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FA-62966 / Insurance premium rating / Open access

Square-root credibility rate indication: Credibility grows linearly with claim count · case 01

Partially credible books get far less weight on their own experience.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Z is computed as n/full instead of the square root.

THE FAILURE

Z is computed as n/full instead of the square root.

Unsuccessful approach: Taking the root before dividing leaves Z far too small.

Case contract

Input claims n, full_standard, observed and complement changes (per mille), cap. n<0 or full<=0 -> 'invalid'. Z (per mille) = min(1000, isqrt(n*10^6 // full)). Indication = floor((Z*obs+(1000-Z)*comp)/1000+1/2), then clamped to [-cap, cap]. Return [Z, indication].

Why this case matters

Credibility weighting decides how far a rate change follows thin experience versus the complement.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x['claims']; full=x['full_standard']
    if n<0 or full<=0: return 'invalid'
    z=min(1000, n*1000//full)
    ind=Fraction(z*x['observed']+(1000-z)*x['complement'],1000)
    ind=math.floor(ind+Fraction(1,2))
    cap=x['cap']
    ind=max(-cap,min(cap,ind))
    return [z,ind]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['partial credibility', {'claims': 468, 'full_standard': 1082, 'observed': 177, 'complement': 60, 'cap': 150}, [657, 137]], ['small volume', {'claims': 43, 'full_standard': 1082, 'observed': 77, 'complement': 53, 'cap': 150}, [199, 58]], ['above full standard', {'claims': 1951, 'full_standard': 1082, 'observed': -79, 'complement': 43, 'cap': 150}, [1000, -79]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': 28, 'complement': 29, 'cap': 150}, [1000, 28]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': -82, 'complement': -23, 'cap': 150}, [0, -23]], ['capped increase', {'claims': 898, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [911, 150]], ['capped decrease', {'claims': 774, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [845, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -107, 'complement': -1, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 673, 'full_standard': 1082, 'observed': 49, 'complement': -23, 'cap': 150}, [788, 34]]], [['partial credibility', {'claims': 239, 'full_standard': 1082, 'observed': -28, 'complement': -25, 'cap': 150}, [469, -26]], ['small volume', {'claims': 23, 'full_standard': 1082, 'observed': -82, 'complement': 40, 'cap': 150}, [145, 22]], ['above full standard', {'claims': 1972, 'full_standard': 1082, 'observed': 21, 'complement': 2, 'cap': 150}, [1000, 21]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -116, 'complement': 58, 'cap': 150}, [1000, -116]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 137, 'complement': -12, 'cap': 150}, [0, -12]], ['capped increase', {'claims': 802, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [860, 150]], ['capped decrease', {'claims': 894, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [908, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -45, 'complement': 36, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 317, 'full_standard': 1082, 'observed': 154, 'complement': 46, 'cap': 150}, [541, 104]]], [['partial credibility', {'claims': 431, 'full_standard': 1082, 'observed': 31, 'complement': 31, 'cap': 150}, [631, 31]], ['small volume', {'claims': 7, 'full_standard': 1082, 'observed': 142, 'complement': 9, 'cap': 150}, [80, 20]], ['above full standard', {'claims': 1564, 'full_standard': 1082, 'observed': 48, 'complement': 19, 'cap': 150}, [1000, 48]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -29, 'complement': -12, 'cap': 150}, [1000, -29]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 136, 'complement': 56, 'cap': 150}, [0, 56]], ['capped increase', {'claims': 914, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [919, 150]], ['capped decrease', {'claims': 737, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [825, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -49, 'complement': 60, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 343, 'full_standard': 1082, 'observed': -32, 'complement': 32, 'cap': 150}, [563, -4]]], [['partial credibility', {'claims': 220, 'full_standard': 1082, 'observed': 10, 'complement': 36, 'cap': 150}, [450, 24]], ['small volume', {'claims': 46, 'full_standard': 1082, 'observed': 76, 'complement': -15, 'cap': 150}, [206, 4]], ['above full standard', {'claims': 1760, 'full_standard': 1082, 'observed': -79, 'complement': -7, 'cap': 150}, [1000, -79]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': 138, 'complement': -10, 'cap': 150}, [1000, 138]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 173, 'complement': 37, 'cap': 150}, [0, 37]], ['capped increase', {'claims': 760, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [838, 150]], ['capped decrease', {'claims': 990, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [956, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': 78, 'complement': 46, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 268, 'full_standard': 1082, 'observed': 127, 'complement': 57, 'cap': 150}, [497, 92]]], [['partial credibility', {'claims': 185, 'full_standard': 1082, 'observed': 50, 'complement': -6, 'cap': 150}, [413, 17]], ['small volume', {'claims': 26, 'full_standard': 1082, 'observed': 115, 'complement': 36, 'cap': 150}, [155, 48]], ['above full standard', {'claims': 1435, 'full_standard': 1082, 'observed': 127, 'complement': 35, 'cap': 150}, [1000, 127]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -88, 'complement': 21, 'cap': 150}, [1000, -88]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': -119, 'complement': 7, 'cap': 150}, [0, 7]], ['capped increase', {'claims': 843, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [882, 150]], ['capped decrease', {'claims': 747, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [830, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -70, 'complement': 10, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 721, 'full_standard': 1082, 'observed': -26, 'complement': 48, 'cap': 150}, [816, -12]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
partial credibility[432, 111][657, 137]Failed
small volume[39, 54][199, 58]Failed
above full standard[1000, -79][1000, -79]Passed
exactly full standard[1000, 28][1000, 28]Passed
zero claims uses complement[0, -23][0, -23]Passed
capped increase[829, 150][911, 150]Failed
capped decrease[715, -150][845, -150]Failed
negative claims rejectedinvalidinvalidPassed
moderate volume[621, 22][788, 34]Failed

SHA-256 / c391457fe78185f48dece5b4dc31c829e040f34fcf50d30e1791182ff8a693f1

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x['claims']; full=x['full_standard']
    if n<0 or full<=0: return 'invalid'
    z=min(1000, math.isqrt(n*1000000)//full)
    ind=Fraction(z*x['observed']+(1000-z)*x['complement'],1000)
    ind=math.floor(ind+Fraction(1,2))
    cap=x['cap']
    ind=max(-cap,min(cap,ind))
    return [z,ind]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['partial credibility', {'claims': 468, 'full_standard': 1082, 'observed': 177, 'complement': 60, 'cap': 150}, [657, 137]], ['small volume', {'claims': 43, 'full_standard': 1082, 'observed': 77, 'complement': 53, 'cap': 150}, [199, 58]], ['above full standard', {'claims': 1951, 'full_standard': 1082, 'observed': -79, 'complement': 43, 'cap': 150}, [1000, -79]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': 28, 'complement': 29, 'cap': 150}, [1000, 28]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': -82, 'complement': -23, 'cap': 150}, [0, -23]], ['capped increase', {'claims': 898, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [911, 150]], ['capped decrease', {'claims': 774, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [845, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -107, 'complement': -1, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 673, 'full_standard': 1082, 'observed': 49, 'complement': -23, 'cap': 150}, [788, 34]]], [['partial credibility', {'claims': 239, 'full_standard': 1082, 'observed': -28, 'complement': -25, 'cap': 150}, [469, -26]], ['small volume', {'claims': 23, 'full_standard': 1082, 'observed': -82, 'complement': 40, 'cap': 150}, [145, 22]], ['above full standard', {'claims': 1972, 'full_standard': 1082, 'observed': 21, 'complement': 2, 'cap': 150}, [1000, 21]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -116, 'complement': 58, 'cap': 150}, [1000, -116]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 137, 'complement': -12, 'cap': 150}, [0, -12]], ['capped increase', {'claims': 802, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [860, 150]], ['capped decrease', {'claims': 894, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [908, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -45, 'complement': 36, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 317, 'full_standard': 1082, 'observed': 154, 'complement': 46, 'cap': 150}, [541, 104]]], [['partial credibility', {'claims': 431, 'full_standard': 1082, 'observed': 31, 'complement': 31, 'cap': 150}, [631, 31]], ['small volume', {'claims': 7, 'full_standard': 1082, 'observed': 142, 'complement': 9, 'cap': 150}, [80, 20]], ['above full standard', {'claims': 1564, 'full_standard': 1082, 'observed': 48, 'complement': 19, 'cap': 150}, [1000, 48]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -29, 'complement': -12, 'cap': 150}, [1000, -29]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 136, 'complement': 56, 'cap': 150}, [0, 56]], ['capped increase', {'claims': 914, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [919, 150]], ['capped decrease', {'claims': 737, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [825, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -49, 'complement': 60, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 343, 'full_standard': 1082, 'observed': -32, 'complement': 32, 'cap': 150}, [563, -4]]], [['partial credibility', {'claims': 220, 'full_standard': 1082, 'observed': 10, 'complement': 36, 'cap': 150}, [450, 24]], ['small volume', {'claims': 46, 'full_standard': 1082, 'observed': 76, 'complement': -15, 'cap': 150}, [206, 4]], ['above full standard', {'claims': 1760, 'full_standard': 1082, 'observed': -79, 'complement': -7, 'cap': 150}, [1000, -79]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': 138, 'complement': -10, 'cap': 150}, [1000, 138]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': 173, 'complement': 37, 'cap': 150}, [0, 37]], ['capped increase', {'claims': 760, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [838, 150]], ['capped decrease', {'claims': 990, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [956, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': 78, 'complement': 46, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 268, 'full_standard': 1082, 'observed': 127, 'complement': 57, 'cap': 150}, [497, 92]]], [['partial credibility', {'claims': 185, 'full_standard': 1082, 'observed': 50, 'complement': -6, 'cap': 150}, [413, 17]], ['small volume', {'claims': 26, 'full_standard': 1082, 'observed': 115, 'complement': 36, 'cap': 150}, [155, 48]], ['above full standard', {'claims': 1435, 'full_standard': 1082, 'observed': 127, 'complement': 35, 'cap': 150}, [1000, 127]], ['exactly full standard', {'claims': 1082, 'full_standard': 1082, 'observed': -88, 'complement': 21, 'cap': 150}, [1000, -88]], ['zero claims uses complement', {'claims': 0, 'full_standard': 1082, 'observed': -119, 'complement': 7, 'cap': 150}, [0, 7]], ['capped increase', {'claims': 843, 'full_standard': 1082, 'observed': 400, 'complement': 50, 'cap': 150}, [882, 150]], ['capped decrease', {'claims': 747, 'full_standard': 1082, 'observed': -400, 'complement': -20, 'cap': 150}, [830, -150]], ['negative claims rejected', {'claims': -3, 'full_standard': 1082, 'observed': -70, 'complement': 10, 'cap': 150}, 'invalid'], ['moderate volume', {'claims': 721, 'full_standard': 1082, 'observed': -26, 'complement': 48, 'cap': 150}, [816, -12]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
partial credibility[19, 62][657, 137]Failed
small volume[6, 53][199, 58]Failed
above full standard[40, 38][1000, -79]Failed
exactly full standard[30, 29][1000, 28]Failed
zero claims uses complement[0, -23][0, -23]Passed
capped increase[27, 59][911, 150]Failed
capped decrease[25, -29][845, -150]Failed
negative claims rejectedinvalidinvalidPassed
moderate volume[23, -21][788, 34]Failed

SHA-256 / a50ee65c8eee225642498290dc0a201d1696af63aadb2f32d13da4155eecd4fd

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The verified repair and its recorded checks are member-only.

This mechanism has 9 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

A deterministic bounded teaching model of a stipulated toy rating contract. Amounts are integer cents and factors exact rationals; it makes no claim of conformance with any filed rating plan, bureau manual or jurisdiction. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:10.119720+00:00.

Case digest / 0e87750b64ad2ffe0e92b048638c0c4a11885d34692e87f411f24dc04e0ec8a8