Text

Updated Prediction of Frequency of Aircraft Crashes at TMI-1 Site
	ML20116N303
Person / Time
Site:	Three Mile Island
Issue date:	04/30/1985
From:	Bier V, Mikschi T, Mosleh A; PLG, INC. (FORMERLY PICKARD, LOWE & GARRICK, INC.)
To:	;
Shared Package
ML20116N281	List: ML20116N277; ML20116N303;
References
	PLG-0411, PLG-411, NUDOCS 8505070108
	Download: ML20116N303 (66)
	v • d • e

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PLG-0411 i

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UPDATED PREDICTION OF THE FREQUENCY OF AIRCRAFT l CRASHES AT THE THREE MILE ISLAND UNIT 1 SITE l

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l Pickard,Lowe andGarrick,Inc. l Engineers e Applied Scientists e Management Consultants l

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UPDATED PREDICTION OF THE FREQUENCY OF AIRCRAFT CRASHES AT THE THREE MILE ISLAND UNIT 1 SITE

!O by Ali Mosleh Thomas J. Mikschl

O vicki M. Bier Stan Kaplan Mark J. Abrams Douglas C. Iden j Frank R. Hubbard

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lO Prepared for GPU NUCLEAR CORPORATION i

Parsippany, New Jersey lO April 1985 l l l

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O Pickard,Lowe and Garrick,Inc. I Engineers e AppliedScientists e Management Consultants l lO Newport Beach, CA Washington, DC l

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O TABLE OF CONTENTS Section Page LIST OF TABLES AND FIGURES iv 1 INTRODUCTION AND

SUMMARY

1-1 2 THE PLANT / AIRPORT GE0 METRY AND THE BASIC ANALYTICAL MODEL 2-1

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3 AIRCRAFT MOYEMENT AND NATIONAL CRASH DATA 3-1 3.1 Number of Aircraft Movements at Harrisburg International Airport 3-1 3.2 National Aerial Crash Statistics 3-1

) 3.3 Plant Target Area 3-11 4 ASSESSMENT OF MODEL PARAMETERS 4-1 4.1 Prediction of Accident Rates from Historical Data 4-1 4.2 Determination of the Spatial Density Functions 4-15

!) 5 REFERENCES . 5-1

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.O LIST OF TABLES AND FIGURES Table Page 1-1 Mean Annual Hit Frequency Result for Various Types and Modes of Aircraft Operation (10 g Crashes Per Year) 1-2 3-1 Aircraft Operations at Harrisburg International Airport (1980 - 1984) 3-2 3-2 Listing of U.S. Air Carrier Landing and Takeoff Accidents

..O in the Contiguous U.S., Involving Destruction of the Aircraft (1956 - 1982) 3-3 3-3 U.S. Air Carrier Accident Rate for Scheduled and Nons:heduled Landings in the Contiguous U.S. 3-12 3-4 U.S. Air Carrier Accident Rate for Scheduled and Nonscheduled Takeoffs in the Contiguous U.S. 3-13

.O- 4-1 Bayesian Results for Accident Rate Distribution -

Scheduled Landings 4-9 4-2 Bayesian Results for Accident Rate Distribution -

Nonscheduled Landings 4-10 4-3 Baye:f an Results for Accident Rate Distribution -

Scheduled Takeoffs 4-11 C 4-4 Bayesian Results for Accident Rate Distribution -

Nonscheduled Takeoffs 4-12 4-5 Accident Rate for Takeoffs - Scheduled and Nonscheduled 4-16 4-6 Accident Rate for Landings - Scheduled and Nonscheduled 4-17 4-7 Bayesian Results for Radial Distribution - All Crashes Combined 4-20

.O 4-8 Bayesian Results for Radial Distribution - Landing Crashes Only 4-24 4-9 _ Bayesian Results for Radial Distribution - Takeoff Crashes Only 4-27 4-10 Bayesian Results for Angular Distribution - Landings and Takeoffs Combined 4-31

O 4-11 Bayesian Results for Angular Distribution - Landings Only 4-33 4-12 Bayesian Results for Angular Distribution - Takeoffs Only 4-36 Figure

O 1-1 Basic Characteristics of the Distribution of Hit Frequency Based on Various Types of Aircraft Operations 1-3 1-2 Cumulative Distribution of the Total Hit Frequency 1-4 i

2-1 Location of TMI Site with Respect to Harrisburg Airport 2-2 2-2 Representation of Spatial Crash Frequency Distribution 2-4 3-1 Historical Accident Rate Versus Time - Landings and

O Takeoffs Combined -

3-14 3-2 Fraction of Crashes Occurring at Radius r or Greater- 3-15 3-3 Scatter Pattern for Takeoff Accidents 3-16 3-4 Scatter Pattern for Landing Accidents 3-17 4-1 Crash Rate Versus Time - Scheduled Landings 4-5 4-2 Crash Rate Versus Time - Nonscheduled Landings 4-6

.O 4-3 Cras., Rate Versus Time - Scheduled Takeoffs 4-7 2

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LIST OF TABLES AND FIGURES (continued)

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4-4 Crash Rate Versus Time - Nonscheduled Takeoffs 4-8 4-5 Crash Rate Versus Time - Takeoffs 4-13 4-6 Crash Rate Versus Time - Landings 4-14 4-7 Fraction of Crashes Occurring at Radius r or Greater -

g Takeoffs and tandings_ Combined 4-21 4-8a The Quantity y R(r) 4-22

- r = 2.7 4-8b The Quantity RL (r) 4-22 r = 2.7 O 4-8c The Quantity RT (r) 4-22 l

r = 2.7 4-9 Fraction of Landing Crashes Occurring at Radius r or Greater 4-25 4-10 Fraction of Takeoff Crashes Occurring at Radius r or Greater 4-28 4-11 Angular Distribution of Crashes - Landings and Takeoffs Combined 4-29 jO 4_12a The Quantity ye(ei- 0 = 34*

4-32 4-12b The Quantity OT(O I 4-32 e = 34 4-12c The Quantity eLI0I 4-32 iO -

- 0 = 34 4-13 Angular Distribution of Landing Crashes 4-34 4-14 Angular Distribution of Takeoff Crashes 4-37

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1. INTRODUCTION AND SUf1 MARY l

'O This report presents an analysis performed to determine the annual l t

frequency of crash by a heavy aircraft during landing or takeoff l operation at Harrisburg International Airport (HIA) into the Three Mile j Island Unit 1 (TMI-1) nuclear power plant. The scope of the present ,

analysis is limited.to updating the results of an earlier analysis I (References 1, 2, and 3), using 1984 statistics on aircraft movements at ;

-O HIA and updated national aerial crash data. Calculation of the hit '

frequencies is based on the breakdown of aircraft movements .into scheduled takeoffs, nonscheduled takeoffs, scheduled landings, and nonscheduled landings. Table 1-1 presents the mean values of the results of this study for various types of aircraft movements. The results are also compared with those obtained in the previous study (Reference 3).

'Ol Figure 1-1 provides a graphical representation of the main characteristics of the distribution of the total annual hit frequency and the various contributions to it. Finally, the cumulative distribution of 4 -the total hit frequency, based on the results of this study as well as the previous study are shown in Figure 1-2.

lO As can be seen from Table 1-1, the nonscheduled operations contribute i i significantly to the total hit frequency. The total mean hit frequency of 3.51 x 10-8 per year calculated in this study is slightly more than

a factor of 5 larger than the frequency presented in Reference 3 based on l 1978 statistics. The increase is essentially due to two factors: (1) use of a target area that was a factor of 2 larger than one used in the i

O previous study-and, (2) increase in the number of operations, especially ;

i nonscheduled landings and takeoffs at HIA. Both of these factors are calculated based on conservative assumptions as discussed in more detail in this report. Also calculated were the hit frequencies based on all takeoffs and all landings without breakdown by scheduled or nonscheduled i operations The total mean hit frequency obtained in this manner is 6.53 x 10-g per year, which underestimates the hit frequency by a O

factor of 5 due to the combined crash frequencies being biased, nonconservatively, toward scheduled crash frequencies. In light of this i

observation, the prediction of the hit frequency is based on the detailed breakdown by scheduled and nonscheduled operations.

Ol The following sections describe how these results were obtained. The basic analytical model used in the analysis is described in Section 2,

! followed by the basic data collected for estimating the model parameters in Section 3. Section 4 provides a detailed discussion on the a

quantification of various components of the model.

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TABLE 1-1. MEAN ANNUAL HIT FREQUENCY RESULTS i() FORVARIOUSTYPEgANDMODESOFAIRCRAFT OPERATION (10- CRASHES PER YEAR)*

lC) Type of _ Mode of Operation Operation Landing Takeoff-Scheduled 1.20 0.08- 1.28 (0.50) (0.03) (0.53) i C) 4 Nonscheduled 22.3 11.5- 33.8 (4.00) (2.10)- -(6.10)

C) Total 23.5 11.5 ~35.1 (4.50) (2.13) (6.63)

Numbers in parentheses are the results of the i previous study-(Reference 3). j I C) - ,

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NONSCHEDULED LANDINGS

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NONSCHEDULED TAKEOFFS Y

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l TOTAL HIT FREQUENCY (PREVIOUS STUDY)

I I I I 10-12 10-11 10-10 10'8 10-8 93 7 s

HIT FREQUENCY (CRASHES PER YEAR) l

FIGURE 1-1. BASIC CHARACTERISTICS OF THE DISTRIBUTION OF HIT FREQUENCY BASED ON VARIOUS TYPES OF AIRCRAFT OPERATIONS 4

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crash frequen:y based on Equation (2.1). Results are also provided for landings and takeoffs without breakdown into scheduled and nonscheduled operstions.

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-2. THE PLANT / AIRPORT GE0 METRY AND THE BASIC ANALYTICAL MODEL The'TMI plant site'is located approximately at a radius of 2.7 miles and

,:O 34*.off the centerline from the southwest end of Runway 13/31 of the Harrisburg, Pennsylvania, airport - as shown in Figure 2-1. The landing strip is called Runway 31 when used in the northwest direction and Runway 13 when used in the southeast direction. The threat to the TMI

' site is from operations at the south end of this strip; that is, from landings taking place in the northwest direction (Runway 31) and takeoffs

.O i 'in the southeast direction (Runway 13). Of the operations on this strip, 70% use Runway 31 and 30% use Runway 13. The number _ of landings and takeoffs are approximately equal on each runway. Thus, if N is the

number of operations per year on the strip, then

.35N = nunber of landings at south end E NL

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.15N = number of takeoffs at south end E NT The aircraft hit frequency into TMI-1 is calculated by using the algorithm o

f=fSL + fST + fNL + fNT (2.1)

!O where f is the annual frequency of aircraft crashes into TMI-1 by heavy

, aircraft using HIA, and fSL. fST. fNL, and fNT are contributors 3

to that frequency from scheduled landings, scheduled takeoffs, nonscheduled landings, and nonscheduled takeoffs. These frequencies are ;

calculated as follows: '

jo fSL:= NSL Cst SL '(r,0) AL (2.2) fST = NST CST ST (r,e) AT (2.3) fNL = NNL CNL SL (r,6) AL (2.4)

O fNT = NNT CNT ST_(r,0) AT (2.5) _

where

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NST and NNT = the annual number of large scheduled and l

O nonscheduled aircraft, respectively, taking !

off on TMI-1 end of the runway; i.e., using

~HIA runway 13.

NSL and NNL = the annual number of-large scheduled and

- nonscheduled aircraft, respectively, ' landing

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on the TMI-1 end of the runway; i.e., using ,

-HIA runway 31.

p AL,~ AT = the effective target area of the plant-I upon landing and takeoff, respectively.

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RESPECT TO HARRISBURG AIRPORT .

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Cst, CNL, CST, and CNT = the applicable accident rate of l scheduled landing, nonscheduled landing, scheduled takeoff, and nonscheduled takeoff.

O and finally SL (r,0) = frequency, per unit area, of the crash occurring at coordinates r,0 from end of runway, given that the crash is on landing.

O ST (r.e) = frequency, per unit area, of the crash occurring at r,0, given the crash is on takeoff.

A visual aid to understanding the physical meaning of these spatial distributions is provided in Figure 2-2. It is assumed that S L(r,0) {

i and ST (r,0) are separable into radial and angular components. l More explicitly, let i

RL (r) E the fraction of landing crashes that occur at radius r j or greater. !

O 6L(0) E the fraction of landing crashes that occur at I angle e or greater.

Then d '360I 1 'd 'I I

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L p RL(r) 7 1 p O L(0) M! I2*0I l

where e is measured'in degrees, r in miles, and SL _in fraction per square mile.

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d I d # I ST (r,0) = .p RT (r) g'360 g OTI0I 1

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l The final -1/2 in these formulae corrects for the fact that in calculating I the function 0 we will lump both positive and negative values of'O f O. . together--thus, in effect, treating all accidents as if they occurred on j the TMI side of the runway. l I

.The issue of separability of S(r,0) has been discussed in Reference-4.

The conclusion was that the assumption of separability does not introduce .

e.ny significant. error.in terms assessing the spatial distribution. j O !

In this analysis, following the method presented in Reference 1, encertainty distributions are assessed for all the frequencies using Bayesian techniques. The final results are presented in probability distribution form for the frequency of crash for each of the four categories-represented by Equations (2.2) through (2.5) and the total O

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3. AIRCRAFT MOVEF"7 "MD NATIONAL CRASH DATA O The data needed to quantify the various parameters of the model are presented in this section. These data include the number of aircraft movements at Harrisburg International Airport and the national aerial crash statistics.

3.1 NUMBER OF AIRCRAFT MOVEMENTS AT HARRISBURG INTERNATIONAL AIRPORT O

Table 3-1 provides the total number of aircraft movements (landings and takeoffs) for various categories of operation for the period 1980

'through 1984 (Reference'5). In this analysis, we are concerned with the number of heavy aircraft movements; i.e., aircraft weighing 200,000 pounds or more. A conservative estimate puts the number of such O operations at less than 1% of the total operations (References 5 and 6).

For instance, for the year 1984, this number is estimated to be less than 1,411.

In order to estimate the number of movements of heavy aircraft in the scheduled and nonscheduled categories, we lfirst observe that Air Taxi and O General Aviation aircraft, by definition,10 not include heavy aircraft.

The total number of movements excluding thase two categories for the year 1984 was 26,684. A total of 8,549 of these operations were

-scheduled. Therefore, the fraction of scheduled operations'is 0.32. The fraction of nonscheduled operations (including military) is then 0.68.

Therefore, the breakdown of heavy aircraft movements based on these O percentages is.

Scheduled: N3 = (0.32)(1,411) = 452

-Nonscheduled: NN = (0.68)(1,411) = 959 (3.1)

O From our earlier discussion regarding the use of runways at the airport, we calculate the following values for the number of scheduled and nonscheduled landings and takeoffs in the TMI-1 direction of the runways.

NSL = (0.35)N3 = 158 O NST = (0.15)N3= 68 l I

NNL = (0.35)NN = 335 NNT = (0.15)NN = 144 (3.2)

O 3.2 -NATIONAL AERIAL CRASH STATISTICS Table 3-2 lists U.S. air carrier landing and takeoff accidents in the contiguous U.S. involving destruction of the aircraft for the years 1956 to 1982. The data for the years 1956 to 1977 were taken from Reference 2. The additional data for the years 1978 to 1982 were o' obtained from the National Transportation Safety Board (NTSB).

computerized briefs of accidents and the detailed accident reports 4

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I TABLE 3-1. AIRCRAFT OPERATL.S A7 "r .!ISBURG INTERNATIONAL AIRPORT iisde -

O Total Nurar of Aircraft Movements Type of Operation ae s and Landngs)

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O 1980 1981 1982 1983 1984 Commercial, Scheduled 8,227 6,954 6,268 6,747 8,549 Commercial, Nonscheduled 1,422 356 690 233 157 O

Air Taxi 23,010 20,135 22,752 22,437 29,724 Military 12,514 11,552 12,231 12,857 17,978 General Aviation 67,525 60,347 62,732 67,189 84,693 O

Total 112,698 99,344 104,673 109,463 141,101 Estimated Number of 1,127 993 1,047 1,095 1,411 O Heavy Aircraft Operations *

Approximately 1% of the total number of aircraft movements.

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O O O O O O O O O O O TABLE 3-2. LISTING OF U. S. AIR CARRIER LANDING AND TAKEOFF ACCIDENTS IN THE CONTIGUOUS U. S., INVOLVING DESTRUCTION OF THE AIRCRAFT (1956 - 1982)

Sheet 1 of 8 Hit Location

Date Location Phase Aircraft Injury Op ration r 0 (miles) (degrees) 1956 2/17 Owensboro, KY L M-404 0 SP 0 0 4/1 Pittsburg, PA T M-404 F SP 0' "

'0 4/2 Seattle, WA T B-377 F SP 4.7 0 11/14 Las Vegas, NV L M-404 0 SP 0 0 1957 1/6 Tulsa, OK .L CV-240 F SP 3.5 0 Y

" 2/1 Rikers Island, NY T DC-6 F SP 0.9 47 9/15 New Bedford, MA L DC-3 F SP 0.8 6 1958 2/13 Palm Springs, CA T CV-240 0 SP 4.0 0 3/25 Miami, FL T DC-7 F SP 3.1 26 4/6 Freeland, MI L Viscount F- SP 0.4 0 6/4 Martinsburg, WV L DC-3 F Training 0.3 90 8/15 Nantucket, MA L CV-240 F SP 0.3 22 8/28 Minneapolis, MN T DC-6 0 SP 0.6 0 11/10 New York, NY T L-1049 0 Training 0 0 l

NOTE: Footnotes and legend appear on the last sheet of this table.

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Sheet 2 of 8 Hit Location *-

Date Location Phase Aircraft Injury Oper tion r- 6 (miles) (degrees) 1959 2/3 New York, NY L L-188 F SP 0.8 0 2/20 San Francisco, CA L DC-7 0 NS/C 0 0 3/15 Chicago, IL L CV-240 0 SC 1.2 28 5/12- Charleston, WV L L-1049 F SP 0 0 8/15 Calverton, NY L B-707 F Training 3.0 13

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9/2 Abilene, TX L C-46 F NS/C 0 0 11/24 Chicago, IL . L L-1049 F SC 0.2 0 12/1 Williamsport, PA L M-202 F SP 1.4 90

, 10/26 Santa Maria,-CA T DC-3 F SP 1.5 NA E 1960 5/23 -Atlanta, GA T CV-880 F Training 0 0 9/14 ! New York, NY L L-188 0 SP 0 0 10/4 Boston, MA T L-188 F SP 1.0 20 10/29 Toledo, OH T C-46 F NS/P 1.1 4 l

1961 7/11 Denver, CO L DC-8 F SP 0 0 9/17 Chicago, IL T L-188 F SP 0.8 90 11/8 Richmond, VA L L-1049 F NS/P 1.1 26 NOTE: Footnotes and legend appear on the last sheet of this table.

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.O O' O O O O O O O- 0; JOL 1 TABLE 3-2 (continued) i Sheet 3 ' of 8 -

, Hit Loce. tion * -

Date ' Location Phase Aircraft Injury Operation r 0 (miles) (degrees) 1962 3/1 Jamaica Bay, NY T B-707 F SP 2.7 90 4/18 Dallas,.-TX T DC-3 F Test 0 0 7/8. Amarillo, TX T V-812 0 SP 1.2 21 8/22 Wilmington, NC L M-404 0 Training 0 0 11/30 New York, NY L .DC-7 F SP 0.8 9 12/14- Hollywood, CA L L-1049 F SC 1.5 0 12/21 Grand Island, NE L CV-340 0 SP 0.8 0 1963 Y

1/29 Kansas City, MO .

L V-812 F SP 0 0 2/3 San Francisco, CA L L-1049 F- SC 0 0 2/16 Puyallup, WA L C-46' 0 NS/C 0.5 0 5/28- Manhattan, KS L L-1049 0 NS/P 0.1 0 7/2 Rochester, NY - T M-404 F SP 0 0 11/29 Morgantown, WV L DC-3 F Ferry 2.5 18 1964 3/10 Boston, MA L DC-4 F SC 1.3 0 3/12 Miles City, MT L DC-3 F SP 1.9 0 11/20 Detroit, MI T C-46 0 NS/C 0.4 0 12/24 San Francisco, CA T L-1049 F SC 4.3 31 l 12/30 Detroit, MI L 'C-46. F NS/C 2.3 13 NOTE: Footnotes and -legend appear on the last sheet of this table.

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6 o o o o o o O O~ O O TABLE 3-2 (continued)

Sheet 4 of 8 Hit Location

Date Location Phase Aircraft Injury Operation r 0 (miles) (degrees) 1965 4/16 Las Vegas, NY T F-27 0 Training 0 0 5/18 Knob Knoster, M0 L DC-6 0 NS/C 0.8 10 7/23 Montoursville, PA T CV-440 0 SP 2.8 45 9/13 Kansas City, M0 T CV-880 0 Training 0.2 27 11/8 Constance, KY L B-727 F SP 2.0 0 11/11 Salt Lake City, UT L B-727 F SP 0.1 0 1966 m 3/21 Norfolk, VA L CL-44 0 SC 0 0 a 4/22 Ardmore, OK L L-188 F NS/P 2.3 90 7/28 Newark, NJ T C-46 0 11/20 New Bern, NC MS/C 1.1 90 L M-404 F SP 4.0 9 1967 1/31 San Antonio, TX L DC-6 F 3/39 Kenner, LA NS/C 4.5 0 L DC-8 Training 11/6 Erlanger, KY F 0.4 27 T B-707 F 11/20 Constance, KY SP 0 0 L CV-880 F 12/21 Denver, C0 SP 1.8 3 T DC-3 F NS/C 0 0 NOTE: Footnotes and legend appear on the last sheet of this table.

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O O ; ~ ~~ ~ '6~ ~ O O O O O O O TABLE 3-2 (continued)

Sheet 5 of 8 Hit Location

Date Location Phase Aircraft Injury Operation r 0 (miles) (degrees) 1968 1/1 0xford, MS L M-404 0 Ferry 0 0 3/21 Chicago, IL T B-727 0 SC 0 0 4/28 Atlantic City, NJ L DC-8 0 Training 0 0 8/10 Charleston, WV L F-227 F SP 0 0 9/27 Cherry Point, NC L DC-7 0 NS/C 0.4 17 12/24 Bradford, PA L CV-580 F SP 2.8 8 12/27 Sioux City, IA T DC-9 0 SP 0 0 12/27 Chicago, IL L CV-580 F SP 0.3 86 y 1969 1/6 Bradford, PA L CV-440 F SP 5.0 0 7/15 Jamaica, NY T DHC-6 F SP 0 0 7/26 Pomona, NJ L B-707 F Training 0 0 10/11 Stockton, CA T DC-8 0 Training 0 0 1970 8/24 Hill AFB, UT T L-188 0 NS/C 0 0 9/8 Jamaica, NY T DC-8 F Ferry 0 0 10/10 Wrightstown, NJ L GA-382 F NS/C 1.0 0 11/14 Huntington, WV L DC-9 i F NS/P 1.1 0 I

NOTE: Footnotes and legend appear on the last sheet of this table.

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TABLE 3-2 (continuel)

Sheet 6 of 8 -

Hit Location

Date Location Phase Aircraft Injury Operation r 6 (miles) (degrees) 1971 3/31 Ontario, CA L B-720 F Training 0 0 6/7 New Haven, CN L CV-580 F SP 0.9 6 1972 3/3 Albany, NY L F-227. F SP 3.8 0 5/18 Ft. Lauderdale, FL L DC-9 0 SP 0 0 5/30 Ft. Worth, TX L DC-9 F Training 0 0 i 12/8 Chicago, IL L B-737 F SP 1.8 10 w 12/20 Chicago, IL T DC-9 F SP 0 0 1973 7/23 St. Louis, M0 F-227 {

L F SP 2.6 4 7/31 Boston, MA L DC-9 F SP 0.6 4 11/3 Boston, MA L B-707 F SC 0 0 11/27 Akron, OH L DC-9 0 SP 0 0 1974 1/16 Los Angeles, CA L B-707 0 SP 0 0 9/11 Charlotte, NC L DC-9 F SP 3.4 0 N0TE: Footnotes and legend appear on the last sheet of this table.

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C .O O O .O O O O O O O JO TABLE 3-2 (continued)

Sheet 7 of 8 Hit Location

Date Location- Phase Aircraft Injury Oper tion r 0 (miles) (degrees) 1975 6/24 Jamaica, NY L B-727 F- SP 0 0 11/12 Jamaica, NY T DC-10 0 NS/P 0 0 1976 2/8 Van Nuys, CA T DC-6 F Ferry 1.5 0 6/23 Philadelphia, PA L DC-9 0 SP O 0 1977 7/6 St. Louis, M0 T L-188 F NS/C 0 0 ca

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. 1978 03/1 Los Angeles, CA T DC-10 F SP 0.1 0 9/25 San Diego, CA L B-727 F SP 3.5 28 1979 2/9 Miami,'FL T DC-9 0 ' Training 0.15 30 1/5 Amiat, AK L 188A 0 NS/CTR 0 0 5/25 Chicago, IL~ T DC-10 F SP 0.87 17 l 6/22. Dag9ett, CA T -DC-7 F M 1.0 20 l 5/15 Mesa, AZ T C-54D 0 Test 0** 0 11/19 McCormick, SC L .C-54D F M 2.5' 35 i

NOTE: Footnotes and legead appear on the last sheet of this table.

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TABLE 3-2 (continued)

Sheet 8 of 8 Hit Location

Date Location Phase Aircraft Injury Oper tion r 0 (miles) (degrees) 1980 6/19 Atlanta, GA L SUD AVN 0 Cargo 0 0 SE-210 Service 11/28 Pecos, TX T DC-78 F M i i 6/22 Columbus, IN' T 1049-H F Ferry 0.87 25 1981 2/17. Santa Ana, CA L B-737 F SP 0 0 w 1982 h 3/13 Glendale, AZ Boston, MA L KC-135A F Military 3.5 0 1/23 L DC-10-30 F SP 0 0

Hit location: r = radial distance of the hit to the end of the runway in use. O is the angle to the runway centerline. r = 0 is considered if the hit occurred within 0.05 mile of the runway, and 0 = 0 is considered if the hit occurred within 200 feet of the extended runway center-line. Note that we.do not distinguish between a positive or negative angle (0).

- This plane ran off the runway after aborted takeoff. The radial distance would be 0.25 mile

'1,300 feet) if final resting place is considered.

l

" Sufficient information unavailable to determine r or 0.

l 1 LEGEND: !

Phase: L = landing; T = takeoff.

Injury: F = one or more occupant fatalities; O = none.

Type operation: SC = scheduled cargo; SP = scheduled passenger; NS/C = nonscheduled cargo; NS/CTR = nonscheduled charter; NS/P = nonscheduled passenger; M = smuggling.

0177G042985

O available from NTSB. Detailed reports for accidents beyond 1982 were not available at the time of this analysis. Table 3-2 also lists hit locations (r,0) for each of the accidents and the phase and type of perati n f r the aircraft involved.

O Tables 3-3 and 3-4 provide the number of takeoffs and landings for scheduled and nonscheduled operations for the period 1956 to 1982 (References 3, 7, 8, and 9). The takeoff and landing crash frequencies, plotted by year in Figure 3-1, show a downtrend in the accident O #9"*"*I'S' Figure 3-2 is a plot of the radial distribution of crashes based on the data in Table 3-2. The angular distribution for takeoffs and landings are presented in the form of scatter diagrams in Figures 3-3 and 3-4, respectively.

O 3.3 PLANT TARGET AREA The following estimates for the TMI station target area for landing and takeoff hits, which are presented in Reference 10, were used in this analysis.

O AL = Landing Target Area = 0.0224 square mile AT = Takeoff Target Area = 0.0066 square mile These areas were calculated by considering " shadow effect" to account for O the dependence of the potential target area on the glide angle of the crashing aircraft and the " skid effect" to account for airplanes that might crash in front of the plant and slide into it. The calculated landing and takeoff target areas are based on glide angles of 10 and 45 degrees, respectively.

O The area used in the previous study (Reference 3) was calculated for one unit of the TML station. In this study, the effective target area of both units is used to account for the fact that most of the critical structures of the two units are closely connected, so the crash of a large aircraft into the structures of one unit might have some impact on the structures of the other unit. This, of course, is a conservative g assumption.

O ,

I o

l 0 3-11 0190G042985

O O O O O O O O O O O TABLE 3-3. U.S. AIR CARRIER ACCIDENT RATE FOR SCHEDULED AND NONSCHEDULED LANDINGS IN THE CONTIGUOUS _U.S.*

Scheduled Nonscheduled Total Landings Opera ions Accident Operajions Acc Accident Operajions Accident Acc W nts ns ccidents (10 ) Rate ** (10~ ) (10 ) Rate ** (10~ ) (10 ) Rate ** (10~ )

1956 3,188 2 .627 90 0 0 3,278 2 .610 1957 3,444 2 581 90 0 0 3,534 2 .566 1958 3,302 2 .606 90 0 0 3,392 2 .590 1959 3,551 5 1.406 90 2 22.2 3,641 7 1.92 1%0 3,501 1 .286 125 0 0 3,626 1 .276 1961 3,400 1 .294 140 1 7.14 3,540 2 .565 1962 3,303 3 .908 175 0 0 3,478 3 .863 1963 3,414 2 .586 155 2 12.9 3,569 4 1.12 1964 3,554 2 .563 95 1 10.5 3,649 3 .822 1965 3,772 2 530 95 1 10.5 3,867 3 .776 1966 3,926 2 509 85 1 11.8 4,011 3 .748 Y 1%7 4,478 1 .223 90 1 11.8 4,568 2 .438 C 1968 4,836 3 .620 105 1 9.52 4,941 4 .810 1%9 4,934 1 .203 115 0 0 5,049 1 .198 1970 4,669 0 0 125 2 16.0 4,794 2 .417 1971 4,558 1 .219 155 0 0 4,713 1 .212 1972 4,601 3 .652 135 0 0 4,736 3 633 1973 4,651 4 860 130 0 0 4,781 4 .837 1974 4,275 2 .468 105 0 0 4,380 2 .457 1975 4,269 1 . 234 110 0 0 4,379 1 228 1976 4,411 1 .227 115 0 0 4,526 1 .221 1977 4,560 0 0 125 0 0 4,685 0 0 1978 4,608 1 .217 116 0 0 4,724 1 .212 1979 4,852 0 0 122 2 16.4 4,974 2 402 1980 4,892 0 0 123 1 8.13 5.015 1 .199 1981 4,664 1 .214 110 0 0 4,774 1 .209 1982 4,455 1 .224 114 1 8.77 4,569 2 .438

Destruct accidents on or off runway but within 5 miles.

- Accidents per landing.

0177G042985

to .O O. O :O O O O O -O O i

TABLE 3-4. U.S. AIR CARRIER ACCIDENT RATE FOR SCHEDULED AND' NONSCHEDULED.

TAKEOFFS IN THE CONTIGU0US U.S.*-

Scheduled Nonscheduled Total Landings

. Year-Operagions ec*Jent Accidents ** "

W *$I'"' # "

Accidents (10 ) Rated- 110~6) W -(10 *$) "* Rate ** (10'6) (10 )- Rate ** (10~6) 1956 3,188 2 .627 90 0 0 3,278 2 .610 1957. 3,444. 1 .290 90 0 0- 3,534 1 .283 1958. 3,302 3 .909 90- 0 0 .3,392 3 .884 1959 -3,551 '1. .281 90. 0 0 3,641 1. .275 1960 3,501 i .286 ,125 1 8.00 3,626. 2 .552 1961 3,400 1. .rJ4 140 0 0 3,540 1 .282 1962 3,303 2 .606 175 0 0 3,478 2 .575 1963 3,414 L1 .293 155 0 0 3,569 1 .280

-1964 3,554 1 .281 :95 1 10.5 3,649 2 .548 1965 3,772 1 .265 95 0 0 3,867 1 .259 m

1966 3,926 0 .0 85 1 11.8 4,011 1 .249

,8 , 1967 -4,478 -1 .223 90 .1 11.1 4,568 2 .438 w 1968 4,836 2 .414 105 0 0 4,941 2 .405 1969 -4,934 1 .203- 115 0 0 5,049 1 .198 1970. '4.669 0 0 125 1 8.0 4,794 1 .209 1971 4,558 0 0 '155 0- 0 4,713~ 0 0 1972 4,601 1 .217 135 0 0 4,736 1 .211 1973 4,651 '0' 0 130 0 0 4.781 0 0 1974 -4,275 _0 0 105 0 0 4,380 0 0 j 1975 4,269 0. 0 110 1 .9.09 4,379 1 .228 1976 4,411 0- -0 -115 .0 0 4,526 0 0 1977 4,560 0 0 125 .1 8.00 4,685 1' . 213 1978 .4,608 1 .217- 116 0 0 .- 4,724 1 .212 1979 -4,852- 1 .206 122 1 8.20 4,974 2 .402 1980 4,892 0 0 123 1 8.13 5.015 1 .199 1981 4,664 0 0 110 0 0 4,774 0 , 0 1982. 4,455 0 0 114 0 0 4,569 0 0

Destruct accidents on or off runw4y but within 5 miles.

- Accidents per takeoff. .

0177G042985

t 1.1 1.0 -

f HISTORICAL DATA

.9 -

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E

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9

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55' 57 59 61 63 65 67 69 '71 73 75 77 79 81 YEAR FIGURE 3-1. HISTORICAL ACCIDENT RATE VERSUS TIME - LAfiDINGS AND TAKE0FFS COMBINED

r - ~ ,e- m -

!O l

1.0

~

10 O t.

I o 'l 5

_ i.

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, s I

- L, e

o -

ll

-.4-i.. ,

O TMl L CATION 1

O , ,

o o 0t , ,

0 1 2 3 4 5 6 7 RADIUS, r (MILES)

O FIGURE 3-2. FRACTION OF CRASHES OCCURRING AT RADIUS r OR GREATER O

3-15

O

, 210 200 190 170 160 1500 0

150 1600 170 0 180 0 190 200 0 210 0 f

O o 5 -

220 0 140 0

140 220 4

230 130 0 130 3

2300 TMi Site

.O V 120 0

240"

120 2 2400 250 0 1100 lO 1 (2 CRASHES) 260 100 1000 250 0 (2 CRASHES) 0 #

270 ; :. ; 90

O 90 270 0 200 0 00 0 80 0 (18 CRASHES) 2800 i 700 290

.O 70 2s0 0 300o 60 600 30f O !

3100 l 0

50 310 i

O 320 39 POINTS TOTAL 400 40o 22 POINTS r < 0.5 m 3200 18 POINTS r = 0

O 330 0 3400 3500 0 10 20 0

\ 30 0 30* 20* 0 350 10 340 330

! l FIGURE 3-3. SCATTER PATTERN FOR TAKEOFF ACCIDENTS (Radius in Miles)

O 3-16 !

l

i O I 210* 2000 190 170 160 0 150 0 0 150 160 170 0 180 0 190 2000 210 0 o

O 5

220* 140 140 g 220 0 4 p(2 CRASHES) o 230 130 130 3 230

' TMI 3 SITE 0 120 240 120 2 oe 240 0 250 0 1100 (2 CRASHES) 110 0 250 (2 CRASHES) 260 0 1000 (2 CRASHES) o 270 0 N

m_ -

90 0 g 900 270 0 280 (27 CRASHES) 800 80 280 0 2g0 0 70 0 0 70 2900 3000 60 0 60 3000 0

.3100 2 50 0 3100 O

3200 70 POINTSTOTAL 400 40 36 POINTS r < 0.5 m 320 27 POINTS r = 0 O 330 340 350 0 10" 70

\30 0 30 200 10 0 3500 .44 0

330*

FIGURE 3-4. SCATTER PATTERN FOR LANDING ACCIDENTS (Radius in Miles) 3 3-17

J

4. ASSESSMENT OF MODEL PARAMETERS 3 In this section we will use the data presented in the previous section to estimate various components of the aircraft crash frequency model presented in Section 2.

4.1 PREDICTION OF ACCIDENT RATES FROM HISTORICAL DATA 3 In this section we develop an estimate of the aircraft accident rate, f, applicable to the plant in 1985 and beyond. Since, of course, we do not know the value of f exactly, we express our estimate in the form of a probability curve against f. The location and shape of this curve will then communicate our state of knowledge about the "true" value of f.

D The historical data curve in Figure 3-1 shows, beginning in the early 1960s, a clear downward trend in accident rates reflecting, presumably, a steady improvement in aircraft equipment, flight safety technology, and safety consciousness.

A direct linear extrapolation of the curve to the years beyond 1982, g however, would yield a crash rate very close to zero. A further extrapolation would go negative. Clearly, then, our extrapolation must reflect a leveling out of the curve. The approach followed in this study for extrapolating the crash frequency is based on Bayesian methods as described in the following:

3 1. We regard the historical data curve in Figure 3-1 as the result of sampling from an underlying population whose crash frequency is assumed to vary with time according to the functional form:

0 f(t) = a + (b-a)e (4.1)

D which reflects a gradual decrease and a leveling out at value a. In other words,, we are saying that the "true" frequency in 1965, for example, is f(1965) as calculated from Equation (4.1). In that year, we selected (see Tables 3-3 and 3-4) a sample of 3,867 departures (7,734 operations) out of which we had a total of 4 accidents.

3 The parameter b controls the initial or starting value of F(t),

A defines its rate of decrease in time, and, finally, a determines its asymptotic behavior for large t.

2. In this form, Equation (4.1), we shall fix the year to, the

) starting point in time for the fit, and assign a value to b that would be the value of F(to). We then determine or " fit" the remaining two parameters, a and A, using Bayes' theorem. That is, we regard the data in Tables 3-3 and 3-4, the experience of the past, as evidence. On the basis of this evidence,. we derive by Bayes' theorem a probability dist,'ibution on the space of a, A pairs.

0189G042985

O

3. From this probability distribution of a, A pairs, we shall derive a probability distribution for the crash frequency for any given year in the future. For instance, M'~'

- A (1985 - to) f(1985) = a + (b-a) (4.2) is the accident rate in 1985, given a, A, and b. The probability distribution of f(1985) is found from the distribution of a, A pairs.

To obtain the quantity in which we are interested; namely, the expected

! crash frequency over the remaining life of the plant, we calculate t=2015 T=h [ f(t) . (4.3) t=1985

., The following provides the details of this " Bayesian Extrapolation" process.

jg Tables 3-3 and 3-4 give us for each year, t, a doublet (nt, mt) that tells the numbers of crashes and the number of operations in that year.

Denote by B the set of such doublets from the year to on:

1982 I4*4I

'O B=f(n'*t)t=to t

B, then, is the experience of the past. Next we assume that the underlying frequency has the time dependence represented by Equation (4.1) with b and to fixed from inspection of the data. We now

-;O ask: What can we say about the values of a, A in light of the experience B?

For this purpose we write Bayes' theorem in the form

'p(Bla,A) l

g p(a,AlB) = p(a,A) (4.5)

, p(B) .

where

, p(a,A) = the probability'we assign to the

O pair a,A ' prior to having information B.

p(a,AlB) = our probability of a,A after having

information B (the posterior).

p(Bla,A) = the probability of experiencing B, given the values a,A. ;

.O p(B) = the prior probability of B.

i 4-2

O 0189G042985 i l

1 O

p(B) = p(a,A)p(Bla,A) dada. (4.6)

O To evaluate p(Bla,A) we note that each pair a, A implies a specific function of time f(t) through Equation (4.1). In any particular year, then, the probability of observing the pair (nt, mt) is:

tm 3 n m -n p(nt'"tl a, A) = l n

[f(t)] [1-f(t)] t t (4,7 )

O i tl For the size mt we are dealing with, the right side of Equation (4.7) may be replaced by n

O [mt f(t)] * - Emt f(t)]

p(nt'"tl a, A) = n!

, t The probability of experiencing the entire set B is then

O n 1982 [m f(t)] g - [mt f(t)]

t

. p(Bla,A) = [1 n! ' I4*9I t=t g t e

To carry out the process numerically, we established a discrete grid over

O the values of a and A as follows a: lay , a2 ... , a y1 lO' A: (A1 . ^2'

' A j) (yrs-1) (4.10)

We then chose a uniform prior over the set of discrete points (at,Aj),

saying thus, that as far as our knowledge goes, each such pair is as likely as any other within the grid. With this choice, Equation (4.5) becomes lO

p(Blag,A3 )

i Pjj = p(aj,AjlB) (4.11)

Ep(Bla,A) g j 1.J

!O with the right side computed from Equation (4.9) using the f(t) given by

~

Equation (4.1). ,

I We now calculate the crash frequency for four different categories of aircraft operation: scheduled landings, nonscheduled landings, scheduled takeoffs, aaa nonscheduled takeoffs and repeat the Bayesian analysis for

.O each category. The historical data in Tables 3-3 and 3-4 are displayed 0189G042985

j graphically for each data category in Figures 4-1 through 4-4. The a, A, and b values used for each category are as follows:

g e Scheduled Landings b = 1.0 x 10-6 to = 1955 a = 10.0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.61 (x 10-6)

O A= h,f,f,...h(yrs-1) e Nonscheduled Landings, b = 16 x 10 -6 t g= 1955 a = 10.0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.61 (x 10-6)-

1 1 1 1 1 1 1 11 A = (7, 4, y, y, 7, ...

p .g gf (yrs -1) e Scheduled Takeoffs b = 0.8 x 10-6 t g= 1955 l

O a = 10.0, 0.025, 0.05, 0.075, 0.1, 0.2} (x 10-6)

Ii 1 1 1 1 1 11 A = jg, 7 g, y g, .. . g, g, y, g J (yrs -1) e Nonscheduled Takeoffs O

b = 10 x 10-6 t = 1955 o

a = 10.0, 1.0, 2.0, 30.0, 4.0, 5.0, 6.0} (x 10-6) l A =I 1g , g , g , g , g , ... g (yrs-1) 1 1 1 1 1 The discrete probability distributions on the a, A grids are given in Tables 4-1 through 4-4. The crash rate versus time is on the left and O the distribution of the average crash rate for the years 1985-2015 is on the right. The resulting expected distributions for the predicted average crash frequency between 1985 and 2015 are displayed at the right of Figures 4-1 through 4-4. Each of these distributions was calculated by obtaining a distribution for the value of F(t) for each value of t in the period 1985 through 2015, using the probability distribution on the O a, A grid and then obtaining the value of T based on Equation (4.3).

The smooth curve on Figures 4-1 through 4-4 is a plot of Equation (4.1),

using the mean values of a and A from the discrete probability distribution. Similar results are provided in Figures 4-5 and 4-6 for H #

4-4 0189G042985

O O O O O O O O O O O i

1.4 1

f(t) = 9.1 x 10-7e-0.085 (t - to) + 9.0 x 104 1 1.0 --

f

=

p ISTORICAL H DATA ,

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d l: I I I l I l I l l l l l .03 .03 -.01 55 57 59 61 63 65 67 69 71 73 75 77 79 81 0 .05 .1 .15 .2 .25 .3 .35 .4 j YEAR ACCIDENTS PER MILLION

, OPERATIONS FIGURE 4-1. CRASH RATE VERSUS TIME - SCHEDULED LANDINGS i

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E ,, _ d l' I I i s I ' I I I J I r I II L 55 57 59 61 63 65 67 69 71 73 75 77 79 81 0 1 2 3 4 5 6 YEAR ACCIDENTS PEH MILLION ,

l

. OPERATIONS FIGURE 4-4. CRASH RATE VERSUS TIME - NONSCHEDULED TAKEOFFS

_ _ _ _ _ _ __ _ _ _ _ _ . . _ _ - _ _ _ - - _ _ _ - - - __ - - - --- - - - - - - - - - - - - - - - - - - - - " ^ - - - - --

O O O- 0 0 0 O o u o u l

TABLE 4-1. BAYESIAN RESULTS FOR ACCIDENT RATE DISTRIBUTION - SCHEDULED LANDINGS

- - VALUES OF PARAMETER A *** D=1.OOE-6 1/LAMDDA

O.OOE-01 5.OOE-08 1.OOE-07 2.OOE-07 3.OOE-07 4.OOE-07 5.OOE-07 6.OOE-07 TOTAL

- - - - e******************************************************************

5

2.10E-17 9.47E-09 1.35E-05 4.12E-03 9.71E-03 2.10E-03 1.06E-04 1.99E-06 1.60E-02 6

7.50E-12 1.30E-06 2.19E-04 1.08E-02 1.15E-02 1.69E-03 7.16E-05 1.28E-06 2.43E-02 7

2.98E-08 5.39E-05 1.76E-03 1.96E-02 1.09E-02 1.17E-03 4.37E-05 7.70E-07 3.36E-02 8

6.61E-06 7.63E-04 7.49E-03 2.61E-02 8.60E-03 7.27E-04 2.49E-05 4.44E-07 4.37E-02 9

2.29E-04 4.64E-03 1.89E-02 2.70E-02 5.91E-03 4.17E-04 1.36E-05 2.51E-07 5.71E-02 10

2.23E-03 1.46E-02 3.17E-02 2.31E-02 3.72E-03 2.31E-04 7.35E-06 1.42E-07 7.55E-02 11

9.72E-03 2.90E-02 3.93E-02 1.71E-02 2.17E-03 1.23E-04 3.92E-06 8.06E-OB 9.74E-02 12

2.37E-02 4.06E-02 3.88E-02 1.14E-02 1.21E-03 6.49E-05 2.10E-06 4.61E-OB 1.16E-01 13

3.82E-02 4.39E-02 3.24E-02 7.05E-03 6.59E-04 3.42E-05 1.14E-06 2.69E-08 1.22E-01 14

4.59E-02 3.94E-02 2.39E-02 4.15E-03 3.54E-04 1.81E-05 6.27E-07 1.60E-08 1.14E-01 15

4.48E-02 3.10E-02 1.62E-02 2.39E-03 1.91E-04 9.77E-06 3.54E-07 9.74E-09 9.46E-02 16

3.75E-02 2.20E-02 1.03E-02 1.33E-03 1.02E-04 5.29E-06 2.02E-07 6.01E-09 7.12E-02 17

2.81E-02 1.46E-02 6.23E-03 7.35E-04 5.51E-05 3.92E-06 1.18E-07 3.78E-09 4.97E-02 p 18

1.97E-02 9.29E-03 3.73E-03 4.12E-04 3.06E-05 1.67E-06 7.10E-OB 2.46E-09 3.32E-02 c 19

1.28E-02 5.61E-03 2.15E-03 2.26E-04 1.68E-05 9.48E-07 4.28E-OB 1.60E-09 2.08E-02 20

G.16E-03 3.38E-03 1.25E-03 1.28E-04 9.57E-06 5.61E-07 2.68E-OB 1.08E-09 1.29E-02 21

5.02E-03 2.OOE-03 7.18E-04 7.21E-05 5.49E-06 3.35E-07 1.70E-08 7.35E-10 7.81E-03 22

3.10E-03 1.20E-03 4.23E-04 4.22E-05 3.28E-06 2.08E-07 1.11E-OB 5.17E-10 4.77E-03 23

1.86E-03 7.03E-04 2.45E-04 2.45E-05 1.95E-06 1.29E-07 7.33E-09 3.64E-10 2.84E-03 24

1.12E-03 4.18E-04 1.45E-04 1.45E-05 1.19E-06 8.24E-08 4.94E-09 2.62E-10 1.70E-03 25

6.71E-04 2.47E-04 8.53E-05 8.66E-06 7.31E-07 5.29E-08 3.36E-09 1.90E-10 1.01E-03

~

TOTALS '

2.83E-01 2.63E-01 2.36E-01 1.56E-01 5.52E-02 6.60E-03 2.76E-04 5.07E-06. 1.OOE+00 MEAN VALUE FOR A =8.7241E-08 MEAM VALUE FOR LAMDDA =. 086 = 1/11.6

O O O O O O O O O O O TABLE 4-2.

BAYESIAN RESULTS FOR ACCIDENT RATE DISTRIBUTION - NONSCHEDULED LANDINGS

- - VALUES OF PARAMETER A *** B=1.60E-4 ,

1/ LAMBDA

O.OOE-01 5.OOE-O

- - - - B 1.OOE-07 2.OOE-07 3.OOE-07 4.OOE-07 5.OOE-07 6.OOE-07 3 ********************************************************** TOTAL 4

9.74E-20 1.47E-14 5.80E-13 4.37E-11 7.46E-10 6.33E-09 3.53E-08 1.48E-071.90E-07 5

9.76E-13 7.15E-11 6.98E-10 1.26E-08 9.07E-08 4.13E-07 1.42E-06 4.01E-06 ,5.95E-06 6

7

- 1.64E-06 7.51E-093.63E-06 4.09E-08 1.42E-07 8.74E-07 3.35E-06 9.76E-06 2.37E-OS 7.09E-06 2.12E-05 5.09E-05 1.06E-04 1.97E-04 3.38E-04 5.06E-05 B.85E-05 8 7.24E-04 9 ** 4.46E-04 4.93E-055.73E-04 7.54E-05 1.11E-04 2.15E-04 3.7BE-04 6.15E-04 9.42E-04 1.37E-03 7.22E-04 3.76E-03 1.09E-03 1.58E-03 2.18E-03 2.90E-03 3.75E-03 1.32E-02 -

10

1.86E-03 2.17E-03 2.51E-03 3.28E-03 4.16E-03 5.15E-03 6.24E-03 7.42E-03 3.28E-02 11 12

4.67E-03 5.15E-03 5.65E-03 6.71E-03 7.84E-03 9.01E-03 1.02E-02 1.14E-02 6.07E-02 13

8.29E-03 8.83E-03 9.36E-03 1.04E-02 1.15E-02 1.26E-02 1.36E-02 1.46E-02 8.93E-02

1.16E-02 1.20E-02 1.25E-02 1.34E-02 1.42E-02 1.49E-02 1.56E-02 1.62E-02 1.10E-01 p

14

1.37E-02 1.40E-02 1.43E-02 1'48E-02 1.53E-02 1.57E-02 1.60E-02 1.63E-02 1.20E-01 g

15 16

1.43E-02 1.45E-02 1.46E-02 1.48E-02 1.50E-02 1.51E-02 1.51E-02 1.51E-02 1.18E-01 17

1.38E-02 1.38E-02 1.38E-02 1.38E-02 1.37E-02 1.36E-02 1.35E-02 1.33E-02 1.09E-01 18 1.25E-02 1.24E-02 1.23E-02 1.22E-02 1.20E-02 1.17E-02 1.15E-02 1.12E-02 9.57E-02 19

1.08E-02 1.07E-02 1.06E-02 1.03E-02 1.01E-02 9.80E-03 9.53E-03 9.24E-03 8.10E-02

9.09E-03 8.96E-03 8.84E-03 8.58E-03 8.32E-03 8.05E-03 7.78E-03 7.50E-03 6.71E-02 20

7.44E-03 7.32E-03 7.19E-03 6.94E-03 6.70E-03 6.45E-03 6.20E-03 5.96E-03 5.42E-02 TOTALS

6.05E-03 5.93E-03 5.82E-03 5.60E-03 5.38E-03 5.16E-03 4.94E-03 4.73E-03

4. 36E -01

1.14E-01 1.~16E-01 1.18E-01 1.22E-01 1.26E-01 1s30E-01 1.34E-01 1.39E-01 1.OOE+00 l

MEAN VALUE FOR A =2.8214E-07 NEAN VALUE FOR LAMDDA =0.074 = 1/13.5

TABLE-4-3. BAYESIAN RESULTS FOR ACCIDENT RATE DISTRIBUTION - SCHEDULED TAKEOFFS

- - VALUES OF PARAMETER A *** B=8.OE-7 1/ LAMBDA.

O.OOE-01 2.50E-OB 5.OOE-08 7.50E-08 1.OOE-07 2.OOE-07 TOTAL 1

1.64E-63 1.64E-11'7.86E-OB 4.93E-06 4.82E-05 2.30E-04 2.83E-04 2

1.82E-24 6.08E-08 1.64E-05-2.35E-04 8.93E-04 6.73E-04 1.82E-03 3

2.86E-12 2.24E-O'S 7.06E-04 3.29E-03 6.10E-03 1.13E-03 1.13E-02 4

7.90E-07 1.19E-03 8.27E-03 1.69E-02 1.82E-02 1.19E-03 4.58E-02 5

4.25E-04 1.30E-02 3.29E-02 3.75E-02 2.74E-02 8.40E-04 1.12E-01 6

1.03E-02 4.52E-02 5.77E-02 4.3RE-02 2.44E-02 4.44E-04' 1.82E-01

.7

4.47E-02 6.99E-02 5.64E-02 3.24E-02 1.49E-02 1.92E-04 2/18E-01 8

7.OBE-02 6.17E-02 3.68E-02 1.74E-02 7.06E-03 7.31E-05 1.94E-01

~

9

6.02E-02 3.72E-02 1.81E-02 7.56E-03 2.81E-03 2.57E-05 1.26E-01 10

3.53E-02.1.-77E-02 7.61E-03 2.92E-03 1.03E-03 8.89E-06 6.46E-02 11-

1.63E-02 7.19E-03 2.85E-03 1.04E-03 3.54E-04 3.03E-06 2.77E-02

? 12

6.52E-03 2.66E-03 1 OOE-03 3.54E-04 1.19E-04 1.04E-06 1.07E-02 3.87E-03 0 .13

2.43E-03 9.42E-04 3.45E-04 1.20E-04 4.02E-05 3.70E-07 14

8.66E-04 3.27E-04 1.18E-04 4.09E-05 1.38E-05 1.35E-07 1.37E-03 15

3.10E-04 1.16E-044.15E-05 1.45E-05 4.90E-06 5.21E-08 4.87E-04 17

3.93E-05 1.47E-05 5.32E-06.1.89E-06 6.61E-07 8.37E-09 6.19E-05 20-

2.22E-06 8.53E-07 3.23E-07 1.21E-07 4.45E-08 7.41E-10 3.56E-06 e f TOTALS

2.4BE-01 2.57E-01 2.23E-01 1.64E-01 1.04E-01 4.81E-03 1.OOE+00 MEAN VALUE FOR A =4.1154E-08 l

NEAN VALUE FOR LAMBDA =. 15 = 1/6.67

+

. TABLE 4-4. BAYESIAN RESULTS FOR ACCIDENT RATE DISTRIBUTION - NONSCHEDULED TAKEOFFS

- - VALUES OF-PARAMETER A *** B=1.CE-5

~ l 1/ LAMBDA'

O.'OOE-01 '1.~00E-06 2.OOE-06 3.OOE-06.4.OOE-06 5.OOE-06'6.OOE-06 TOTAL

~

O. 1 '

4.96-614 2.39E-03 5.39E-02 9.10E-02 5.32E-02 1.74E-02 3.95E-03 2.22E-01

0. 5

2.93-117 2.11E-03 4.81E-02 8.25E-02 4.89E-02 1.62E-02'3.74E 2.02E-01

1. 0

2.53E-55 1.58E-03 3.63E-02 6.39E-02 3.92E-02 1.35E-02 3.21E-03 1.58E-01 ,

R2. O ' '

1.106-24 1.29E-03.2.35E-02 4.01E-02'2.53E-02 9.16E-03 2.33E-03 1.02E-01

3. 0

8.48E-15 1.46E-03 1.81E-02 2.77E-02 1.72E-02 6.40E-03 1.71E-03 7.25E-02 !

- 4. 0

4.13E-10'1.94E-03 1.53E-02 2.03E-02 1.22E-02 4.59E-03 1.28E-03 5.55E-02 i

' 5. 0

1.71E-07-'2.65E-03 1.34E-02 1.54E-02 8.83E-03 3.36E-03 9.72E-04 4.47E-02

6. 0

6.60E-06 3.53E-03 1.19E-02 1.19E-02 6.54E-03 2.50E-03 7.4BE-04 3.72E-02

7. 0

6.79E-05 4.45E-03 1.06E-02 9.32E-03-4.92E-03'1.89E-03 5.82E-04 3.18E-02

8. 0 *.3.14E-04 5.27E-03 9.29E-03 7.33E-03 3.74E-03 1.44E-03 4.59E-04 2.78E-02 ,

9. O .

8.64E-04 5.83E-03 0.06E-03 5.'80E-03 2.88E-03 1.12E-03 3.67E-04 2.49E-02 p 10.0

1.69E-03 6.09E-03 6.91E-03 4.61E-03 2.24E-03 8.82E-04 2.97E-04 2.27E-02

~

l " TOTALS *'2.94E-03 3.86E-02 2.55E-01 3.80E-01 2.25E-01 7.85E-02 1.97E-02 1.OOE+00 MEAN VALUE FOR A =3.0997E-06

, MEAN VALUE FOR LAMBDA =2.9 =1/.34 4

7

O O O O O O O O O O O.

1.0 -

~

p f(t) = 5.7 x 10-7e-0.10 (t - to) + 7.6 x 10-8 9 '8 -

5 /

5

n. .7 -

O 2

9 a

.6 d HISTORICAL DATA 2 .5 -

J E

p .4 -

e Z

~ W .38 w

y'4

~

9 .3 - -

4

.2 -

u3 1

.2 ~ .18 l 1

\

.1 - .08 i i i i i Lii i i i ! . 2_

55 57 59 61 63 65 67 69 71 73 75 77 79 81 .01 .05 .1 .15 .2 .25 .3 YEAR ACCIDENTS PER MILLION OPERATIONS FIGURE 4-5. CRASH RATE VERSUS TIME - TAKEOFFS

~ '

O 6 0 .O O O O O O' O O 4

1 2.0 -

1.8 -

1.6 -

" ' * * + **

m E 1.4 -

O z

.9

.a 1.2 -

1.0 -

"' ^^

? E m

.. s 1 g .t; --

f 1

.5 z

w ,

'4 -

y ,6 -

.31 o 28

< m

.3 -

/

\

4 -

.20

/ o2 -

.15

.2 -

7 . .. _/ V ,1 -

.07 1 I I l l l l l l l 1 I I !

55 57 59 61 63 65 67 69 71 73 75 77 79 81 .02 .i .2 .3 .4 5 .6

) EAR ACCIDENTS PER MILLION OPERATIONS FIGURE 4-6. CRASH RATE VERSUS TIME - LANDINGS

g-all' takeoffs and landings, respectively. Tables 4-5 and 4-6 present the

~ discrete probability distributions on the a, A grid for these two cases.

iO The mean annual crash rates for variou cases are summarized as follows: ;

Scheduled Landings = 1.27 x 10- Crashes per Year Nonscheduled Landings = 1.13 x 10- Crashes per Year Scheduled Takeoffs = 4.57 x 10- Crashes per Year Nonscheduled Takeoffs = 3.11 x 10- Crashes per Year g All Landings Combined = 2.11 x 10- Crashes per Year All Takeoffs Combined = 9.89 x 10- Crashes per Year 4.2 DETERMINATION OF THE SPATIAL DENSITY FUNCTIONS In this section, we apply the Bayesian approach to find probability g_ distribution, for the bracketed quantities in Equation (2.6). We begin with the radial distribution of landing crashes.

4.2.1 THE RADIAL DENSITY R(r) r=r g

C 4.2.1.1 General Approach The data shown in Figure 3-2 suggests that R(r) may be well fit by a step at r = 0, followed by a decaying exponential, i.e.,

,r=0

!O R(r) = h l*0 ,

(4.12) ae , r > 0.

This being so, the derivative of R(r) contains a delta function at r = 0

-A r R(r) = (1-a) 6(r) + Aae (4.13)

o .dr

.We seek to estimate the value of this derivative at the radius of the plant. Thus, we seek

-Ar 0 2

0 D(r) = hR(r)r = Aae (4.14)

. o where ro = 2.7 miles. We will obtain this estimate by first obtaining a discretized probability distribution (DPD) on the space of doublets, (a,A), and then converting this to a DPD against the desired derivative

.O through Equation ~ (4.14). To begin this process, we discretize the sets of possible'a's and A's a:tal,.a2, a3 ..., aI) .. ( 4.15 )

A:tA 1 , A 2. A 3. . AJ ) (4.16)

O

.n - 4-15

, 0189G042985i 7 _

i

~

O O O O O O O O O O O w

TABLE 4-5. ACCIDENT RATE FOR TAKE0FFS - SCHEDULED AND NONSCHEDULED

- - VALUES OF PARAMETER A *** B=6.5E-7 1/ LAMBDA

0.00E-01 1.00E-07 2.00E-07 3.00E-07 4.00E-07 5.00E-07 6.00E-07

- - - - TOTAL 1

2

9.2 2-122 5.14E-07 1. 08 E-03 1.13 E-03 4. 80E-05 3. 4 6E-07 7. 98 E-10 2.26E-03 3

1.77E-51 1.13E-05 3.42E-03 1.69E-03 5.23E-05 3.35E-07 7.73E-10 5.17E-03 4

1.0 7E-2 8 1. 5 2E-04 8. 34 E-03 2.18 E-03 5.18 E-05 3.0S E-07 7. 3 9 E-10 1.07E-02 5

6.41E-18 1.17E-03.1.53E-02 2.36E-03 4.64E-05 2.69E-07 6.94E-10 1.39E-02 6

7.12E-12 5.40E-03 2.15E-02 2.19E-03 3.78E-05 2.24E-07 6.43E-10 2.91E-02 7

- 3.04E-08 1.55E-02 2.41E-02'1.78E-03 2.87E-05 1.80E-07 5.90E-10 4.14E-02 a 8 6.78E-06 3.12E-02 2.26E-02 1.32E-03 2.06E-05 1.40E-07 5.37E-10 5.52E-02 L 9

' 2. 26E-04 4. 68E-02 1. 87 E-02 9.17E-04 1. 44 E-05 1.08 E-07 4. 87E-10

6.67E-02 10

2.24E-03 5.60E-02 1.40E-02 6.10E-04 9.87E-06 6.34E-03 4.42E-10 7.29E-02 11

9.65E-03 5.64E-02 9.95E-03 4.00E-04 6.79E-06 6. 45 E-0 3 4.02E-10 7.64 E-02 12

2.45 E-02 5.01 E-0 2 6.74 E-03 2.5 9 E-04 4. 66 E-06 5.01 E-n8 3.67 E-10 S.16E-02 13

4.27E-02 4.05E-02 4.44E-03 1.67E-04 3.23E-06 3.91E-J8 3.36E-10 8.78E-02 14

5.68E-02 3.06E-02 2.89E-03 1.09E-04 2.26E-06 3.09E-08 3.09E-10 9.04E-02 15 *

6. 2 3 E-0 2 2. 21 E-02 1. 87 E-03 7.12 E-0 5 1.60E-06 2.47E-08 2.85E-10 8.64E-02 16

5.93E-02 1.55E-02 1.22E-03 4.75E-05 1.16E-06 1.99E-08 2.64E-10 7.66E-02 17

5. 20E-0 2 1.06E-02 7.90 E-04 3.18 E-05 8. 40E-07 1. 6 2 E-08 2. 46E-10 6.34E-02 18

4. 2 0E-0 2 7.17E-03 5.16 E- 94 2.16E-05 6. 20 E-07 1. 33 E-08 2. 2 9E-10 4.97E-02 19

3.26E-02 4.87E-03 3.45E-04 1.51 E-05 4.67E-07 1.11 E-03 2.15 E-10 3.78E-02 20

2.41E-02 3.24E-03 2.29E-04 1.05E-05 3.52E-07 9.29E-09 2.02E-10 2.76E-02

- 1.76E-02 2.20E-03 1.56E-04 7.52E-06 2.72E-07 7.87E-09 1.91E-10 1.99E-02 TOTALS

4.26E-01 4.00E-01 1.58E-01 1.53E-02 3.32E-04 2.28E-06 8.75E-09 1.00E+00 MEAN VALUE FOR A =7.63E-s MEAN VALUE FOR LAMSDA =0.10 = 1/10.0

O O O O O O O O O O. O:

9-TABLE 4-6. ACCIDENT RATE FOR LANDINGS - SCHEDULED AND NONSCHEDULED

- - VALUES OF PARAMETER A *.* B=1.40E-6 1/ LAMBDA

0.00E-01 1.COE-07 2.00E-07 3.00E-07 4.00E-07 5.00E-07 6.00E-07 7.00E-07 8.00

. . . . . . . . . .*. . . . . . . . . . . . . . . . . . . . . . . . s a . . . * = = * * * * * *

e * * * * * * * * * = e . * *

e * *

e m e e* = = 7 9. 0 0 TOTAL

a e

e e

E - 0...*=***e.*.....

.*******ena*** E -0 7 1. 0 0 E- 0 6 -

1 2 3.3 7-263 3.22E-23 1.5 4 E-11 1.5 2E-0 6 2.37E-04 1.03 E-03 4.55E-04 4.12E-05 1.16E-06 1.33E-08 7.52 E-11 1.77E-03 3 e'3.48-110 5.25E-19 1.69E-09 1.84E-05 3.53E-04 1.79E-03 5.04E-04 3.47E-05 8.37E-07 9.00E-09 5.07E-11

3.20E-03 4 1.44E-60 6.00E-15 1.76E-07 2.28E-04 3.19E-03 3.222-03 5.73E-04 2.97E-05 6.10E-07 6.10E-09 3.42E-11 7.24E-03 5 =

4.41E-37 1.96E-11 9.28E-06 1.80E-03 3.58E-03 4.49E-03 5.34E-04 2.18E-05 3.94E-07 3.76E-09 2.14E-11 1.54E-02 6

6.73E-24 1.45E-08 2.15E-04 S.10E-03.1.53E-02 4.59E-03 3.90E-04 1.31E-05 2.18E-07 2.06E-09 1.23E-11 2.E6E-02 7 5.72 E-16 2.2 7E-06 2.12 E-03 2 09E-0 2 1.95 E-02 3.53 E-03 2.30E-04 6.78E-06 1.07E-07 1.04 E-09 6.64 E-12 4.53E-02 8 -=

7.79E-11 1.01E-04 1.05E-02 3.42E-02 1.61E-02 2.13E-03 1.14E-04 3.05E-06 4.77E-08 4.82E-10 3.39E-12 6.31E-02 9

1.71E-07 1.47E-03 2.78 E-02 3.7 9E-02 1.08E-02 1.08E-03 4. 96E-05 1.2 6E-06 2.00E-08 2.16E-10 1.69 E-12 7.91E-02 10

2.65E-05 8.67E-03 4.51E-02 3.09E-02 5.99E-03 4.80E-04 1.99E-05 4.96E-07 8.17E-09 9.57E-11 8.41E-13 9.13E-02 J* 11

6.69E-04 2.51E-02 4.99E-02 2.03E-02 2.92E-03 2.00E-04 7.80E-06 1.94E-07 3.37E-09 4.31E-11 4.27E-13 9.91E-02

d. 12

5.34E-03 4.36E-02 4.16E-02 1.12E-02 1.29E-03 7.89E-05 2.96E-06 7.53E-08 1.39E-09 1.96E-11 2.19E-13 1.03E-01

-4 13

1. 8 7E-0 2 5.13 E-02 2.80 E-02 5.5 2E-0 3 5. 34E-04 3.02 E-05 1.12 E-06 2.95 E-0 8 5.8 3E-10 9.06 E-12 1.14 E-13 1.04E-01 14

3.61E-02 4.52!-02 1.61E-02 2.51E-03 2.15E-04 1.16E-05 4.30E-07 1.1BE-04 2.52E-10 4.33E-12 6.16E-14 1.00E-01 15

4.61E-02 3.22E-02 8.32E-03 1.03E-03'8.46E-05 4.43E-06 1.68E-07 4.86E-09 1.12E-10 2.13E-12 3.40E-14 8.78E-02 16

4.37E-02 1.982-02 4.02E-03 4.59E-04 3.37E-05 1.75E-06 6 81E-08 2.0$E-09 5.20E-11 1.09E-12 1.95E-14 6.80E-02 17 e 3.33E-02 1.0 55-0 2 1.82 E-03 1.8 SE-0 4 1.33 F-05 6.9 2 E-0 7 2.79 E-0 8 9.0S E-10 2. 46E-11 5.66E-13 1.13 E-14 4.62E-02 18

2.17E-02 5.492-03 8.01 E-04 7.71 E-05 5.3 3 E-06 2.81 E-07 1.18E-08 4.09E-10 1.20E-11 3.04E-13 6.77E-15 2.81E-02 19

1.2 8E-02 2.69E-03 3.5 5 E-04 3.2 5 E-0 5 2.23 2-06 1.20E-07 5.2 8E-09 1.95 E-10 6.17E-12 1.71 E-13 4.21 E-15 1.59E-02 20 = 6.S4E-03 1.24E-03 1 50E-04 1.33E-05 9.17E-07 3.0BE-08 2.35E-09 9.25E-11 3.17E-12 9.63E-14 2.62E-15 8.24E-03 3.54E-03 5.74E-04 6.60E-05 5.75E-06 4.00E-07 2.29E-08 1.11E-09 4.66E-11 1.72E-12 5.69E-14 1.70E 4.18E-03 TOTALS

2.2 9E-01 2.48 E-01 2.37 E-01 1.76E-01 8.47E-02 2.27 E-02 2.88 E-03 1.5 2E-04 3.41E-06 3.61 E-08 2.07E-10 1.00E+00 -

MEAN VALUE FOR A =1.72E-7 MEAN VALUE FOR LAMBDA =0.10 = 1/10.0 e

r

= __ _o _ _ _ _

O We then consider the space of a, A doublets t(aj, Aj)) (4.17)

O On this space, we will establish a discrete probebility distribution by assigning a probability, pij, to each such doublet, i.e.,

i<ptj, (aj,Aj)>l (4.18)

To explain the next step, let us introduce the notation U

g(a,A) = Aae (4.19)

!O and d0 (4.20) 9 93 = g(ag ,A)) = Ajgae Then, the DPD Equation (4.18) converts through Equation (4.20) to a DPD

0

=

for g:

i<pjj, gij>l (4.21)

This is then the DPD for our desired derivative in Equation (4.14).

'O We obtain the DPD on (a,A) space by applying Bayes' theorem .in the form p(Blag,A3 )

p(ag,A3 lB) = p(ag,A3 ) (4.22) p(ag,Aj ) p(Blag,A3 )

'O where B = the information we get from our historical data.

d p(aj,AjjB) = the probability we assign to the . doublet (aj,Aj) iO after we have the information B. l i

, p(aj,Aj) = the probability we assign to the doublet (aj,Aj) prior to having the information B.

p(Blaj,Aj) = the likelihood of event-B . happening, given that aj,Aj "O are true.

In our case, B is the set of radii at which crashes occurred.

We note that B contains a total of 110 points; 45 points have r = 0, and the remainder we will write as l O !

tr I "

n 1, r 2' **** #65 1 -(4.23) l

-I 1

l JO 4-10 0189G042985

I 10' From Equation (4.13), then, the probability of these 110 crashes I occurring the way they did is l

p(Blag ,A)) = (1-ag)45 g, y )65 **P -A j I n

(4.24)

Again, for our case we have O

{r n=1 n

= 108.7 miles (4.25) so that 108.7) p(Bla ,A)) = (1-a )45 }ag)65j ,I-A g g All that remains before carrying out the calculaticas using Equation (4.22) is to specify the ai and Aj numerica.ily and, then,

, to set the prior. We choose aj,Aj as follows:

O tag} E 10.4, .45, .5, .55, .6, .65, .7} (4.27) 1 1 1 1

_A}E (j - 7g, 1.0' TT6' * * * ' 3.2g (4.28)

To reflect an initial state of knowledge, we shall choose the prior to be uniform over the (aj,Aj); Equation (4.22) then reduces, using l Equation (4.26), to a

O -Aj l08.7 ,

(1-ag )45 (a^g,'.3)65 e '

i p(a,AlB)- (4.29) 1-j -A 108.7 E (1-a )45 g g )65 e d i,j i

The results of this calculation are shown in Table 4-7. From these results, we obtain the curve in Figure 4-7 for the function R(r) using i the average a and A. Figure 4-8a shows the DPD-obtained derivative of '

R(r) at r = c.7, which is obtained by applying the results in Table 4-7 ar, in Equations (4.20) and (4.21).

!O- 1 I

D 1 1

I I

O 0189G042985'

TABLE 4-7. BAYESIAN RESULTS FOR RADIAL DISTRIBUTION - ALL CRASHES COMBINED

- - VALUES OF PARAMETER A ***

1/ LAMBDA

4.OOE-01 4.50E-01 5.OOE-01 5.50E-01 6.OOE-01 6.50E-01 7 TOTAL

- - - - .OOE-01 O.75

5.15E-17 2.17E-15 2.80E-14 1.20E-13 1.71E-13 7.65E-14 9.18E-15 1.00 4.07E-13 1,25

.* 2.07E-09 8.73E-08 1.13E-06 4.83E-06 6.89E-06 3.08E-06 3.69E-07 1.64E-05 i 'h 4.

1.50'

2.87E-06 1.21E-04 1.56E-03 6.69E-03 9.55E-03 4.26E-03.5.12E-04 2.27E-02 1.75

4.01E-05 1.69E-03 2.18E-02 9.35E-02 1.33E-01 5.96E-02 7.15E-03 3.17E-01 !

2.00

5.60E-05 2.36E-03 3.05E-02 1.30E-01 1.86E-01 8.31E-02 9.-98E-03 4.43E-01 2.25

2.25E-05 9.46E-04'1.22E-02 5.23E-02 7.47E-02 3.33E-02 4.OOE-03 1.78E-01 2.50

-4.38E-06 1.84E-04 2.38E-03 1.02E-02 1.46E-02 6.50E-03 7.81E-04 3.46E-02

-2.75-

5.92E-07 2.49E-05 3.22E-04 1.3BE-03 1.97E-03 8.79E-04 1.06E-04 4.68E-03 3.00

6.45E-08 2.72E-06 3.51E-05 1.50E-04 2.14E-04 9.58E-05 1.15E-05 5.10E-04 3.25

5.75E-09 2.42E-07 3.13E-06 1.34E-05 1.91E-05 8.55E-06 1.03E-06 4.55E-05

- 5.46E-10 2.30E-08 2.97E-07 1.27E-06 1.82E-06 8.11E-07 9.73E-08 4.32E-06 TOTALS

1.26E-04 5.33E-03 6.G9E-02 2.95E-01 4.21E-01 1.88E-01 2.25E-02 1.OOE+00 MEAN.VALUE FOR A =0.589 MEAN VALUE FOR LANDDA =0.589 = 1/1.70 I 4 4

O i

1.0 a

.O

~

I

'O -

l HISTORICAL DATA j

~

lO 1

! z "

9 h 0.1

O E 1

N

- BAYES FIT

~

0.59e lO 1.70 i

~

lO

TMl LOCATION

- i O

' " I O.01 I l I I I O 1 2 3 4 5 6 7 RADIUS, r (MILES) 1

O.

FIGURE'4-7. FRACTION OF CRASHES OCCURRING AT PADIUS r CR GREATER -

TAKEOFFS AND LANDINGS COMBINED O

4-21 i

r

f O

1 0

0.6 (LANDINGS AND TAKEOFFS l 0.5 COfABINED) 0.44O J h -

O s 04 -

lis 1 .c 0.3 -

o a: 0.2 n.

0.1 -

0.04 0.06 iO O

211--

- D '

O.04 0.06 0.08 1.0 FIGURE 4-8a. THE QUANTITY hR(r) -

r = 2. 7 1

40 0.6 0.5 - (LANDINGS ONLY) 0.47 j > -

l 4

$0.4 -

' iii 0.3 -

0.28

.O

! O 0.2 c.

g8 l 0.1 -

0.04 0.06 0.08 1.0 0

FIGURE 4-8b. THE QUANTITY RL (r) r = 2.7 O.5

O (TAKEOFFS ONLY)

> 0.4 -

0.36 t- -

d D

0.3 -

~

0.22 l N 0.2 -

9 '

8 9.d2 .: !. l

.: 0 7

0 0'01 O

j 0.04 0.06 0.03 1.0 FJdVRE 4-8c. THE QUANTITY RT (r) r = 2.7

<O O 4-22 1 1

g 4.2.1.2 The Radial Densities for Landings, RL (r) , and Takeoffs, 3 .

-d

, dr RT (r) r=r g In this section we repeat the analysis of the previous section to

.O determine the radial dependence separately for landing and takeoff accidents.

In the case of landings, B is the set of radii at which landing crashes occurred. Thus, from Table 3-2 we have:

O 8 = to,- 0, 3.5, 0.8, 0.4, ... , etc.)

We note that B contairs a total of 70 points; 27 points have r = 0, and the remainder have sum 43 O Er =n 73.8 miles (4.30) n=1 Then, as in Equation (4.26), the probability of these 70 crashes occurring as they did is:

d p(Blag,A y 3 ) = (1-ag)27 (,j j)43 e (4.31)

For this calculation the same a and A sets were chosen as in the O previous section.

The results are shown in Table 4-8 and Figure 4-8b. The Bayes' fit using the mean a, A is shown as the straight line in Figure 4-9. The staircase. function is the historical data.

O In the case of takeoff crashes, B, from Table 3-2, is the set:

. B = 10, 4.7, 0. 9, 4.0, 3.1, 0.6, . . . , etc.}

B for takeoff contains a total of 40 points,18 having r = 0.

O -The remainder have the sum 22 Er = n34.9 miles (4.32) n=1

O L 4-23 f 0189G042985-

4 TABLE 4-8. BAYESIAN RESULTS FOR RADIAL DISTRIBUTION - LANDING CRASHES ONLY I

4

- - VALUES OF PARAMETER A ***

, OLAMBDA

4.OOE-01 4.50E-01 5.OOE-01 5.50E-01 6.OOE-01 6.50E-01 7.OOE-01 TOTAL ********

a O.75

4.93E-13 7.45E-12 5.27E-11. 1.ESE-10 3.24E-10 2.75E-10 1.04E-10 j

9.47E-10 A3 1.00-

9.95E-0811.50E-06 1.06E-05 3.73E-05 6.54E-05 5.55E-05 2.09E-05 i

1.'25 1.91E-04 1.50

1.74E-05 2.63E-04 1.86E-03 6.53E-03 1.14E-02 9.71E-03 3.66E-03 3.35E-02 1.75

1.28E-04 1.94E-03 1.37E-02 4.81E-02 8.43E-02 7.16E-02 2.70E-02 2.47E-01

~2.00

is 1.92E-04 2.90E-03 2.05E-02 7.19E-02 1.26E-01 1.07E-01 4.04E-02 3.69E-01 2.25-1.20E-04 1.81E-03 1.28E-02 4.49E-02 7.88E-02 6.69E-02 2.52E-02 2.31E-01 2.50

4.53E-05 6.84E-04 4.84E-03 1.70E-02 2.97E-02 2.52E-02 9.52E-03 8.70E-02 2.75

1.31E-05 1.98E-04 1.40E-03L4.91E-03 8.60E-03-7.30E-03 2.75E-03 2.52E-02 3.00

3.23E-06 4.89E-05 3.46E-04 1.21E-03 2.12E-03.1.80E-03 6.80E-04 6.22E-03 3.25

6.93E-07 1.'05E-05 7.42E-05 2.60E-04 4.55E-04 3.87E-04 1.46E-04. 1.33E-03 i

- 1.53E-07 2.31E-06 1.64E-05 5.73E-05-1.01E-04 8.54E-05 3.22E-05 2.94E ' ,

LTOTALS

5.20E-04 7.86E-03 5.56E-02.1.95E-01 3.42E-01 2.90E-01 1.09E-01 1.OOE+00 MEAN VALUE FOR A =0.609 HEAN VALUE FOR LAMBDA =0.569 = 1/1.76 i

t-a

i

'O O i.0 l -

O O HISTORICAL DATA 5

h 0.1 -

4 -

O E _

_ BAYES FIT

76 1

i O

TMl LOCATION l

O l

0.01 I I " l I I l l 0 1 2 3 4 5 6 7 RADIUS, r (MILES)

FIGURE 4-9. FRACTION OF LANDING CRASHES OCCURRING AT RADIUS r OR GREATER O 4-25

O The probability of these 40 takeoff crashes occurring as they did is 18 22 {-A d 34.9}

n p(Bl ag ,A j ) = (1-ag ) (ag3A) e (4.33) v

!' The results for the takeoff calculation are shown in Table 4-9 and Figure 4-8c. Figure 4-10 compares the mean Bayes' fit with the 3

J i historical takeoff crash data.

10 The mean value of the distribution of the radial density for various cases are summarized as follows:

Radial Density, Landings = 7.39 x 10-2 Radial Density, Takeoffs = 6.40 x 10-2 Radial Density, Combined = 7.04 x 10-2

,0 I '

4.2.2 THE ANGULAR DENSITY 0 (0) 0=0 0

{

The same kind of reasoning can now be applied to determine the (

i O e dependence, using as data only those crashes occurring at a radius of l

> .5 mile. However, it is evident from Figure 4-11 that a simple I

exponential is not going to give a good fit to the angular data. I Therefore, we need to modify the procedure used for the radial l dependence. In doing this, we need to recognize that the important point is that the fit be good in the neighborhood of 34*, the location of the O plant. At the same time, we wish to include the experience at the extremes (0* and 90*) of the e range. Finally, if we can, we prefer to retain a fitting fraction with two parameters, rather than the complication of a three or four-parameter form.

4.2.2.1 Geaeral Approach O

The following approach appears to satisfy these requirements. We define 6(0) as the fraction of crashes occurring at angle e or greater.

We then choose the form

,0 ete) = e- * + b, 0* 5 e 5 70* (4.34)

J and use them to fit the data within the 0* to 70* range. Within this range, we may expect, from Figure 4-11, that this form has the ,

flexibility to give a good fit. Outside the range, of course, it cannot l

{

fit since it levels off, whereas the actual data goes to zero. To blend '

O in appropriately at 0 = 70*, and to account for the data of 90*, we choose the following b value: '

b = 0.098 (4.35) l We then use a Bayesian procedure to establish probability distributions O on a,A in the following way. -

f C 0189G042985 26

UO U V

~ -

~O U O O-~-~ 0 0 T C

TABLE 4-9. BAYESIAN RESULTS FOR RADIAL DISTRIBUTION - TAKE0FF CRASHES ONLY

- - VALUES OF PARAMETER A ***

1/ LAMBDA

4.OOE-01 4.50E-01 5.OOE-01 5.50E-01 6.OOE-01 6.50E-01 7.OOE-01 TOTAL

- - - - a***

i O.75

3.83E-06 1.07E-05 1.95E-05 2.38E-05 1.94E-05 1.02E-05 3.25E-06 9.08E-05 C3 1.00

7.64E-04 2.13E-03 3.89E-03 4.75E-03 3.87E-03 2.03E-03 6.48E-04 1.81E-02 1.25

6.05E-03 1.69E-02 3.OBE-02 3.76E-02 3.06E-02 1.61E-02 5.13E-03 1.43E-01 1.50

1.15E-02 3.20E-02 5.84E-02 7.14E-02 5.81E-02 3.06E-02 9.73E-03 2.72E-01 1.75

1.07E-02 2.9GE-02 5.45E-02 6.66E-02 5.42E-02 2.85E-02 9.08E-03 2.53E-01 2.00

6.87E-03 1.91E-02 3.50E-02 4.27E-02 3.48E-02 1.83E-02 5.82E-03 1.63E-01 2.25

3.55E-03 9.90E-03 1.81E-02 2.21E-02 1.80E-02 9.46E-03 3.01E-03 8.41E-02 2.50

1.66E-03 4.63E-03 8.45E-03 1.03E-02 8.40E-03 4.42E-03 1.41E-03 3.93E-02 2.75

7.32E-04 2.04E-03 3.73E-03 4.55E-03 3.71E-03 1.95E-03 6.21E-04 1.73E-02 3.00

3.05E-04 8.49E-04 1.55E-03 1.89E-03 1.54E-03 8.11E-04 2.58E-04 7.21E-03 3.25

1.31E-04 3.65E-04 6.66E-04 8.14E-04 6.63E-04 3.48E-04 1.11E-04 3.10E-03 TOTALS

4.22E-02 1.18E-01 2.15E-01 2.63E-01 2.14E-01 1.12E-01 3.5BE-02 1.OOE+00 l

l MEAN VALUE FOR A =0.548 '

MEAN VALUE FOR LAMBDA =0.603 = 1/1.66 l

l

O O 1.0 O _

O

_ 'L O

5_

b 0.1 -

HISTORICAL DATA

~

O _

,1 l

O

- \ I I

i BAYES FIT O ~

-r !

TMI LOCATION 0.5 %

_ 1.66 O

I "

0.01 L I I I I O 1 2 3 4 5 6 7 RADIUS, r (MILES)

O FIGURE 4-10. FRACTION OF TAKEOFF CRASHES OCCURRING AT RADIUS r OR GREATER O 4-28 l

- _ _ - _ _ - _ _ _ _ _ _ l

O 1 1

3 ,

~

l l

O .

HISTORICAL DATA O L BAYES FIT

% -0 0.53e g + 0.098 o I 5 -

0,1 -

E O

O -

O TMt LOCATION O

0.01 O

I I I I d I 10 20 30 40 50 60 70 ANGLE OFF RUNWAY,0 (DEGREES)

O FIGURE 4-11.

ANG'JLAR DISTRIBC TION OF CRASHES - LANDINGS AND TAKE0FFS COMBINED 0 4-29

10 From Equation (4.34) we have the frequency density O e (e) = (1-a-b) 6(e) + aAe # (4.36) de now take B to be the set of crash points in the 0" to 70* range (and having r > .5 mile). Thus, from Table 3-2:

B = 10, 01, 47, 61, 0, 26, 0, ...}

O a total of 46 crashes with 19 at 0 = 0. Thus, 27

-A O p(Bla,A) = (1-a-b)19(aA)27 e E1 i (4.37)

O where 27 E0$ = 486 (4.38) 1 O

The resulti.ig DPDs are shown in Table 4-10. The corresponding distribution for the desired derivative quantities is shown in Figure 4-12a. As a matter of interest, Figure 4-11 shows the goodness of fit using the mean a,A, to the experimental data.

O 4.2.2.2 The Quantities - eL(OI e and eT(0) 9 0 _ 0 We new apply the analysis of the previous section to the landing and O takeoff data separately. For landings, there is a total of 34 crashes; 15 at 0 = 0 and 2 at 90 . We, therefore, set b=h=.059 (4.39)

O and summing over the points less than 90*, we have 17 Eog = 230 (4.40) i=1 O The resulting distribution over the (a,A) space is shown in l Table 4-11. The histogram for the desired derivative is plotted as Figure 4-12b. The Bayes' fit with average a,A is pictted with the historical data in Figure 4-13.

O O

0189G042985

TABLE 4-10. BAYESIAN RESULTS FOR ANGULAR DISTRIBUTION - LANDINGS AND TAKE0FFS COMBINED

- - VALUES OF PARAMETER A *** DsO.098 1/ LAMBDA

2.OOE-01 3.OOE-01 4.OO

- - - - E-01 5.OOE-01 6.OOE-01 7.OOE-01 TOTAL

******************n*************** *********

5 10

7.52E-23 2.31E-19 1.73E-17 1.05E-16 6.29E-17 1.94E-18 1.07E-16

? 15

7.17E-10 2.20E-06 1.6'4E-04 9.99E-04 5.99E-04 1.85E-05 1.78E-03 b! 20

1.38E-07 4.22E-04 3.16E-02 1.92E-01 1.15E-01 3.55E-03 3.42E-01 25

1.91E-07 5.85E-04 4.38E-02 2.66E-01 1.60E-01 4.92E-03 4.75E-01 30

5.96E-OB'1.83E-04 1.37E-02 8.30E-02 4.98E-02 1.54E-03 1.48E-01 35

1.10E-OB 3.36E-OS 2.51E-03 1.53E-02 9.15E-03 2.82E-04 2.73E-02 40

1.77E-09 5.42E-06 4.06E-04 2.46E-03 1.48E-03 4.56E-05 4.40E-03 45

2.69E-10

4.2SE-11 8.24E-07 6.17E-05 3.75E-04 2.25E-04 6.93E-06 6.69E-04 50 1.30E-07 9.74E-06 5.92E-05 3.55E-05 1.09E-06 1.06E-04

7.39E-12 2.26E-08 1.70E-06 1.03E-05 6.17E-06 1.90E-07

1.84E-05 TOTALS l

4.02E-07 1.23E-03 9.22E-02 5.60E-01 3.36E-01 1.04E-02 1.OOE+00 MEAN VALUE FOR A =0.526 MEAN VALUE FOR LAMBDA =0.0537 = 1/18.6 l

O 0.5 0.40 (LANDING AND TAKEOFFS 0 .4 -

COMBINED) o t 2 0.3 -

0.24 0 g 2

m 0.2 -

o ec 8-0.1 -

0.06 O , 0 Y 0 1 2 3 4 5 6 7 x 10-3 ,

N -

, FIGURE 4-12a. THE QUANTITY ,hO(0)

. . . . . 0 = 34 0 -

0.s -

g 0.4 -

> 0.35 L , , 0.31 O -

g u.3 - -

0.2 -.. 'M _0.14 0.1 -

0.04 0 l '

O o i 2 3 ~ 5 6 7 a x 104 FIGURE 4-12b. THE QUANTITY phO(0) T 0 = 34 i O -

1 0.5 ~

f.0.4 >

(1.ANDINGS ONLY)

"3 0.30 E 0.3 f'

0.23 ~

0.24 O I -

^

@ 0.2 0.14 0.1 -

0.0S -

l O _ -

t 0 1 2 3 4 5' 8 7 , x 10-3

~~ ~

O - s. 1s ; .

i

~

FIGURE 4-12c. THE QUANTITY 8 \

de L(0) 0 = 34o

, e f- \. .,g j E m '%

% N

, r O- ' - '

4 -

W &

- )_b'

UM U O O- O: O O O O O O O O J

TABLE 4-11. BAYESIAN RESULTS FOR ANGULAR DISTRIBUTION - LANDINGS ONLY 1

[

r- *** VALUES OF PARAMETER A *** B=,b.90E-02 y

1/LAMDDA

2.OOE-01 3.OOE-01 4.OOE-01 5. OOE-01 6. OOE-01 2'/. OOE-01 TO

- - - - r**************TAL 5

6. 61E-10 7. 40E-08 7. 73E-07 1. 60E-06 7. 50E-0;' 5. 65E-08 3.26E-06 10

4.91E-05 5.50E-03 5.75E-02 1.19E-01 5.5BE-02 4.20E-03 2.42E-01 15

1.06E-04 1.19E-02 1.24E-01 2.58E-01 1.21E-01 9.09E-03 5.24E-01 a 20

da 3.70E-Ob 4.14E-03 4.33E-02 8.96E-02 4.20E-02 3.16E-03 1.82E-01 25

8.31E-06 9.31E-04 9.72E-03 2.01E-02 9.43E-03 7.11E-04

"' 4.09E-02 30

1.72E-06 1.93E-04 2.01E-03 4.17E-03 1.95E-03 1.47E-04 8.47E-03 35

3.82E-07 4.27E-05 4.46E-04 9.24E-04 4.33E-04 3.26E-05 1.88E-03 40

8.87E-OB 9.93E-06 1.04E-04 2.15E-04 1.01E-04 7.59E-06 4.37E-04 45

2.24E-OB 2.51E-06 2.62E-05 5.43E-05 2.55E-05 1.92E-06 1.10E-04 50

75

6.31E-09 7.06E-07 7.38E-06 1.53E-05 7.16E-06 5.40E 3.11E-05 100

2.86E-11 3.21E-09 3.35E-OB 6.94E-08 3.25E-OB 2.45E-09 1.41E-07 125

4.80E-13 5.37E-11 5.62E-10 1.16E-09 5.45E-10 4.11E-11 2.36E-09 1.71E-14 1.92E-12 2.OOE-11 4.15E-11 1.94E-11 1.46E-12 8.43E-11 TOTALS

2.03E-04 2.27E-02 2.37E-01 4.92E-01 2.30E-01 1.74E-02 1.OOE+00 MEAN VALUE FOR A =4.9816E-01 NEAN VALUE FOR LAMBDA =7 0191E-02 =1/14.2

.O g 1.0 O .

~

a

~

l O_ h HISTORICAL DATA O L 1

z BAYES FIT i O.

0.1 -

} + 0.059 k -

O -

O .

O TMI LOCATION O

0.01 I l' I l l I O 10 20 30 40 50 60 70 ANGLE OFF RUNWAY,0 (DEGREES)

O FIGURE 4-13. ANGULAR DISTRIBUTION OF LANDING CRASHES O

4-34 L

Q

' For takeoffs, there is a total of 17 crashes; 4 at 0 = 0 and 3 at 90'.

In this case '

3.

b=h=.176 (4.41) I The sum of the angles in this case is 10 3 0j = 256, (4.42)

The results are given in Table 4-12 and Figures 4-12c and 4-14. The mean value of the distribution of the angular density for various cases are summarized as follows:

Angular Density, Landings = 3.31 'x 10-3 Angular Density, Takeoff = 5.75 x 10-3.

Angular Density, Con:bined = 4.52 x 3 3

O 1

O O l I

O O

O. 4-35 0189G042985

L o- o o u o u u u-- e e e TABLE 4-12. BAYESIAN RESULTS FOR ANGULAR DISTRIBUTION - TAKE0FFS ONLY

- - VALUES OF PARAMETER A *** B=0.176 1/ LAMBDA

2.OOE-01 3.OOE-01 4.OOE-01 5.OOE-01 6.OOE-01 7 TOTAL

- - - - .OOE-01 5

1.57E-15 4.50E-14 3.42E-13 1.09E-12 1.54E-12 6.75E-13 10 3.69E-12 15

2.01E-07 5.76E-06 4.39E-05 1.39E-04 1.97E-04 8.64E-05 4.73E-04 20

1.78E-05 5.11E-04 3.89E-03 1.24E-02 1.75E-02 7.67E-03 4.19E-02

? 25

7.11E-05 2.04E-03 1.55E-02 4.93E-02 6.97E-02 3.06E-02 1.67E-01 M 30

9.87E-05 2.63E-03 2.16E-02 6.84E-02 9.68E-02 4.25E-02 2.32E-01 35-

8.77E-05 2.52E-03 1.92E-02 6.08E-02 8.60E-02 3.77E-02 2.06E-01 40

6.38E-05 1.83E-03 1.L?E-02 4.42E-02 6.26E-02 2.75E-02 1.50E-01 45

4.18E-05 1.20E-03 9.12E-03 2.90E-02 4.10E-02 1.80E-02 9.83E-02 50

- 2.61E-05 7.48E-04 5.69E-03 1.81E-02 2.56E-02 1.12E-02 4.14E-02 75 1.61E-05 4.63E-04 3.52E-03 1.12E-02 1.5BE-02 6.94E-03 3.79E-02 100

1.52E-06 4.35E-05 3.31E-04 1.05E-03 1.49E-03 6.52E-04 3.57E-03 125

2.04E-07 5.84E-06 4.45E-05 1.41E-04 2.OOE-04 8.77E-05 4.79E-04

- 3.65E-08 1.05E-06 7.97E-06 2.53E-05 3.58E-05 1.57E-05 8.59E-05 TOTALS

4.25E-04 1.22E-02 9.28E-02 2.95E-01 4.17E-01 1.83E-01 1.OOE+00 MEAN VALUE FOR A =0.566 MEAN VALUE FOR LAMBDA =0.0363 = 1/27.5

O O .

HISTORICAL DATA L.

O _

1 BAYES FIT

- -9 0.57e 27.5 + 0.176

o- -

O 5

h 0.1 -

g -

iO- -

.O _

O TMI LOCATION

O I I I " l I I 0.01 O '10. 20 30 40 50 60 70 ANGLE OFF RUNWAY,0 (DEGREES)

O FIGURE 4-14. ANGULAR DISTRIBUTION OF 'iAKE0FF CRASHES O 4_37

O l

5. REFERENCES

'1. Kaplan, S., J. M. Vallance and C. L. Cate, " Prediction of the O. Frequency of Aircraft Crashes at the Three Mile Island Site,"

Pickard, Lowe and Garrick, Inc., October 1978.

2. Vallance, J. M., Testimony before the Atomic Safety and Licensing Appeal Board in the matter of Metropolitan Edison Company, Docket O No. 50-320, Rev. 1, December 8, 1978.

3. Vallance, J. M., and S. Kaplan, Supplemental Testimony before the Atomic Safety and Licensing Appeal Board, in the matter of Metropolitan Edison Company, Docket No. 50-320, January 9,1979.

O 4. Kaplan, S., Supplemental Testimony before the. Atomic Safety and Licensing Appeal Board, Docket No. 50-320, March 20,1979.

5. Letter of verification for aircraft movements from Mr. Dennis Hampshire, Assistant General Manager, Harrisburg International Airport, Pennsylvania.

6. Burgess, J. A., Memorandum to R. K. Locke, GPU Nuclear Corporation, January 25, 1985.

7. Federal Aviation Administration, "FAA Statistical Handbook of Aviation," calendar years 1978 - 1983.

O 8. Civil Aeronautics Board, " Airport Activity Statistics of Certificated Route Air Carriers," calendar years 1977.- 1982.

.9.- National Transportation Safety Board, " Annual Report to the l Congress," calendar years 1977 - 1983.

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10. GPU Nuclear Corporation, TMI-1 FSAR, Section 2, July 1983.

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