xyz
→ open_po_count=3, next_expected_at_min="2026-04-01"

Result:
  posterior_mean_reliability = 0.765   (was 0.82 static)
  credible_lower_90          = 0.634
  evidence_weight            = "strong"

SupplierX's real reliability (0.77) is lower than their static score (0.82).
6 late deliveries in recent history are pulling the score down.
For critical Q4 orders, consider requesting a delivery commitment with
penalty clauses given the 63% conservative lower bound.

Feeds Into

• leadtime-risk-estimator — uses posterior_mean_reliability to inflate lead-time variance
• multi-attribute-utility-scorer — uses posterior_mean_reliability as u_sla input for utility scoring
• expected-utility-action-ranker — used in tie-breaking when two suppliers have equal utility scores