MIL-P-1629’s failure mode and effects analysis (1949)

The US military procedure MIL-P-1629, Procedures for Performing a Failure Mode, Effects and Criticality Analysis (9 November 1949), asked designers to go through a system part by part, list each way the part can fail, trace the effect of each failure and classify it by its consequence for the mission and for safety. NASA used the method on Apollo, and the automotive industry later made it routine, ranking each mode by a risk priority number, severity times occurrence times detection, each scored from 1 to 10 (risk_priority_number(), fmea_ranking()). Where failure rates are known the military standard’s criticality number \(C_m = \beta\alpha\lambda_p t\) (failure_mode_criticality()) ranks modes by expected losses instead.

import matplotlib.pyplot as plt
import numpy as np

from engineeringkit.reliability import failure_mode_criticality, fmea_ranking

An FMEA of a centrifugal pump

(severity, occurrence, detection) for each failure mode.

modes = {
    "mechanical seal leak": (6, 6, 3),
    "bearing seizure": (8, 3, 5),
    "impeller erosion": (5, 4, 7),
    "motor winding short": (9, 2, 4),
    "coupling misalignment": (4, 5, 5),
    "cavitation": (5, 5, 6),
    "casing crack": (10, 1, 6),
}
fmea = fmea_ranking(modes)
for name, s, o, d, rpn in zip(fmea.modes, fmea.severity, fmea.occurrence, fmea.detection, fmea.rpn):
    print(f"{name:22s} S={s:2d} O={o:2d} D={d:2d} RPN={rpn:4d}")
fig, ax = fmea.plot()
fig.set_size_inches(7, 4)
fig.tight_layout()

cavitation             S= 5 O= 5 D= 6 RPN= 150
impeller erosion       S= 5 O= 4 D= 7 RPN= 140
bearing seizure        S= 8 O= 3 D= 5 RPN= 120
mechanical seal leak   S= 6 O= 6 D= 3 RPN= 108
coupling misalignment  S= 4 O= 5 D= 5 RPN= 100
motor winding short    S= 9 O= 2 D= 4 RPN=  72
casing crack           S=10 O= 1 D= 6 RPN=  60

What the RPN hides

The casing crack has the lowest RPN but a severity of 10. Because the scores are ordinal, a high severity is reviewed whatever its product.

critical = [name for name, s in zip(fmea.modes, fmea.severity) if s >= 9]
print("modes reviewed for severity alone:", critical)

modes reviewed for severity alone: ['motor winding short', 'casing crack']

Criticality numbers from failure rates

The seal of a pump with \(\lambda_p\) = 50 failures per million hours fails by leaking (60% of failures, of which 20% stop the mission) or by sudden rupture (40%, all of which stop it); the mission is 2000 h.

leak, rupture = failure_mode_criticality(np.array([0.6, 0.4]), np.array([0.2, 1.0]), 50e-6, 2000.0)
print(f"criticality: leak {leak:.3f}, rupture {rupture:.3f} expected losses per mission")

assert fmea.modes[0] == "cavitation" and fmea.rpn[0] == 150
assert "casing crack" in critical and fmea.modes[-1] == "casing crack"
assert np.isclose(leak + rupture, 50e-6 * 2000 * (0.6 * 0.2 + 0.4))

plt.show()

criticality: leak 0.012, rupture 0.040 expected losses per mission