vamseeachanta 1. Sample Size Selection (+1)
1. Sample Size Selection
def determine_sample_size(
target_pf: float,
confidence_level: float = 0.95
) -> int:
"""
Determine required sample size for target failure probability.
Rule of thumb: N ≈ 10/Pf for reasonable confidence
Args:
target_pf: Target probability of failure
confidence_level: Confidence level
Returns:
Recommended sample size
Example:
>>> n = determine_sample_size(target_pf=1e-4, confidence_level=0.95)
>>> print(f"Recommended samples: {n}")
"""
# Basic rule: need at least 10 failures
# So N * Pf ≥ 10
# N ≥ 10 / Pf
n_basic = int(10 / target_pf)
# For higher confidence, increase further
if confidence_level >= 0.99:
n_recommended = n_basic * 5
elif confidence_level >= 0.95:
n_recommended = n_basic * 3
else:
n_recommended = n_basic * 2
return max(n_recommended, 1000) # Minimum 1000 samples
2. Convergence Checking
def check_monte_carlo_convergence(
data: np.ndarray,
window_size: int = 1000
) -> dict:
"""
Check if Monte Carlo simulation has converged.
Args:
data: Simulation output data
window_size: Window size for moving average
Returns:
Dictionary with convergence metrics
"""
n = len(data)
# Calculate cumulative mean
cumulative_mean = np.cumsum(data) / np.arange(1, n + 1)
# Calculate moving coefficient of variation
if n > window_size:
moving_std = np.std(data[-window_size:])
moving_mean = np.mean(data[-window_size:])
cov = moving_std / moving_mean if moving_mean != 0 else 0
else:
cov = np.std(data) / np.mean(data) if np.mean(data) != 0 else 0
# Convergence criterion: COV < 5%
converged = cov < 0.05
return {
'converged': converged,
'cov': cov,
'final_mean': cumulative_mean[-1],
'samples_used': n
}