Safety Analysis for Reduction ofLongitudinal Time Separation
Minima on Oceanic Routes
Ryota Mori(Electronic Navigation Research Institute)1

Background (1)• More efficient use of airspace is expectedwith the growth of air demand.
• Vertical separation– RVSM (Reduced Vertical Separation Minima)• Separation of the altitude is changed from 2000 ft
to 1000 ft.

• Longitudinal separation– Distance based separation (50 NM/ 30NM)• An aircraft pair (ADS system and RNP/RNAV
authorization required) can apply the distancebased separation.
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Background (2)• The time based separation (15 minutes) is
still widely used.
– There are still many aircraft without ADSsystem.
• It costs more or less money to introduce and use
ADS system.

 Reduced time based separation to 10
minutes is expected.
Minimum 15 min.
Minimum 10 min.

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Safety analysis• When a new system is introduced, asafety analysis is required.
– The target level of safety (TLS) in the en-routephase is set to 5.0x10-9 per flight hour in eachdimension by ICAO.
– Qualitative analysis is also required.
 This time, the risk of collision between two
aircraft is calculated based on the aircraft
navigation performance.
4How to calculate the risk ofcollisiony (0) z (0) 2x  x
N ax  Py (0) Pz (0)  Ex (t )Qx (t )2 y2z xT  2x Py (0)  Pz (0)  Px (0)lateral vertical longitudinal• A collision happens when a pair of aircraftis superposed vertically, laterally, andlongitudinally.
– Py (0)  0.20
– Pz (0)  0.5380– How to estimate Px (0) ?

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Conventional lossdistribution• Loss time > Initial time separation
Infringed longitudinal separation.
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How to calculate Px(0)Px (0)   Ex (t )Qx (t )dtQx (t )   l ( )dt

• Ex(t): The proportion of the initialtime separation equal to t.
• Qx(t): The probability of the loss
time greater than t.
• L(t): The probability density
function of the loss time.
7The target routes of thestudy• Oceanic routes bound south in Fukuoka FIR.
– Airspace A: segment 1, 2, 3, 4: 306~318 NM– Airspace B: segment 5, 6, 7, 8: 245~253 NM• Data obtained between May 2008 and May 2010.
– About 28,000 pairs of aircraft data in each airspace are used.

12 35 6 74A8B

8Initial time separation (Ext)
5 minutes shift

Obtained distribution in Airspace A

Estimated distribution in Airspace A(The minimum is 15 min.)(The minimum is 10 min.)9

Loss distribution (Lt)
• Loss distribution is modeled by double
exponential (Laplace) distribution.
– The loss distribution is obtained only when theInitial time separation is less than 60 minutes.
– The loss time is discretized by 1 minute.
1
 |t  |l (t;  ,  ) exp 2Qx (t )   l ( )dt

10Parameter estimation• MLE (Maximum Likelihood Estimation)1
  | ti   | lik   exp 
i 1 2
nis maximized.

• LSM (Least Square Method)Fpact ( t) 0 log( pact( ))t log(p( est)) t

 is minimized.
2

t11

The expected risk ofcollision• The expected risk of collision is calculated
assuming that the minimum initial time
separation is set to 10 minutes.
– Airspace A: 4.977×10-8– Airspace B: 2.688×10-8– TLS: 5.0×10-9• The risk of collision is greater than the TLS.
Is it risky to introduce 10 min. time
separation?
 The conventional calculation method causes anover-estimation.
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Reasons for overestimation 440kt 400kt 2 min. loss time
• The relative speed

20 min.

18 min.

– The distribution model is usually used to model theuncertainty of the system.
– Assuming that the following aircraft flies faster thanthe preceding aircraft, a positive loss time is to beexpected.

• The range of the initial time separation consistingof the loss distribution– Why does the loss distribution consist of the data
which have less than 60 minutes initial time
separation?
– The loss distribution by 60 minutes initial time
separation and 15 minutes initial time separation canbe different according to some factors (windconditions..).
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The relationship between
loss time & relative speedl  aV  b

Airspace A• A positive relative TAS (true air speed) is definedin the case when the following aircraft flies fasterthan the preceding aircraft.
• There seems to be a relationship between therelative TAS & the average loss time.
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Refined loss time
• Refined loss time: t  ti  (aVi  b)newl
• Refined loss distribution: m (t )• The probability that the loss time is greater

new
new
Q(t)
e(V)l(  (aV  b))dthan t: x


t m
V
newi

The relative TAS * the refined loss time
Original loss time distribution

can be different.

• The distribution of the convolution of thetwo dependent parameters can bedifferent from the original distribution.

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Refined risk of collision (1)Risk of collisionconsidering relative TAS

Risk of collision by
conventional method

Airspace A

1.949×10–8

4.977×10–8

Airspace B

5.462×10–9

2.688×10–8

TLS

5.0×10–9• The risk of collision is decreased when the relative
TAS is considered, but is still greater than the TLS.
Next, the range of the initial time separationconsisting of the loss distribution is considered.

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Abnormal values• The black line fits better with the data between -6and 6 minutes.
– The distribution gets wider wrongly because of a few17
abnormal values surrounded by blue rectangles.

Number of abnormal values
Initial timeseparation x
0 < x <= 20
20 < x <= 30
30 < x <= 40
40 < x <= 50
50 < x <= 60

Airspace A

Airspace B

0/526
0/1358
1/1187
1/972
2/761

0/506
0/1262
4/11152/862
2/722

The number of abnormal values / The number of all data

• The result implies that the number of abnormal
values depends on the initial time separation.
 Check by binomial test
– It CANNOT be said that the number of the abnormal
values is NOT related to the initial time separation. 18

The refined risk of collision(2)
Risk of collisionconsidering relative
TAS & 30 min. initialtime separation

Risk of collisionconsidering relative
TAS

Risk of collision by
conventional
methodAirspace A

2.394×10–9

1.949×10–8

4.977×10–8

Airspace B

1.425×10–10

5.462×10–9

2.688×10–8

TLS

5.0×10–9• The risk of collision issmaller than the TLS
in each airspace.
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Conclusions• A safety analysis was conducted under 10
minutes time-based separation in Fukuoka
FIR.
– The conventional safety assessment waslikely to cause an over-estimation
 Two factors were considered:• The relative true airspeed• The initial time separation– Using the refined method, it was proven thatthe risk of collision was less than the TLS.
This safety analysis was conducted under just one
hazardous condition.

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