statistical analysis of aircraft-bird strikes resulting in engine failure

1

STATISTICAL ANALYSIS OF AIRCRAFT–BIRD STRIKES 1

RESULTING IN ENGINE FAILURE 2

3 4 5

by 6 7 8 9

10 Kivanc A. Avrenli* 11

Graduate Research Assistant, Department of Civil and Environmental Engineering 12 B114 Newmark Civil Engineering Laboratory 13

University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA 14 E-Mail: [email protected] Phone:(217) 819-7856 15

16 Barry J. Dempsey 17

Professor Emeritus, Department of Civil and Environmental Engineering 18 1210 Newmark Civil Engineering Laboratory 19

205 N. Mathews Ave. Urbana, IL 61801 20 E-Mail: [email protected] Phone:(217) 333-3963 21

22 23 24 25

26 27 28 29 30

August 1, 2013 31 32 33

Word Count: 6,129 34 Figures and Tables: 5 × 250= 1,250 35

Total Word Count: 7,379 36 37

38 Submitted for presentation and publication at the 93rd Annual Meeting of the Transportation Research 39

Board 40

41

42

43 *: Corresponding Author 44 45

46

TRB 2014 Annual Meeting Original paper submittal - not revised by author

2

ABSTRACT 1

Engine failure due to bird strike can particularly be perilous for today’s typically twin-engine aircraft. 2 Although large bird populations have increased substantially since 1970s, modern-day turbofan engines 3 are not tested for large birds. Instead, it is acceptable for contemporary turbofan engines to lose all power 4 due to large bird ingestion. With the increasing use of turbofan engines and air traffic, not only more bird 5 strikes are expected in the near future, but also more bird strikes are anticipated to result in engine failure. 6 This study identifies the factors that are statistically associated with a higher probability of engine failure 7 in the event of a bird strike. A large sample of over 42,000 U.S. bird strikes is used. The missing data in 8 the sample are multiply imputed using an approximate Bayesian method. Using the multiply imputed 9 data, fourteen different factors are statistically analyzed. Six of those factors are found significantly 10 associated with the probability of engine failure in the event of a bird strike: altitude above ground level, 11 bird size, number of birds struck, flight phase, daylight and sky conditions. A logistic regression model is 12 developed and a detailed probabilistic interpretation of the model is given for practitioners. Using the 13 findings: i) aviation authorities can improve bird strike hazard mitigation strategies; ii) flight crews can 14 reduce the potential of bird strikes resulting in engine failure; iii) researchers can better understand the 15 nature of bird strikes, and develop a scientific approach to minimize the likelihood of engine failure in the 16 event of a bird strike. 17

INTRODUCTION 18

Bird strikes pose a growing threat to aviation. The annual number of reported bird strikes increased over 19 five times in the last three decades [1]. Since 1990, bird strikes led to 23 fatalities and 202 injuries [1]. 20 The economic losses due to bird strikes are alarming as well. Between 1990 and 2010, bird strikes gave 21 rise to 448,138 hours of aircraft downtime and $394.4 million monetary losses [1]. 22

Bird strikes can particularly be perilous if they result in bird ingestion and engine failure. On September 23 15, 1988, an Ethiopian Airlines Boeing 737-260 ingested a flock of pigeons into both engines shortly after 24 take-off from Bahir Dar Airport, Ethiopia. The aircraft had dual engine failure and attempted a gear-up 25 landing at Bahir Dar Airport. During the landing roll, it caught fire and 31 people aboard were killed [2]. 26 On September 22, 1995, a military Boeing 707 ingested multiple Canada geese shortly after take-off from 27 Elmendorf Air Force Base, Alaska. After the failure of the first and second engines, the aircraft crashed 28 into a wooded area and caught fire. All 26 people aboard were killed [3]. On November 10, 2008, a 29 Ryanair Boeing 737-800 went through several bird strikes on final approach to Ciampino Airport at 30 Rome, Italy. The bird strikes damaged both engines and affected engine thrust, but the aircraft 31 subsequently landed with no fatalities or serious injuries [4]. On September 29, 2009, a Ryanair Boeing 32 737-800 struck a flock of birds shortly after takeoff from Trapani Birgi Airport at Sicily, Italy. Both 33 engines received damage to fan blades, but the aircraft returned uneventfully to Trapani Birgi Airport [5]. 34 On January 15, 2009, a US Airways Airbus A320 struck multiple Canada geese and lost thrust in both 35 engines shortly after take-off from La Guardia Airport, New York. The aircraft was ditched on the 36 Hudson River, and one flight attendant was injured [6]. 37

PROBLEM DEFINITION 38

Engine failure due to bird strike can particularly pose threat to modern-day aircraft. This is because more 39 than 90 percent of the US fleet consists of twin-engine aircraft, which provide less redundancy than 40 yesterday’s three- or four-engine aircraft [1]. In the near future, more bird strikes are expected to result in 41 engine failure due to the following: 42

1. There has been a continuous increase in the populations of large (> 8.0 lb. /3.6 kg) birds owing to 43 several environmental protection actions. For example: 44


3

o The population of Canada geese1 has increased from around one million to more than four 1 million since 1990 [7]. 2

o The population of snow geese has increased from around 50,000 to more than one million since 3 1966 [7]. 4

o The populations of 13 other largest bird species increased significantly in the last four decades 5 [8]. 6

2. Despite the substantial increase in large bird populations, modern-day aircraft engines are not tested 7 for birds weighing greater than 8.0 lb [8]. 8 3. It is acceptable for a transport aircraft to lose all power due to ingestion of large2 birds as long as the 9 engines can be shut down and the damage is contained within the engine casing [8]. 10 4. Air traffic and the use of faster turbofan engines are continuously increasing [1]. 11

In view of the aforementioned factors, not only more bird strikes are expected in the near future [7], but 12 also more bird strikes are anticipated to result in engine failure. 13

OBJECTIVES AND POTENTIAL USES OF THE STUDY 14

The objective of this study is to identify the factors that are statistically associated with the probability of 15 engine failure in the event of a bird strike. For this purpose, the study uses FAA Wildlife Strike Database 16 that is publically available online [9]. Considering the available data, the study analyzes the following 17 fourteen factors: altitude above ground level (AGL), bird size, number of birds struck, daylight 18 conditions, engine position on aircraft, fog, aircraft mass, number of engines, phase of flight, 19 precipitation, season, sky conditions, airspeed and advance warning of birds. The goal is to find out the 20 statistical relationship between these factors and the probability of engine failure in the event of a bird 21 strike. Identifying this statistical relationship can bring about the following benefits: 22

1. Aviation authorities can more effectively assess the bird strike hazard to aircraft. 23 2. Bird strike hazard mitigation strategies can be improved in view of the findings. 24 3. The findings can be incorporated into pilot training programs so that flight crews become 25 knowledgeable about the risk of engine failure in the event of a bird strike. 26 4. Flight crews can utilize the findings to reduce the potential of bird strikes leading to engine failure. 27 5. The findings can help researchers understand the nature of bird strikes that result in engine failure. 28 Thereby, researchers can develop a scientific approach to reduce the potential of engine failure in the 29 event of a bird strike. 30

BACKGROUND 31

Although bird strikes pose growing threat to civil and military aviation, there is a limited number of 32 studies that statistically analyze bird strikes. Dolbeer [10] analyzed the altitude distribution of the bird 33 strikes that occurred between 1990 and 2004 in the US. He found that bird strike rates declined by a factor 34 of around 1.5 per 1000-ft. interval from 500 ft. AGL to 20,500 ft. AGL. 35

In another study, Dolbeer et al. [1] analyzed the wildlife strike reports submitted to the FAA between 36 1990 and 2010. Based on those reports, engines were the most frequently damaged aircraft component. 37 There were 3,663 bird strikes with one engine damaged, 118 with two engines damaged, one with three 38 engines damaged, and one with four engines damaged [1]. 39

Zalakevicius analyzed the bird strikes in Lithuania for the periods 1958 – 1978 and 1987 – 1991 [11]. 40 Most of those bird strikes occurred in the month of July (27 percent) and during the phase of descent (47 41 percent). Moreover, Jacoby [12] analyzed the pattern of bird strikes in Europe and discussed the 42 possibility of using bird strike prevention measures. 43

1 Weigh on average 9.2 lb. 2 Here, “large” refers to 1.8, 2.7 or 3.6 kg, depending on engine size.


4

DATA DESCRIPTION 1

The study uses data from the FAA wildlife strike database [9]. A large sample of 42,905 bird strikes is 2 analyzed. The sample includes all bird strikes that: 3

• occurred between January 1, 19903 and November 30, 2012; 4

• involved turbofan engine civil aircraft; 5

• occurred while the aircraft was airborne. 6

Thus, all findings apply to airborne aircraft-bird strikes that involve turbofan engine civil aircraft. 7 The data in the FAA Wildlife database are collected through voluntary reporting by pilots or airlines. 8 Table 1 lists the questions in the wildlife strike submission report. In view of these questions, fourteen 9 predictor variables and one response variable are analyzed. The response variable is called “ENG_FAIL”. 10 It is of binary nature and has two possible outcomes: “no engine failure” and “engine failure”. “No engine 11 failure” means that no engine stopped running or was shut down due to the bird strike. Conversely, 12 “engine failure” means that at least one engine stopped running or was shut down due to the bird strike. 13 Twelve of the fourteen predictor variables are categorical. The crosstabs of the categorical variables vs. 14 the response variable are given in Table 2. Variables such as “aircraft mass” and “number of birds struck” 15 are analyzed as categorical predictors because the FAA Wildlife Strike Database does not provide their 16 exact value. Table 3 presents the detailed coding of the categorical predictors for statistical analysis. All 17 categorical predictors having more than two levels have to be converted into dummy variables for 18 statistical analysis. The dummy variables used in the statistical analysis are given in the last column of 19 Table 3. 20

In addition to the twelve categorical predictors, there are two continuous predictors. The first one is 21 ALTITUDE, which indicates the altitude above ground level (AGL) that the bird strike occurred. The 22 second one is AIRSPEED, which shows the indicated airspeed of the aircraft at the time of the bird strike. 23

MISSING DATA 24

Since the data in the FAA Wildlife database are collected through voluntary reporting, some reports may 25 contain unanswered questions. Consequently, all unanswered questions result in missing data. The 26 amount of missing data in the study sample is as follows: ALTITUDE: 25.1%, BIRDSIZE: 14.4%, 27 B_STRUCK: 1.0%, DAYLIGHT: 16.5%, ENG_FAIL: 4.6%, ENG_POS: 0.0%, FOG: 30.5%, MASS: 28 5.4%, NO_ENG: 5.3%, PHASE: 8.3%, PRECIP: 29.6%, SEASON: 0.0%, SKY: 28.2%, AIRSPEED: 29 37.1%, WARNED: 38.6%. 30

Missing Data Mechanism 31

Since the data set includes extensive amount of missing data, the missing data mechanism should be 32 explored first. There are three different types of missing data mechanism [13]: 33 1. Missing Completely at Random (MCAR): The missing data mechanism is not related to the value of 34 any variables. For example, the data would be missing completely at random if some pilots accidentally 35 skipped questions in the wildlife strike submission report. 36 2. Missing at Random (MAR): The missing data mechanism is not related to the missing values, but it 37 is related to the observed values of other variables. For instance, the missing data for BIRDSIZE may not 38 be related to the actual bird size, but may be related to the values of DAYLIGHT. Perhaps some pilots 39 could not clearly see the birds during nighttime, and could not report BIRDSIZE. Thus, the amount of 40 missing data for BIRDSIZE may be greater for nighttime strikes. 41 3. Non-ignorable (NI): The missing data mechanism is related to the missing values. For example, 42 some pilots might not report the value of WARNED if they had not received advance warning. So when 43 the actual value of WARNED is “0” (see Table 3), it is more likely to be missing. 44

3 The starting date of the FAA Wildlife Strike Database.


5

Table 1. Questions in the FAA Wildlife strike submission report [9] 1

1. Name of Operator/ Carrier 2. Aircraft Make/ Model 3. Engine Make/ Model

4. Aircraft Registration 5. Data of Incident 6. Local Time of Incident

6A. Flight Number 6B Wildlife/ Bird Remains

�Collected �Sent to Smithsonian

7. Airport Name/ ID 8. Runway Used 9. Location if En Route and/ or Distance From Airport

10. Height (AGL) 11. Speed (IAS)

___________________ ft. __________________ kts.

12. Phase of Flight 13. Part(s) Struck or Damaged 13. (Con't)

Struck Damaged Struck Damaged

A. Radome H. Propeller

B. Windshield I. Wing/ Rotor

C. Nose J. Fuselage

D. Engine #1 K. Landing Gear

E. Engine #2 L. Tail

F. Engine #3 M. Lights

G. Engine #4 N. Other

Bird(s) Ingested? � (Specify if "N. Other is checked)

14. Effect on Flight 15. Sky Condition 16. Precipitation

�None �No cloud �Fog

�Aborted Take-Off �Some cloud �Rain

�Precautionary Landing �Overcast �Snow

�Engine Shutdown �None

�Other(specify)

17. Bird/ Other Wildlife Species 18. Number Seen and/ or Struck 19. Size of Birds

�Small

�Medium

�Large

20. Pilots Warned of Birds/ Wildlife? �Yes �No

22. Aircraft time out of service

________________ hours

23. Estimated cost of repairs or replacement (US$)

24. Estimated other costs (US$)

2

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �


6

Table 2. Crosstabs of the categorical predictors vs. the response variable 1

Variable and Name of Variable Levels

Number of bird strike events

No engine failure

Engine failure Missing

Bird size

(BIRDSIZE)

Small 18,941 15 823

Medium 16,132 57 640

Large 2,511 62 127

Missing 6,047 32 518

Number of birds struck (B_STRUCK)

One 2-10 More than 10 Missing

36,981 5,791

382 476

99 55 13 0

1,614 478

15 1

Daylight conditions (DAYLIGHT)

Daytime 18,100 85 1142

Nighttime 15,358 35 779

Twilight (Dusk/ Dawn) 2,736 30 56

Missing 7,437 16 131

Engine position on aircraft (ENG_POS)

Under-wing 26,302 87 1009

Aft-fuselage 15,888 78 1060

Both under-wing and aft-fuselage 1,441 1 39

Missing 0 0 0

Is there fog? (FOG)

No fog 28,947 120 2011

Fog 764 4 43

Missing 13,920 42 54

Aircraft Mass (kg) (MASS)

Less than 2,250 300 0 19

2,251 - 5,700 490 7 26

5,701 - 27,000 6,274 28 274

27,001 - 272,000 33,722 115 1756

Heavier than 272,000 398 16 11

Missing 2,447 0 22

Number of turbofan engines (NO_ENG)

Two 35,906 131 1719

Three 4,404 15 315

Four 903 20 53

Missing 2,418 0 21

Flight phase (PHASE)

Climb 10,821 139 536

Descent 28,854 27 1464

Cruise (i.e. En-route) 242 0 4

Missing 3,714 0 104

Is there precipitation? (PRECIP)

No precipitation 28,384 117 1958

Rain /Sleet /Snow 1,722 9 150

Missing 13,525 40 0

Season (SEASON)

Winter 4,706 31 223

Spring 10,991 46 487

Summer 12,118 29 586

Fall 15,816 60 812

Missing 0 0 0

Sky Conditions (SKY)

Clear 16,322 43 1189

Some Clouds/ Overcast 14,417 87 888

Missing 12,892 36 31

Pilots warned of birds? (WARNED)

No 16,696 65 1239

Yes 9,615 44 511

Missing 17,320 57 358 2

3

4


7

Table 3. Categorical variables analyzed in this study 1

Variable Name

Variable Description

Levels Dummy variables

ENG_FAIL BIRDSIZE B_STRUCK DAYLIGHT ENG_POS FOG MASS NO_ENG PHASE PRECIP SEASON SKY WARNED

At least one engine stopped running due to strike or pilot shut down the engine after strike Bird size as reported by the flight crew Number of birds that struck the aircraft Whether the bird strike occurred during daytime, nighttime, or dusk/ dawn Where engines are mounted on aircraft Was there fog? Aircraft mass Number of turbofan engines that aircraft has Phase of flight during which strike occurred Was there precipitation? Did the strike occur during the birds’ migration season (i.e. Spring/ Fall)? Was there any cloud cover? Were the pilots warned of birds?

0=Noa 1=Yes 0=Smalla 1=Medium 2=Large 0=One birda

1=2-10 birds 2=More than 10 birds 0=Daytimea 1=Nighttime 2=Twilight (dusk/ dawn) 0=All below the winga 1=All on the aft fuselage 2=Both below the wing and on the aft fuselage 0=Noa 1=Yes 0=Below 2,250 kga 1=2,251 – 5,701 kg 2=5,701 – 27,000 kg

3=27,001 – 272,000 kg 4=Above 272,000 kg 0=Twoa 1=Three 2=Four 0=Climba 1=Decent/ Approach/ Landing 2=En-route 0=No precipitationa 1=Rain/ sleet/ snow 0=Wintera 1=Spring 2=Summer 3=Fall 0=Cleara (no cloud cover) 1=Cloudy/ overcast 0=Noa 1=Yes

Same as ENG_FAIL

B1=1 for BIRDSIZE=1; 0 otherwise. B2=1 for BIRDSIZE=2; 0 otherwise. C1=1 for B_STRUCK=1; 0 otherwise. C2=1 for B_STRUCK=2; 0 otherwise. D1=1 for DAYLIGHT=1; 0 otherwise. D2=1 for DAYLIGHT=2; 0 otherwise. E1=1 for ENG_POS=1; 0 otherwise. E2=1 for ENG_POS=2; 0 otherwise. Same as FOG

M1=1 for MASS=1; 0 otherwise. M2=1 for MASS=2; 0 otherwise. M3=1 for MASS=3; 0 otherwise. M4=1 for MASS=4; 0 otherwise. N1=1 for NO_ENG=1; 0 otherwise. N2=1 for NO_ENG=2; 0 otherwise. P1=1 for PHASE=1; 0 otherwise. P2=1 for PHASE=2; 0 otherwise. Same as PRECIP

S1=1 for SEASON=1; 0 otherwise. S2=1 for SEASON=2; 0 otherwise. S3=1 for SEASON=3; 0 otherwise. Same as SKY

Same as WARNED

a:Reference level for the given categorical variable 2

3


8

“Little’s MCAR Test” [14] and “Separate Variance t-Tests” [13] are run to determine if the data are 1 MCAR and MAR, respectively. All tests returned p-values well below α=0.05. Thus, there is sufficient 2 evidence to believe that the data are neither MCAR nor MAR. It is concluded that the missing data 3 mechanism is non-ignorable. 4

Handling Non-Ignorable Missing Data 5

There are three approaches to handle missing data [13], [15]: 6 1. Complete-case analysis (list-wise deletion): All bird strike cases with at least one missing value are 7 excluded from analysis, and the remaining cases are analyzed. 8 2. Single imputation: A plausible value is substituted for each missing value, and the filled-in data set is 9 analyzed as if it’s complete. 10 3. Multiple imputation: Each missing value is substituted with a set of plausible values to represent the 11 uncertainty about the prediction of the missing values. 12

In the case of non-ignorable missing data, complete-case analysis produces sample selection bias [16] 13 because the probability of a missing value depends on the variable itself. Thus, the missing data should be 14 imputed prior to statistical analysis. Single imputation is computationally less demanding than multiple 15 imputation. However, it does not incorporate the uncertainty about the predictions of the missing values 16 because each missing value is imputed by only one plausible value. Thus, single imputation 17 underestimates the standard errors of the parameter estimates [15]. On the other hand, multiple imputation 18 accounts for uncertainty about the predictions of the missing values [17]. So the missing data are multiply 19 imputed in the following section. 20

Multiple Imputation 21

While there are several different multiple imputation techniques, Siddique and Belin’s [17] Approximate 22 Bayesian Bootstrap (ABB) method is chosen to multiply impute the missing data because of the following 23 reasons: 24

• The imputations are based on values observed elsewhere. Thereby, the method imputes realistic 25 values that are not outside the range of the possible values [18]. 26

• It does not require the definition of an explicit model for the distribution of the missing values [18]. 27

• It can properly reflect parameter uncertainty [19]. 28

• It can incorporate all available information into the imputation model [19]. 29

• Contrary to most other multiple imputation methods, it is capable of imputing non-ignorable 30 missing data [17]. 31

• Through a simulation study, Siddique and Belin showed that their ABB method can produce 32 unbiased estimates of the true parameters when the amount of complete cases is as low as 50% [17]. 33

Siddique and Belin’s ABB method is a hot-deck imputation method that imputes one variable at a time. 34

To briefly explain the steps of the method, take the case of a random variable called �, for instance. 35 Suppose variable Y is one of the several variables in a data set. Variable � has �� observed values, 36 and �� missing values. Thus, there are �� cases in the data set with the value of variable � missing. 37

To impute variable �, the following steps are followed [19]: 38

1. A bootstrap sample of �� cases is randomly drawn with replacement4 from the �� cases in the 39

data set. The probability of drawing case � into the bootstrap sample is defined by Equation (1) [17]: 40

�� = ��∑ ��=1 (1)

4 Since sampling with replacement is carried out, some cases may appear more than once in the bootstrap sample whereas some others may not appear at all.


9

where 1 ��: Probability of drawing case � into the bootstrap sample. 2 �: The ith observed value of �. 3 �: Constant. 4

2. If the other variables in the bootstrap sample have missing values, they are temporarily imputed with 5 starting values. Once all variables are imputed with starting values, they are re-imputed iteratively until 6 convergence criteria are achieved [18]. 7 8 3. Using the bootstrap sample, variable � are regressed over all other variables. Then using the 9

regression model, predicted values (��) are computed for all cases in the data set. This step is called 10 predictive mean matching [20]. 11 12

4. The jth missing value of � (i.e. donee �) is imputed with a randomly selected observed value of � 13 (i.e. donor). The probability of imputing donee �with donor � is defined by Equation (2) [18]: 14

��, �� = � �� !�"#�$⁄∑ � ��& ��!�"#�$⁄'()*&+,

(2)

where 15 ��: Probability of imputing donee �with donor �. 16 ��: Predicted value for donee �. 17 ��/ ��: Predicted value for donor �/ donor .. 18 / = .�� − �� for all � = 1,… , �� and �� ≠ ��. 19 3: Closeness parameter; 3 = 1 (Siddique and Belin [17] recommend using 3 in the range of 1 − 2 to 20 avoid shrinking the size of the donor pool for non-ignorable missing data). 21

Following steps 1-4, one variable is imputed at a time in the study sample. In predictive mean matching 22 (step 3), all other variables in the data set are used as predictors to make use of all available information. 23 In addition to the variables listed in Table 3, two “auxiliary” categorical variables that are not later 24 incorporated into statistical analysis are used in predictive mean matching. These auxiliary variables are: 25 5� INGESTION (i.e. whether birds are ingested into at least one engine or not); 55� ENGINE_DAMAGE 26 (whether at least one engine is damaged or not due to bird strike). Using auxiliary variables can help 27 minimize bias in predictive mean matching [21]. 28

Steps 1-4 are repeated five times so that five different imputed data sets are created. Siddique and Belin 29 [17] recommend using a different closeness parameter for each imputed data set. This approach is called a 30 “mixture ABB approach”. It can account for more uncertainty and avoid overly precise parameter 31 estimates [17]. The closeness parameters should be selected based on missing data assumptions. Missing 32 data assumptions are always required in multiple imputation of non-ignorable missing data, and they 33 should reflect the presumed cause of missingness [17]. The following section explains the missing data 34 assumptions in this study. 35

Missing Data Assumptions 36

Since the FAA wildlife strike database relies on voluntary reporting of bird strikes, missing data occur 37 when respondents skip one or more questions in the FAA wildlife strike submission report. However, as 38 shown in Table 1, the report consists of a single page that can be effortlessly filled out. So the question is: 39 why are there so many skipped questions among the submitted reports? 40

One reason is that some wildlife strike reports might not be submitted by the flight crew. If someone other 41 than the flight crew fills out the report, he/ she may not know all the details regarding the bird strike. 42


10

However, if the report is filled out by the flight crew, what would be a major cause for skipped questions? 1

A probable reason for skipped questions is explained as follows: Take the case of variable WARNED in 2 Table 3, for instance. WARNED equals 1 if the pilots received advance warning of birds; 0 otherwise. It 3 is assumed that pilots who had not received advance warning were more likely to skip the question 4 “Pilots warned of birds?” in the report (see Table 1). Thus, WARNED is more likely to be missing if its 5 actual value is 0. Likewise, take the case of the variable PRECIP in Table 3, for example. It is assumed 6 that pilots were more likely to skip the question regarding precipitation if there had been no precipitation 7 at the time of the bird strike. Thus, PRECIP is more likely to be missing if its actual value is 0. So overall, 8 missing values are assumed to be less than observed values. 9

When missing values are deemed overall less than observed values, Siddique and Belin [17] recommend 10 using = 6−3,−2,−1, 0, 19 in Equation (2). So five imputed data sets are created using 3 =11 6−3,−2,−1, 0, 19. Negative values of 3 assign higher probability to donors with smaller values because 12 missing values are deemed overall less than observed values. Conversely, positive values of 3 (i.e. 3 =13 1) assign higher probability to donors with bigger values. The reason for using 3 = 1 is to account for 14 some uncertainty about the missing data assumption, and reduce the effect of subjectivity [17]. 15

STATISTICAL ANALYSIS 16

Multivariate Logistic Regression Model 17

After creating five imputed data sets, each data set is analyzed separately first. Since the response variable 18 (i.e. ENG_FAIL) is binary, the five data sets are analyzed using multivariate logistic regression, which is 19 the most popular statistical model for binary response data [22]. The general form of a multivariate 20 logistic regression model is given in Equation (3) [22]: 21

:� ; <�� <�= = >?@ + ∑ B� ∗ >?�D�E� (3)

where 22 = Estimated probability of engine failure in the event of a bird strike. 23

<��"<�= Estimated odds of engine failure in the event of a bird strike. 24

:� ; <�� <�== Natural logarithm of the estimated odds of engine failure in the event of a bird strike (i.e.“logit 25

function”). 26

>?@= Estimated intercept. 27 B�= Predictor i (continuous or categorical). 28

>?�= Estimated coefficient of predictor i. 29

As shown in Equation (3), a multivariate logistic regression model assumes linear relationship between 30

the predictors (i.e. B�) and the natural logarithm of the estimated odds, i.e. :� ; <�� <�=. 31

Variable Selection 32

All continuous and dummy variables (see Table 3) are initially included in the model. To select the 33 predictor variables that significantly contribute to the model in Equation (3), the following steps are 34 followed [23]: 35

1. Starting with initial guess for the predictor coefficients (>�), the log-likelihood function is computed 36 for each imputed data set using Equation (4): 37


11

:� GH ;>?�=I = ;>?�JB�=�� − � ∗ :� G1 + KL ;>?�J B�=I (4)

where 1 .: Number of imputed data set. 2 >?�J : Vector of estimated coefficients for imputed data set m. 3 B�: Vector of the predictors for imputed data set m. 4 ��: Vector of the response variable (ENG_FAIL) for imputed data set m. 5

H ;>?�=: The value of the likelihood function for >?�. 6

�: Sample size. 7 8

2. Using Fisher’s scoring algorithm [22], the coefficient estimates (>?�) that maximize the likelihood 9

function in Equation (4) is found. 10 11 3. The estimated covariance matrix of the coefficient estimates is computed using Equation (5): 12

M��N = B�JOP�B�� (5)

where 13 M��N : Estimated covariance matrix for >?�. 14

OP�: A diagonal matrix with entries � ∗ Q�1 − Q��. Q� is the estimated probability of engine 15

failure for � trials given B�. 16

17 4. The inferences across the five imputed data sets are combined following the rules of nested multiple 18 imputation [24]. The coefficient estimates in the final model are computed using Equation (6) [24]: 19

>?� = �R∑ >?�,�R�E� (6)

where 20 >?�: Coefficient estimate of predictor i in the final model. 21 .: Number of imputed data set. 22 >?�,�: Coefficient estimate of predictor i in imputed data set m. 23

24 5. The estimated standard errors of the coefficient estimates in the final model are computed using 25 Equation (7) [24]: 26

M�� = �R S∑ M��,�R�E� + ∑ >?�,� − >?��NR�E� T (7)

where 27 M��: Estimated standard error of >?�. 28 M��,�: Estimated standard error of >?�,�. 29

30 6. The Wald statistic is computed for each predictor using Equation (8): 31

U�N = �>?� M��⁄ �N (8)

where 32 U�N: Wald statistic for predictor i. 33 34 For large samples, the Wald statistic is adequate to assess the contribution of the predictors to the model 35


12

[22]. It asymptotically follows Chi-Square distribution with one degree of freedom and tests for 1 H0: >� = 0 vs. HA: >� ≠ 0. 2 3 7. A continuous variable is dropped if its Wald Statistic returns a p-value greater than α=0.05. A 4 categorical predictor is dropped if the Wald statistics of all its dummy variables return p-values greater 5 than α=0.05. 6 7 8. Dropping one predictor at a time, steps 1-7 are repeated until no more predictors can be dropped. In 8 the end, six predictors are found to contribute significantly (α=0.05) to the model: ALTITUDE, 9 BIRDSIZE, B_STRUCK, DAYLIGHT, PHASE, SKY. These are called “main effects” in the 10 multivariate logistic regression model. 11 12

9. There are also �VN� = 15 possible two-way interaction terms that can be included in the model (e.g. 13

ALTITUDE*SKY). To find out if any of the two-way interaction terms contribute significantly to the 14 model, one of the 15 possible two-way interaction terms is added to the existing predictors in the model. 15 Then steps 1-5 are run. If the Wald statistic of the two-way interaction term is found significant at α=0.05, 16 it is kept in the model; otherwise, it is dropped. 17

18 10. The following two-way interaction term is added to the existing predictors in the model, and steps 1-5 19 are repeated until all 15 two-way interaction terms are tested. In the end, only one two-way interaction 20 term is found to contribute significantly (α=0.05) to the model: ALTITUDE*PHASE. The final model is 21 given in Equation (9), and the coefficient estimates are summarized in Table 4. 22 23

:� X 1 + Y = −6.80 − 0.17 ∗ ^ + 1.90 ∗ �� + 3.51 ∗ �N + 1.22 ∗ �� + 2.59 ∗ �N − 0.24 ∗ a�

+0.68 ∗ aN − 2.42 ∗ � − 14.02 ∗ N + 0.65 ∗ � + 0.18 ∗ ^ ∗ � + 0.24 ∗ ^ ∗ N

(9)

24 where 25 = Estimated probability of engine failure in the event of a bird strike. 26 ^= Altitude above ground level (in 1000 ft.). 27 ��=1 if the bird strike involves medium-sized bird(s); 0 otherwise. 28 �N=1 if the bird strike involves large-sized (i.e. > 8.0 lb) bird(s); 0 otherwise. 29 ��=1 if 2-10 bird(s) are struck; 0 otherwise. 30 �N=1 if more than 10 bird(s) are struck; 0 otherwise. 31 a�=1 if the bird strike occurs during nighttime; 0 otherwise. 32 aN=1 if the bird strike occurs during twilight; 0 otherwise. 33 �=1 if the bird strike occurs during descent, approach or landing; 0 otherwise. 34 N=1 if the bird strike occurs when the aircraft is en-route; 0 otherwise. 35 �=1 if the bird strike occurs in cloudy or overcast sky conditions; 0 otherwise. 36 37

38 39 40 41 42 43


13

Table 4. Summary of the coefficient estimates for the final model 1

Variable

Coefficient Estimate

(>?�) Estimated Standard

Error

Wald StatisticUN�

p-valuea of

the UN

Intercept -6.80 0.40 283.5 0.000 ALTITUDE -0.17 0.07 5.9 0.015 B1 1.90 0.39 23.7 0.000 B2 3.51 0.37 91.4 0.000 C1 1.22 0.25 23.5 0.000 C2 2.59 0.90 8.3 0.004 D1 -0.24 0.32 0.6 0.451 D2 0.68 0.31 4.7 0.030 P1 -2.42 0.34 50.3 0.000 P2 -14.02 0.67 439.8 0.000 SKY 0.65 0.24 7.2 0.007 ALTITUDE*P1 0.18 0.10 3.4 0.065 ALTITUDE*P2 0.24 0.09 6.7 0.009

a: The p-value tests “H0: The coefficient of the predictor in the model is 0.” vs. “HA: The coefficient of the predictor 2 in the model is not 0.” 3

Model Goodness-of-Fit 4

The Hosmer and Lemeshow Test [25] is widely used to assess the goodness-of-fit for logistic regression 5 models. The test ranks the data based on predicted probabilities, and then divides the ranked data into 10 6 groups of equal size. Next, it compares the observed and predicted probabilities within each group. The 7

test statistic, cH, approximately follows UN distribution with eight degrees of freedom and tests for 8 H0: The predicted and observed probabilities do not differ significantly. vs. HA: The predicted and 9 observed probabilities differ significantly. The test statistic is computed using Equation (10): 10

cH = ∑ �de fe�gfe∗�� fe De⁄ ��@hE� (10)

where 11 i= Group number (1, 2,…, 10). 12 cH= Hosmer and Lemeshow test statistic. 13 jh= Observed count of engine failure in data group i. 14 kh= Summation of the predicted probabilities of engine failure in data group i. 15 �h= Number of observations in data group i. 16

17 However, there is no standard way of applying the Hosmer and Lemeshow Test for multiply imputed 18 data. This is because the predicted probabilities and the data groups vary across multiply imputed data 19 sets [26]. In a recent simulation study, Sullivan and Andridge [26] compared different methods of 20 applying Hosmer and Lemeshow Test to multiply imputed data. They found that Meng and Rubin’s 21 Likelihood Ratio Test (LRT) Combining Method [27] was the most promising in controlling Type I Error 22 rate when the method is applied to 3-6 multiply imputed data sets. Meng and Rubin’s LRT Combining 23 Method is summarized as follows [27]: 24 25 1. Using the final coefficient estimates found from Equation (6), compute the cH statistic for each 26 multiply imputed data set. 27

2. Calculate the average of the cH statistics found in step 1. This test statistic is called cHl�D�mno�Dpq. 28


14

3. Using the data set-specific coefficient estimates, compute the “regular” cH statistic for each 1 multiply imputed data set. 2

4. Calculate the average of the cH statistics found in step 3. This test statistic is called 3 cHrDl�D�mno�Dpq. 4

5. The final test statistic s� approximately follows t distribution with 3, u� degrees of freedom 5 under the null hypothesis. The statistic s is computed using Equation (11): 6

s = cH��vw^��KaxG�" &y,$&z,�∗||}~'�('*��'�� |}�('*��'��|I ∼ t3, u� (11)

where 7 3 = i − 2 = 10 − 2 = 8 8 . = Number of multiply imputed data sets (. = 5). 9

u = 4 + 3 ∗ . − 3 − 4� ∗ �1 + ;1 − Nx∗� ��= ∗ �.+13�.−1�∗�cH��vw^��Ka−cH��vw^��Ka�� 10

11 The test statistics are found as follows: cHl�D�mno�Dpq = 9.51, cHrDl�D�mno�Dpq = 3.78, 12 u = 102,s = 0.57, and the p-value for s is 0.798. The p-value for s does not indicate sufficient 13 evidence (α=0.05) against the null hypothesis. Therefore, it is concluded that the model can accurately 14 predict the probability of engine failure in the event of a bird strike. 15

MODEL IMPLICATIONS FOR PRACTITIONERS 16

Equation (9) can be rearranged to estimate the probability of engine failure () in the event of a bird strike 17 as follows: 18

= K V.�@ @.��o"�.�@�,"�.R��g"�.NNl,"N.R�lg @.N�q,"@.V�qg N.�N<, ��.@N<g"@.VR�"@.��o<,"@.N�o<g1 + K V.�@ @.��o"�.�@�,"�.R��g"�.NNl,"N.R�lg @.N�q,"@.V�qg N.�N<, ��.@N<g"@.VR�"@.��o<,"@.N�o<g (12)

Using Equation (12), the predicted probability of engine failure in the event of a bird strike is plotted 19 versus altitude AGL in Figures 1a-1e for certain combinations of predictors. With the help of Figures 1a-20 1e, the following sections explain the statistical relationship between each predictor and the predicted 21 probability of engine failure in the event of a bird strike. 22

It should be noted that Figures 1a-1e illustrate the predicted probabilities up to an altitude of 7,000 ft. 23 AGL. This is because more than 95% of the observed bird strikes occurred below this altitude. Hence, the 24 results inferred in this section typically apply up to an altitude of 7,000 ft. AGL. 25

Altitude AGL 26

The results in Table 4 indicate significant interaction between altitude and flight phase. So for each flight 27 phase, there is a different pattern of relationship between altitude AGL and the probability of engine 28 failure in the event of a bird strike. Figure 1a illustrates this relationship for the flight phases of climb and 29 descent, assuming medium-sized birds, 2-10 birds struck, daytime and clear sky conditions. The predicted 30 probability of engine failure in the event of a bird strike declines by around 15% with every 1,000-ft. 31 altitude gain during climb, controlling for bird size, number of birds struck, daylight and sky conditions.32


(a)

(b)

(c)

(d)

(e)

Figure 1. Probability of engine failure vs. altitude AGL, highlighting the statistical associations with: (a) Flight phase (b) Bird size, (c)

Number of birds struck, (d) Sky conditions, (e) Daylight conditions.


16

Comparison of the observed5 and predicted probabilities illustrated in Figure 1a confirms the accuracy of 1 the estimated pattern. 2

During the phase of climb, lower altitudes are significantly more hazardous in terms of engine failure in 3 the event of a bird strike. Therefore: 4

• Wildlife management programs should particularly focus on airport environments. 5

• During the initial climbout, which is statistically the most hazardous period of flight in terms of 6 engine failure due to bird strike, flight crews should be extremely vigilant. 7

• The more hazardous lower altitudes should be cleared as rapidly as possible. This can be achieved 8 by using speeds closer to Vx

7 or Vy6, and flap settings that provide higher rate of climb. For instance, if 9

there is sufficient runway length, Boeing 737-800 pilots can use flaps 1 instead of flaps 5 to increase the 10 rate of climb. 11

Contrary to the phase of climb, the predicted probability of engine failure in the event of a bird strike 12 remains virtually constant with altitude AGL during descent, controlling for bird size, number of birds 13 struck, daylight and sky conditions. Comparison of the observed and predicted probabilities plotted in 14 Figure 1a confirms this fairly constant pattern. 15

Flight Phase 16

Figure 1a shows the statistical relationship between flight phase and probability of engine failure in the 17 event of a bird strike. Although most bird strikes occur during approach/ descent (see Table 2), bird 18 strikes during climb are more likely to result in engine failure. At lower altitudes (i.e. <1,000 ft. AGL), a 19 bird strike during climb is statistically around 11 times more likely to lead to engine failure than that 20 during approach. At higher altitudes such as 6,000 ft. AGL, a bird strike during climb is statistically 21 around four times more likely to cause engine failure than that during descent. Therefore, bird strikes 22 during climb are substantially more hazardous in terms of engine failure than those during approach/ 23 descent. Hence, the following should be considered by aviation experts: 24

• Airports with limited resources are recommended to prioritize the prevailing aircraft climb paths in 25 their wildlife management programs. 26

• Generally, climb speeds closer to Vy6 are preferred over Vx

7 for two main reasons: 5� Climb 27 speeds closer to Vy provide better fuel economy [28]. 55� Climb speeds closer to Vy minimize the time 28 spent at the more hazardous lower altitudes. However, climb speeds closer to Vx can better improve flight 29

safety for two reasons: 5� Because Vx is always significantly lower than Vy, it can reduce the impact 30 energy in the event of a bird strike and reduce the likelihood of severe engine damage and engine failure 31

[28]. 55�Using Vx during climb provides the aircraft with maximum power-off gliding range if all 32 engines fail due to bird strike [29]. This enhances the likelihood of safely returning to a runway when all 33 engines fail due to bird strike. 34

• Pilot training programs should give more prominence to emergency landing procedures initiated 35 after single or dual engine failure due to bird strike during climb. 36

• Since more bird strikes are expected to result in engine failure in the near future, more bird strikes 37 can result in dual engine failure as in the case of Ethiopian Airlines Flight 604 or US Airways Flight 38 1549. Thus, software programs can be developed to optimize the emergency landing path of twin-engine 39 aircraft on a real-time basis in the event of a dual engine failure due to bird strike during climb. 40

41

5 Observed probabilities are computed from all five imputed data sets. 6 Best rate of climb speed. 7 Best angle of climb speed.


17

Bird Size 1

Assuming phase of climb, 2-10 birds struck, daytime and clear sky conditions, Figure 1b exemplifies the 2 relationship between bird size and the predicted probability of engine failure in the event of a bird strike. 3 A bird strike involving medium-sized bird(s) is statistically around six times more likely to lead to engine 4 failure than that involving small-sized bird(s), controlling for altitude AGL, number of birds struck, flight 5 phase, daylight and sky conditions. Mallard and herring gull accounted for 14 and 11 percent8 of the bird 6 strikes with engine failure, respectively, involving medium-sized birds. 7

A bird strike involving large (i.e. > 8.0 lb.) bird(s) is statistically around 30 times more likely to bring 8 about engine failure than that involving small-sized bird(s), controlling for altitude AGL, number of birds 9 struck, flight phase, daylight and sky conditions. Thus, large birds are extremely hazardous. Canada geese 10 accounted for 38 percent8 of the bird strikes with engine failure involving large bird species, followed by 11 double-crested cormorant (14%), snow goose (12%), black vulture (6%) and turkey vulture (6%). 12

In view of the continuous increase in large bird populations, aviation practitioners should consider the 13 following: 14

• Future designs of turbofan engines are strongly encouraged to be tested for large birds to provide 15 protection against large bird ingestions beyond the current FAA requirements [8]. 16

• Wildlife management programs at airport environments should involve species-specific means of 17 controlling attractants, particularly for large bird species such as Canada goose, double-crested cormorant, 18 snow goose and black/ turkey vulture. 19

Number of Birds Struck 20

Figure 1c illustrates the relationship between number of birds struck and the predicted probability of 21 engine failure in the event of a bird strike, assuming phase of climb, medium-sized birds, daytime and 22 clear sky conditions. A bird strike involving 2-10 birds is statistically around three times more likely to 23 result in engine failure than that involving a single bird, controlling for altitude AGL, bird size, flight 24 phase, daylight and sky conditions. If the bird strike involves more than 10 birds, it is statistically around 25 12 times more likely to result in engine failure that that involving a single bird. Flocks of gulls and 26 Canada geese accounted for 26 and 21 percent8 of the bird strikes, respectively, that involved multiple 27 birds and led to engine failure. 28

If flocks of birds are observed near the runway: 29

• Flight crews should delay take-off until runway is clear of birds. 30

• Flight crews should consider delaying landing (if fuel permits) or diverting to another runway that 31 is clear of birds. Otherwise, they should plan on additional landing distance because a possible bird strike 32 may disable thrust reversers [7]. 33

Daylight and Sky Conditions 34

Assuming phase of climb, medium-sized birds, 2-10 birds struck, and clear sky conditions, Figure 1d 35 exemplifies the relationship between daylight conditions and the predicted probability of engine failure in 36 the event of a bird strike. While most bird strikes occur during daytime (see Table 2), the predicted 37 probability of engine failure in the event of a bird strike is the highest during twilight (i.e. dusk/ dawn), 38 controlling for the other covariates in the model. Statistically, the probability of engine failure in the event 39 of a bird strike is around 90 percent higher during twilight than during daytime, controlling for altitude, 40 flight phase, bird size, number of birds struck and sky conditions. Canada geese, though not particularly 41

8 Among the cases in which the bird species were identified.


18

known for being crepuscular9 [30], were involved in 20 percent10 of the bird strikes with engine failure 1 during twilight, followed by mourning doves (15%) and gulls (15%). 2

Figure 1e illustrates the relationship between sky conditions and the predicted probability of engine 3 failure in the event of a bird strike, assuming phase of climb, medium-sized birds, 2-10 birds struck, and 4 daytime. Statistically, the probability of engine failure in the event of a bird strike is around 80 percent 5 higher during cloudy sky conditions than during daytime, controlling for altitude, flight phase, bird size, 6 number of birds struck and daylight conditions. Gulls account for 21 percent10 of the bird strikes with 7 engine failure in cloudy sky conditions, followed by Canada geese (18%) and double-crested cormorant 8 (7%). 9

It is not known why there is such a statistically significant increase in the probability of engine failure in 10 the event of a bird strike during twilight and cloudy sky conditions. However, the FAA Wildlife Strike 11 Data [9] provide strong evidence for this since the estimated coefficients of both D2 and SKY in Equation 12 (9) return p-values well below α=0.05 (see Table 4). 13

As for the nighttime, Canada geese and snow geese accounted for 27 and 15 percent10 of the bird strikes 14 with engine failure, respectively. Although many bird species are not nocturnal [30], bird strikes can still 15 occur at night and result in engine failure. Equations (9) and (11) suggest that a bird strike during 16 nighttime is statistically 20 percent less likely to result in engine failure compared to a daytime strike, 17 controlling for altitude, bird size, number of birds struck, flight phase and sky conditions. However, there 18 is not strong evidence to justify this because the coefficient of D1 in Equation (9) returns a p-value of 19 0.451, which is considerably higher than α=0.05 (see Table 4). Nevertheless, the results are noteworthy in 20 that they invalidate a number of wide misconceptions such as “Birds don’t fly in poor visibility such as in 21 clouds, etc.” or “Birds don’t fly at night” [7]. Indeed, the results confirm that bird strikes during reduced 22 visibility conditions are no less perilous than those during good visibility conditions, and flight crews 23 should be extremely vigilant when visibility drops. 24

SUMMARY AND CONCLUSIONS 25

26 1. Not only more bird strikes are expected in the near future, but also more bird strikes are anticipated to 27

result in single or dual engine failure because of the 5� continuous increase in large (i.e. >8.0 lb.) bird 28 populations,55�continuous increase in air traffic, 555� increasing use of faster turbofan engines, 5��the 29 fact that present-day turbofan engines are not tested for large birds. 30 31 2. Engine failure due to bird strike can particularly pose threat to modern-day commercial jets due to the 32 increasing trend towards twin-engine aircraft. 33 34 3. To find out the factors that are statistically related to the probability of engine failure in the event of a 35 bird strike, data from the FAA Wildlife Strike Database are analyzed. The data include all airborne bird 36 strikes between January 1990 and November 2012 that involved turbofan engine civil aircraft. Missing 37 data are multiply imputed using an approximate Bayesian bootstrap hot-deck imputation method that is 38 applicable to non-ignorable missing data. 39 40 4. Using the multiply imputed data, a logistic regression model is built and the model goodness-of-fit is 41 verified using a likelihood ratio test combining method. The model statistically relates the probability of 42 engine failure in the event of a bird strike to altitude AGL, bird size, number of birds struck, flight phase, 43 daylight and sky conditions. The results provide strong evidence for the following: 44

• Statistically, the probability of engine failure in the event of a bird strike declines by around 15% 45

9 Active at dawn or dusk. 10 Among the cases in which the bird species were identified.


19

every 1,000-ft. altitude gain during the phase of climb, but it remains fairly constant with altitude AGL 1 during the phase of approach/ descent, controlling for the other covariates in the model. 2

• A bird strike during climb is statistically up to 11 times more likely to result in engine failure 3 compared to one during approach/ descent, controlling for the other covariates in the model. 4

• Large (> 8.0 lb) birds are statistically around 30 times more likely to bring about engine failure in 5 the event of a bird strike than small birds, controlling for the other covariates in the model. 6

• A bird strike involving more than 10 birds is statistically around 12 times more likely to result in 7 engine failure compared to one involving a single bird, controlling for the other covariates in the model. 8

• A bird strike during twilight is statistically around 90 percent more likely to result in engine failure 9 compared to a daytime strike. Likewise, a bird strike during cloudy sky conditions is statistically 80 10 percent more likely to result in engine failure compared to one during clear sky conditions. Contrary to 11 the wide misconception that “Bird do not fly in poor visibility”, bird strikes not only can happen during 12 reduced visibility conditions, but also are no less perilous than those during good visibility conditions. 13

14 5. In view of the results, aviation practitioners should consider the following: 15

• Wildlife management programs should particularly focus on airport environments and involve 16 species-specific means of controlling attractants, particularly for large bird species such as Canada goose, 17 double-crested cormorant, snow goose and black/ turkey vulture. In case of airports with limited 18 resources, bird deterrent programs should give prominence to prevailing aircraft climb paths. 19

• Flight crews should be extremely vigilant at lower altitudes and in reduced visibility such as 20 twilight and cloudy sky conditions. 21

• During climb, lower altitudes should be cleared using speeds and flap settings that provide higher 22 rate of climb. Climb speeds around Vx

11 are recommended as opposed to Vy12 since they offer enhanced 23

flight safety benefits. Lower flap settings are recommended (if runway length permits) since they induce 24 less drag during climb. 25

• Future designs of turbofan engines are strongly recommended to be tested for large birds beyond 26 the current FAA requirements. 27

• Flight crews should delay take-off or landing if flocks of birds are reported. If landing cannot be 28 delayed, flight crews should plan on additional landing distance because a possible bird strike may disable 29 the thrust reversers. 30

• As more bird strikes are expected to result in engine failure in the near future, pilot training 31 programs should particularly underscore emergency landing procedures initiated after a single or dual 32 engine failure due to bird strike during climb. A software program can also be developed to optimize the 33 emergency landing path of twin-engine aircraft on a real-time basis in case of a possible dual engine 34 failure. 35 36

REFERENCES 37

[1] R. A. Dolbeer, S. E. Wright, J. Weller and M. J. Begier, "Wildlife Strikes to Civil Aircraft in the United States 1990-2010," Federal Aviation Administration National Wildlife Strike Database Serial Report Number 17, Washington, DC, 2012.

[2] "Aviation Safety Network," Flight Safety Foundation, 2013. [Online]. Available: http://aviation-safety.net/database/record.php?id=19880915-0. [Accessed 11 June 2013].

[3] F. S. Foundation, "Military Boeing 707 Strikes Birds After Liftoff; Damage to Engines No. 1 and No. 2 Results in Loss of Power and Impact with Terrain," Accident Prevention, vol. 53, no. 11, November 1996.

[4] NTSB, "Foreign Notification Aviation. NTSB ID: ENG10WA002," National Transportation Safety

11 Best angle of climb speed. 12 Best rate of climb speed.


20

Board, Washington, D.C., 2010.

[5] NTSB, "Foreign Notification Aviation. NTSB ID: DCA09RA010," National Transportation Safety Board, Washington, D.C., 2010.

[6] NTSB, "Loss of Thrust in Both Engines After Encountering a Flock of Birds and Subsequent Ditching on the Hudson River. US Airways Flight 1549 Airbus A320‐214, N106US. Weehawken, New Jersey. January 15, 2009," National Transportation Safety Board, Washington, D.C., 2010.

[7] R. Nicholson and W. S. Reed, "Strategies for Prevention of Bird-Strike Events," Aero Quaterly, pp. 17-24, March 2011.

[8] R. A. Dolbeer, "Birds and Aircraft - Fighting for Airspace in Ever More Crowded Skies," Human-

Wildlife Conflicts, vol. 3, no. 2, pp. 165-166, 2009.

[9] F. A. Administration, "FAA Wildlife Strike Database," 31 1 2013. [Online]. Available: http://wildlife.faa.gov/database.aspx. [Accessed 02 2013].

[10] R. A. Dolbeer, "Height Distribution of Birds Recorded by Collisions with Civil Aircraft," Air Safety

Week, vol. 19, no. 43, 7 11 2005.

[11] M. Zalakevicius, "Bird Strike Analysis in Lithuania," Acta Ornithologica Lituanica, Vols. 9-10, pp. 87-90, 1994.

[12] V. Jacoby, "Analysis of Bird Collision with Planes and Possibility of Utilization of the Bird Strike Prevention Measures," in Bird Strike Committee Europe (BSCE), 20th Meeting, Helsinki, Finland,

May 21st-25th, 1990, Working Papers, Helsinki, 1990.

[13] D. G. Garson, Missing Values Analysis & Data Imputation, Statistical Associates Publishers - Blue Book Series, 2012.

[14] R. J. A. Little, "A Test of Missing Completely at Random for Multivariate Data with Missing Values," Journal of the American Statistical Association:Theory and Methods, vol. 43, no. 404, pp. 1198-1202, December 1988.

[15] D. B. Rubin, "Multiple Imputation for Nonresponse in Surveys," John Wiley & Sons, Inc., New York, 1987.

[16] B.-J. Lee and L. C. Marsh, "Sample Selection Bias Correction for Missing Observations," Oxford

Bulletin of Economics and Statistics, vol. 62, no. 2, pp. 305-322, 2000.

[17] J. Siddique and T. R. Belin, "Using an Approximate Bayesian Bootstrap to Multiply Impute Nonignorable Missing Data," Computational Statistics and Data Analysis, vol. 53, pp. 405-415, 2008.

[18] J. Siddique and T. R. Belin, "Multiple Imputation Using an Iterative Hot-Deck with Distance-Based Donor Selection," Statistics in Medicine, vol. 27, pp. 83-102, 2008.

[19] J. Siddique and T. R. Belin, "MIDAS: A SAS Macro for Multiple Imputation," Journal of Statistical

Software, vol. 29, no. 9, February 2009.

[20] N. Schenker and J. M. Taylor, "Partially Parametric Techniques for Multiple Imputation," Computational Statistics and Data Analysis, vol. 22, no. 4, pp. 425-446, 1996.

[21] L. M. Collins, J. L. Schafer and C. M. Kam, "A Comparison of Inclusive and Restrictive Strategies in Modern Missing Data Procedures," Psychological Methods, vol. 6, pp. 330-351, 2001.

[22] A. Agresti, An Introduction to Categorical Data Analysis, Second Edition ed., Hoboken, New Jersey: John Wiley & Sons, Inc., 2007.

[23] S. Weisberg, Applied Linear Regression, Third Edition ed., Hoboken, New Jersey: John Wiley & Sons, 2005.

[24] Z. J. Shen, Nested Multiple Imputation, Cambridge, MA: Department of Statistics, Harvard University, 2000.


21

[25] D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, Second Edition ed., Hoboken, NJ: John Wiley & Sons, Inc., 2000.

[26] D. Sullivan and R. Andridge, Hosmer-Lemeshow Goodness-of-Fit Test for Multiply Imputed Data,

San Diego, CA: American Statistical Association, 2012.

[27] X.-L. Meng and D. B. Rubin, "Performing Likelihood Ratio Tests with Multiply-Imputed Data Sets," Biometrika, vol. 79, no. 1, pp. 103-111, March 1992.

[28] H. C. Smith, The Illustrated Guide to Aerodynamics, New York: TAB Books/ McGraw-Hill, 1992.

[29] D. F. Rogers, "Possible "Impossible" Turn," Journal of Aircraft, vol. 32, no. 2, pp. 392-397, March-April 1995.

[30] J. L. Dunn and J. Alderfer, National Geographic Field Guide to the Birds of North America, Fifth Edition ed., Washington, D.C.: National Geographic Society, 2006.

[31] NTSB, "Crash of Cessna 500, N113SH Following an In-Flight Collision with Large Birds. Oklahoma City, Oklahoma. March 4, 2008.," National Transportation Safety Board, Washington, D.C., 2009.

[32] Y. Sakamoto, M. Ishiguro and G. Kitagawa, Akaike Information Criterion Statistics, Dordrecht Reidel Publishing Company, 1986.

[33] G. Schwarz , "Estimating the Dimension of a Model," The Annals of Statistics, vol. 6, no. 2, pp. 461-464, 1978.

[34] R. A. Dolbeer, S. E. Wright, J. Weller and M. J. Begier, "Wildlife Strikes to Civil Aircraft in the United States 1990-2008," Federal Aviation Administration, WAshington, D.C., 2009.

[35] R. A. Dolbeer, "Birds and Aircraft - Fighting for Airspace in Crowded Skies," in Proceedings of the

19th Vertebrate Pest Conference, 2000.

[36] "Ethiopian Airlines Plane Crashes Since 1970," Airsafe.com, 3 April 2012. [Online]. Available: http://www.airsafe.com/events/airlines/eth.htm. [Accessed 11 June 2013].

[37] K. Grace-Martin, "Missing Data Mechanisms," Cornell University, Cornell Statistical Consulting Unit, Ithaca, 2001.

1 2


statistical analysis of aircraft-bird strikes resulting in engine failure

Documents