Statistical Evidence & Confidence Levels

"""Statistical confidence calculations for SOTIF residual risk."""
import math
from scipy import stats

def required_scenarios_no_failure(target_prob: float,
                                   confidence: float) -> int:
    """
    Calculate N scenarios needed with zero failures to claim
    failure probability <= target_prob at given confidence.
    Uses one-sided binomial confidence interval.
    Formula: N = ln(1 - confidence) / ln(1 - target_prob)
    """
    N = math.log(1 - confidence) / math.log(1 - target_prob)
    return math.ceil(N)

def confidence_after_n_no_failure(n_scenarios: int,
                                   target_prob: float) -> float:
    """
    Calculate achieved confidence after n scenarios with zero failures.
    C = 1 - (1 - target_prob)^n
    """
    return 1 - (1 - target_prob) ** n_scenarios

# AEB example: target P(miss) < 0.1% = 0.001 at 95% confidence
target_failure_prob = 0.001  # max 1 miss per 1000 scenarios
confidence_target   = 0.95

n_required = required_scenarios_no_failure(target_failure_prob,
                                            confidence_target)
print(f"Target: P(failure) < {target_failure_prob} at C={confidence_target}")
print(f"Required scenarios with zero failures: {n_required}")
print()

# How does confidence grow with more tests?
for n in [500, 1000, 2000, 3000]:
    c = confidence_after_n_no_failure(n, target_failure_prob)
    print(f"  {n:5d} scenarios: achieved confidence = {c:.3f}")