Risk management and SMS

Example 1 A geofence and a flight termination system sharing one GNSS

The top event is a flyaway when the link is lost together with a GNSS fault. The two preventive barriers are a geofence and a flight termination system; the mitigations are the chance that no one is at the impact point and a parachute. All values are assumed for teaching.

rate_top = 2e-3        # link loss with GNSS fault per flight hour (assumed)
p_geofence = 0.10      # probability the geofence fails
p_fts = 0.05           # probability flight termination fails
p_people = 0.30        # probability people are at the impact point
p_chute = 0.20         # probability the parachute does not reduce severity

def injury_rate(shared_gnss):
    if shared_gnss:
        # geofence and termination share one GNSS: when GNSS fails, both fail together
        p_escape = 1.0
    else:
        p_escape = p_geofence * p_fts
    return rate_top * p_escape * p_people * p_chute

for name, shared in [("independent barriers", False), ("shared GNSS", True)]:
    r = injury_rate(shared)
    print(f"{name:21s} injury rate {r:.1e} per flight hour"
          f" = one per {1/r:,.0f} h")

independent barriers  injury rate 6.0e-07 per flight hour = one per 1,666,667 h
shared GNSS           injury rate 1.2e-04 per flight hour = one per 8,333 h

If the two barriers were independent, the injury rate would be about one per 1.7 million flight hours. But because both take position from the same GNSS, when GNSS fails both fail together, and the rate becomes two hundred times worse. The fix is to separate the barriers’ data sources, for example triggering flight termination from link loss or an independent position source, and to prove it by testing.

Example 2 Is the link really failing more often this quarter?

The company recorded link-loss events over the past six quarters. This quarter had 7 events in 180 flight hours (hypothetical data).

import numpy as np
from scipy.stats import chi2

events = np.array([3, 4, 2, 5, 3, 4])            # link-loss events per quarter, previous 6 quarters
hours = np.array([150, 160, 140, 170, 150, 160])  # flight hours per quarter
rate = events / hours * 100                       # per 100 flight hours
mean, sd = rate.mean(), rate.std()                    # population SD as in ICAO Doc 9859
print(f"past rates per 100 h: {np.round(rate, 2)}")
print(f"mean {mean:.2f}  SD {sd:.2f}  alert (mean + 2SD) {mean + 2*sd:.2f}")

k, h = 7, 180                                     # current quarter
lo = chi2.ppf(0.025, 2*k) / 2 / h * 100
hi = chi2.ppf(0.975, 2*(k + 1)) / 2 / h * 100
print(f"current {k/h*100:.2f} per 100 h, exact 95% CI {lo:.2f} to {hi:.2f}")

past rates per 100 h: [2.   2.5  1.43 2.94 2.   2.5 ]
mean 2.23  SD 0.48  alert (mean + 2SD) 3.19
current 3.89 per 100 h, exact 95% CI 1.56 to 8.01

This quarter’s rate of 3.89 per 100 hours exceeds the 3.19 alert level, so a review is required. But the 95% confidence interval runs from 1.56 to 8.01, which includes the previous mean of 2.23, so one quarter’s data cannot yet show a real change. A good review looks at the details of all seven events for a common cause, such as a new area, new firmware or a changed antenna, rather than judging from the number alone.