The Analytic Blunder Risk Model (ABRM)

A computer model for predicting collision risk

Kenneth GeisingerOperations Research AnalystFederal Aviation Administration (retired)

aircraft collisions

Historically relatively rare

• About 10 midair collisions per year

• One involving an air carrier in about 10 years

But increasingly likely

• Doubling traffic increases risk by a factor of four

• Risky situations are increasing 10 to 25 percent per year

Examples of BlundersOperational error

• Controller mistakenly puts aircraft on conflicting courses

• Controller fails to take timely intervention

Pilot deviation• Pilot disobeys controller instructions

• Pilot breaks air traffic regulations

Equipment failure• Radio communication blocked or garbled

• Aircraft mechanical failure

Runway incursion• Aircraft or vehicle crosses active runway without clearance.

Purpose of the ABRM

The ABRM computes the risk of a specific blunder resulting in a collision. It considers “what-ifs”, such as:

• What if one the two aircraft had been at a slightly different location or on a slightly different heading when the blunder occurred?

• What if the controller had been slightly slower in responding?

• What if communication had been blocked temporarily?

Types of Models Step simulation models• The most common type of computer model

• Moves aircraft through space one step at a time and computes the results.

• Flexible but inefficient. Fairly easy to construct.

Analytic models• Uses mathematical equations rather than repeated steps.

• Efficient but requires simplifying assumptions. Relatively difficult to develop.

ABRM Assumptions

linear paths• Aircraft are assumed to maintain a constant speed and direction between the blunder and the point where the paths cross in the horizontal plane.

aircraft shape

• Aircraft are assumed to be discs with a specified thickness and radius, oriented parallel to the horizontal plane.

two aircraft

• Blunderer – the aircraft experiencing the blunder• Evader – the aircraft threatened by the Blunderer

Blind Flying Risk

Pbf depends upon the speed, direction, and sizes of the aircraft, and the number of aircraft per hour on the evader’s path. In order for this to be non-zero, the paths must cross in the horizontal plane within a vertical distance permitting the discs to touch.

Blind flying risk, Pbf, is defined as the probability of a collision assuming both aircraft continue on course without any avoidance action or maneuver.

If a blind-flying collision can occur, the time between the blunder and thecollision is computed.

Risk amelioration

aircraft not on a collision course Because the volume of sky is so large and the size of aircraft so relatively small, the chance of a collision should be small, even if nothing is done.

controller intervention

If either aircraft is under ATC, a controller most likely will intervene and cause one or both aircraft to alter course.

Pilot (visual and/or CAS) intervention

Suppose a blunder occurs. There are a number of reasons why it won’t result in a collision:

Either aircrew could detect the threat and correct for it, either by visual observation or a collision alerting device.

controller interventionThe probability of a successful controller intervention in time to preventa pending collision depends on the time it takes to complete three independent steps. (These are hypothetical data for illustration.)

0 2 4 6 8 10 12 seconds

Probability1.0

0.0

0 2 4 6 8 10 12 seconds0 2 4 6 8 10 12 seconds

0 2 4 6 8 10 12 seconds

Probability1.0

0.0

Probability1.0

0.0

Probability1.0

0.0

Controller reaction time

Airframe reaction time

Aircrew reaction time

total reaction time

1

3

2

Result

pilot interventionThe probability of a successful pilot intervention in time to preventa pending collision depends on the time it takes to complete three independent steps. (These are hypothetical data for illustration only.)

1.0 0.8 0.6 0.4 0.2 0 miles

Probability1.0

0.0

0 2 4 6 8 10 12 seconds0 2 4 6 8 10 12 seconds

0 2 4 6 8 10 12 seconds

Probability1.0

0.0

Probability1.0

0.0

Probability1.0

0.0

Pilot detects the threat

Airframe reaction time

Aircrew reaction time

total reaction time

1

3

2

Result

Hypothetical response time dataEVADER CONTROLLER ASSISTED RESPONSE TIMETotal time from blunder to evader avoidance manuever - computed. No user input.

MIN EVADER CONTROLLER ASSISTED RESPONSE TIME 46SECMAX EVADER CONTROLLER ASSISTED RESPONSE TIME 216 SECAVG EVADER CONTROLLER ASSISTED RESPONSE TIME 86.9 SECPROB. OF NO ATC DIRECTED EVADER CORRECTION: 0.0290

SEC PROB CUM46 0.0017 0.0017 0.07863748 0.0123 0.0140 0.58943550 0.0186 0.0326 0.92835352 0.0253 0.0578 1.3148954 0.0270 0.0849 1.4595756 0.0240 0.1089 1.34290758 0.0211 0.1300 1.22396360 0.0188 0.1487 1.12741562 0.0161 0.1649 1.00071264 0.0144 0.1793 0.92449766 0.0172 0.1966 1.13767268 0.0186 0.2152 1.26804970 0.0217 0.2369 1.51808372 0.0251 0.2620 1.80454774 0.0249 0.2869 1.84342976 0.0288 0.3156 2.18665878 0.0340 0.3496 2.64829980 0.0366 0.3862 2.92476382 0.0388 0.4250 3.18167284 0.0365 0.4614 3.06342286 0.0320 0.4934 2.75166788 0.0298 0.5232 2.62009290 0.0263 0.5495 2.36594792 0.0254 0.5749 2.33813994 0.0240 0.5989 2.25148696 0.0258 0.6246 2.47307598 0.0262 0.6508 2.570669

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

46 62 78 94 110

126

142

158

174

190

206

TIME (SEC)

EVADER CONTROLLER ASSISTED RESPONSE TIME

PROB

CUM

Visual detectionassuming that the aircraft are on a collision course

Collision point x

blunderer

evader

apparent path

evader path

blunderer path

Visual detection depends on:1.Visibility2.The size of the other aircraft3.Time available4.Closing rate5.Cockpit crew size6.Field of view

Apparent position of blunderer in evader field of view x

Apparent position of evader in blunderer field of view x

Probability of a CollisionThe probability of a collision, Pc, is then computed by:

Pc = Pbf *(1-Pba)*(1-Pbp)*(1-Pea)*(1-Pep)

Where:Pbf = probability of a blind-flying collisionPba = probability of blunderer ATC correctionPbp = probability of blunderer pilot correctionP ea = probabilit of evader ATC correctionPep = probability of evader pilot correction

Sensitivity analysesThe chance of a collision is very small and depends on the exact value ofmany variables which are not knowable except within a range of values. This is a graph of collision risk as a function of a combination of vertical and horizontal blunder angles computed within the ABRM for a sample problem.

Input data

Output data

RESULTS HORIZONTAL CLOSING RATE HCR 428.3 FPS VERTICAL CLOSING RATE VCR 35.2 FPS TOTAL CLOSING RATE TCR 429.7 FPS TIME UNTIL CROSSING TC 170.28 SEC

P(BLIND FLYING COLLISION | BLUNDER) PCC 9.75E-05

P(CONTROLLER ASSISTED BLUNDERER CORRECTION)PBC 0.9080 P(BLUNDERER SELF CORRECTION) PSC 0.4545 P(CONTROLLER ASSISTED EVADER EVASIVE ACTION) PEC 0.9687 P(TCAS CORRECTION) PT 0.976 P(NO CORRECTION) PNC 0.00004

P(COLLISION | BLUNDER) PCON 3.68E-09

NOTE:1. PCC = Probability of blind flying collision, given blunder2. PNC = (1-PBC)x(1-PSC)x(1-PEC)x(1-PT)3. PCON = PCCxPNC

Sample problem #1 airborne blunder - An MD-80 begins a descent across the path of an oncoming B-757 in level flight.Both are doing about 400 kts. The crossing angle is 60 degrees. The Blunderer is 6 nm from the path intersection when the blunder occurs. The visibility is 10 nm. There is one evader per hour on the evader path.

resultsTime between blunder and collision is 55 secondsBlind-flying collision probability = 1.03x 10 –4Probability of controller intervention on the Blunderer = 0.913Probability of controller intervention on the Evader = 0.959Probability of Blunderer visual detection and correction = 0.302Probability of Evader visual detection and correction = 0.223Probability of TCAS detection and correction = 0.976Probability of no correction = 5 x 10 –5Probability of collision = 4.7 x 10 - 9

Sample problem #2 surface blunder - A truck doing 20 kts. suddenly crosses an active runway in the path of anB757 doing 65 kts. in a take-off roll. The paths cross at a 90-degree angle.The Blunderer is 0.05 nm from the path intersection when the blunder occurs. The visibility is 2 nm. There are 35 Evaders per hour on the evader path.

resultsTime between blunder and collision is 8.5 seconds.Blind-flying collision probability = 3.22x 10 –2Probability of controller intervention on the Blunderer = 0.0Probability of controller intervention on the Evader = 0.0026Probability of Blunderer visual detection and correction = 0.012Probability of Evader visual detection and correction = 0.0014Probability of TCAS detection and correction = 0.0Probability of no correction = 0.984Probability of collision = 3.17 x 10 - 2

Conclusion

The ABRM is a practical tool for estimating collision risk under a wide range of scenarios.

The ABRM requires much data that are difficult to obtain. The ABRM allows hypothetical data to be used in the absence of real data to produce results that are approximately correct.

The ABRM is relatively easy to modify and extend .