DesclassificadoDocumento

DOW-UAP-D48, Department of the Air Force Report, 1996

Agência: Departamento de Guerra
Data do incidente: 10/09/1996
Liberação: 08/05/2026
Ano: 1996

Este relatório descreve a Modelagem de Falhas Improváveis de Propulsores Espaciais em Cálculos de Risco, documentando modos históricos de falha de lançamento e recomendando ações corretivas para abordá-los usando novas técnicas de modelagem.

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This report describes the Modeling of Unlikely Space-Booster Failures in Risk Calculations, documenting historical launch failure modes and recommending corrective actions to address them using novel modelling techniques.

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RESEARCH TRIANGLE INSTITUTE /RTI

Contrato Nº FO4703-91-C-0112
Relatório RTI Nº RTI/5180/77-43F
10 de setembro de 1996

Modelagem de Falhas Improváveis de Propulsores Espaciais em Cálculos de Risco

Relatório Final

Preparado para

Departamento da Força Aérea
45th Space Wing (AFSPC)
Safety Office - 45 SW/SE
Patrick AFB, FL 32925

e

Departamento da Força Aérea
30th Space Wing (AFSPC)
Safety Office - 30 SW/SE
Vandenberg AFB, CA 93437

Distribuição autorizada a agências do Governo dos EUA e seus contratados para proteger dados de uso administrativo/operacional, 10 de setembro de 96. Outras solicitações para este documento devem ser encaminhadas ao Safety Office (30 SW/SE) da 30th Space Wing (AFSPC), Vandenberg AFB, CA 93437, ou ao Safety Office (45 SW/SE) da 45th Space Wing (AFSPC), Patrick AFB, FL 32925.

[...]

Resumo

Os históricos de desempenho de mísseis e veículos espaciais contêm muitos exemplos de falhas que causam, ou têm o potencial de causar, desvios significativos do veículo em relação à linha de voo pretendida. No programa de análise de risco da RTI, DAMP, tais falhas são referidas como respostas de falha de Modo-5. Embora as respostas de falha de Modo-5 sejam muito menos propensas a ocorrer do que aquelas que resultam em impactos próximos à linha de voo, os estudos de análise de risco estão incompletos sem elas. Este relatório mostra como os impactos das falhas de Modo-5 são modelados no programa DAMP. A função de densidade de impacto usada para este propósito contém duas constantes de modelagem que controlam a taxa na qual a função de densidade cai em valor à medida que o desvio angular da linha de voo e o alcance do impacto aumentam. Certos mau funcionamentos de Modo-5 são simulados, e as duas constantes de modelagem são então escolhidas por tentativa e erro para que os impactos dos mau funcionamentos simulados e a função de densidade teórica estejam em estreita concordância.

Um apêndice do relatório contém uma listagem e um breve histórico narrativo de falhas dos lançamentos de mísseis e veículos espaciais Atlas, Delta e Titan das Bases Leste e Oeste desde o início de cada programa até agosto de 1996. Cada entrada fornece a configuração do veículo, se o voo foi um sucesso, a fase de voo em que ocorreu qualquer comportamento anômalo e uma classificação do comportamento do veículo de acordo com os modos de resposta a falhas definidos. Várias técnicas de filtragem ou ponderação de dados são descritas. Os dados empíricos são então filtrados para estimar (1) probabilidades de falha para Atlas, Delta e Titan, e (2) porcentagens de falhas futuras que resultarão em respostas de Modo-5 (e outros Modos).

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== �-== -=--=- �=------===--====-==-=--=-=-==-__;;;;.______________

RESEARCH TRIANGLE INSTITUTE /RTI

Contract No ■- FO4703-91-C-0112
RTI Report No. RTl/5180/77-43F
September 10, 1996

Modeling Unlikely Space-Booster
Failures in Risk Calculations
Final Report

Prepared for

Department of the Air Force
45th Space Wing (AFSPC)
Safety Office - 45 SW/SE
Patrick AFB, FL 32925

and

Department of theAir Force
30th SpaceWing (AFSPC)

19961025 122 Safety Office- 30 SW/SE
Vandenberg AFB, CA 93437

'mJC QUALITY INSPECTED ff

3000 N. Al1antic Avenue • Cocoa Beach, Flo 0ida 329315029 US/1
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Contract No. FO4703-91-C-0112 RTI Report No. RTI/5180/77-43F
Task No. 10/95-77, Subtask 2.0 September 10, 1996

Modeling Unlikely Space-Booster
Failures in Risk Calculations

Final Report

Prepared by

James A. Ward, Jr.
Robert M. Montgomery

Research Triangle Institute
Center for Aerospace Technology
Launch Systems Safety Department

Prepared for

Department of the Air Force
45th Space Wing (AFSPC)
Safety Office - 45 SW/SE
Patrick AFB, FL 32925

and

Department of the Air Force
30th Space Wing (AFSPC)
Safety Office - 30 SW /SE
Vandenberg AFB, CA 93437

Distribution authorized to US Government agencies and their contractors to protect administrative/
operational use data, 10 September 96. Other requests for this document shall be referred to the 30th Space
Wing (AFSPC) Safety Office (30 SW/SE), Vandenberg AFB, CA 93437, or 45th Space Wing (AFSPC)
Safety Office (45 SW/SE), Patrick AFB, FL 32925.
Form Approved
REPORT DOCUMENTATION PAGE 0MB No. 0704-0188
Public tel)Ort1ng burden for this collection of information is estimated to average 1 hour per response. induding the time for reviewing instructions, searching exi5ting data sources.
gathering and maintain in!,! the data needed, and completing and rev,ew,ng the collection of Information. Send comments r~ardlng tlils burden estimate or any other aspect of this
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Davis Highway, Suite 1204, Arlington, VA 12202-4302, and to the Office of Management and Budget. Paperwork Reduction Project(0704-0188), Washington. DC 20503.

1. AGENCY USE ONLY (Leave blank) ~.• REPORT DATE 3. REPORT TYPE AND DATES COVERED
. eptember 10, 1996 1 Final
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
f.1odeling Unlikely Space-Booster Failures in Risk Galculations C: F04703-91-C-o112
TA:10/95-TT
6. AUTHORW •
James A. ard, Jr.
Robert M. Montgomery
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
REPORT NUMBER
Research Triangle Institute * ACTA, Inc. **
113000 N. Atlantic Avenue · Skypark3 RTl/5180m-43F
Cocoa Beach, FL 32931 23430 Hawthorne Blvd., Suite 300
Torrance, CA 90505
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/ MONITORING
AGENCY REPORT NUMBER
Department of the Air Force (AFSPC) Department of the Air Force (AFSPC)
30th Space Wing 45th Space Wing r\~'1~.1
- - -m.-t1<a-a
Vandenberg AFB, CA 93437 Patrick AFB, FL 32925
-Mr. Martin Kinna (30 SW/SEY) Louis J. Ullian, Jr. (45 SW/SED)
11. SUPPLEMENTARY NOTES
* Subcontractor
" Prime Contractor
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Distribution authorized to US Government agencies and their contractors to protect
administrative/operational use data; 10 September 96. Other requests for this document shall
be referred to the 30th Space Wing (AFSPC) Safety Office (30 SW/SE),Vandenberg AFB, CA
93437, or 45th Space Wing (AFSPC) Safety Office (45 SW/SE), Patrick AFB, FL 32925. (!__,
13. ABSTRACT (Maximum 200 words)
Missile and space-vehicle performance histories contain many examples of failures that cause, or have the
potential to cause, significant vehicle deviations from the intended flight line. In RTl's risk-analysis program,
DAMP, such failures are referred to as Mode-5 failure responses. Although Mode--5 failure responses are much
less likely to occur than those that result in impacts near the flight line, risk-analysis studies are incomplete without
them. This report shows how Impacts from Mode-6 failures are modeled in program DAMP. The impact density
function used for this purpose contains two shaping constants that control the rate at which the density function
drops In value as the angular deviation from the flight line and the impact range increase. Certain Mode--5
•malfunctions are simulated, and the two shaping constants then chosen by trial and error so that impacts from the
simulated malfunctions and the theoretical density function are in close agreement. An appendix to the report
contains alisting and brief narrative failure history of the A~as, Delta, and Titan missile and space-vehicle launches
from the Eastern and Western Ranges from the beginning of each program through August 1996. Each entry
gives the vehicle configuration, whether the flight was asuccess, the flight phase in which any anomalous behavior
occurred, and aclassification of vehicl~ behavior in accordance with defined failure-response modes.
14. SUBJECT TERMS 15. NUMBER OF PAGES·
launch risk, unlikely failure modeling, booster failure probabilities 180
16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT
OF REPORT OF THIS PAGE OF ABSTRACT
Unclassified lJnclassified lnclasslfled SAR
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)
Prescribed by AIIISI Std. Z39-18
298·102
Abstract
Missile and space-vehicle performance histories contain many examples of failures that
cause, or have the potential to cause, significant vehicle deviations from the intended
flight line. In RTI's risk-analysis program, DAMP, such failures are referred to as
Mode-5 failure responses. Although Mode-5 failure responses are much less likely to
occur than those that result in impacts near the flight line, risk-analysis studies are
•incomplete without them. This report shows how impacts from Mode-5 failures are
modeled in program DAMP. The impact density function used for this purpose
contains two shaping constants that control the rate at which the density function drops
in value as the angular deviation from the flight line and the impact range increase.
Certain Mode-5 malfunctions are simulated, and the two shaping constants then chosen
by trial and error so that impacts from the simulated malfunctions and the theoretical
density function are in close agreement.
An appendix to the report contains a listing and brief narrative failure history of the
Atlas, Delta, and Titan missile and space-vehicle launches from the Eastern and
Western Ranges from the beginning of each program through August 1996. Each entry
gives the vehicle configuration, whether the flight was a success, the flight phase in
which any anomalous behavior occurred, and a classification of vehicle behavior in
accordance with defined failure-response modes. Various filtering or data weighting
techniques are described. The empirical data are then filtered to estimate (1) failure
probabilities for Atlas, Delta, and Titan, and (2) percentages of future failures that will
result in Mode-5 (and other Mode) responses.

9/10/96 RTI
Table of Contents ·

1. Introduction............................................................................................................................... 1

2. Examples Showing Need for Mode 5 ................................................................................ 3

3. Understanding the Mode-5 Failure Response ................................................................... 7
3.1 Effects of Mode-5 Shaping Consta.nts................................. ".....................................-...... 9
3.2 Effects of Shaping Constant on DAMP Results ........................................................ 9

4. Methodology for Assessing Failure Probabilities ........................................................... 13
4.1 The Parts-Analysis Approach .................................................................................. 13'-
4.2 The Empirical Approach .......................................................................................... 15

5. Computation of Failure Probabilities ............................................................................... 16
5.1 Overall Failure Probability....................................................................................... 16
5.2 Relative and Absolute Probabilities for Response Modes ..................................... 24
5.3 Relative Probability of Tumble for Response-Modes 3 and 4 ............................... 30
6. Shaping Constants Through Simulation .......................................................................... 31
6.1 Malfunction Tum. Simulations...........•...................................................................... 31
6.1.1 Random-Attitu.de Failures ...............-............................................................... 31
6.1.2 Slow-Tum Failures ........................................................................................... 32
6.1.3 Factors Affecting Malfunction-Tum Results ................................................ 33
6.1.4 Malfunction-Tum Results for Atlas IIAS ...................................................... 35
6.2 Shaping Constants for Atlas IIAS ............................................................................ 37
6.2.1 Optimum Mode-5 Shaping Constants ........................................................... 37
6.2.2 Launch-Area Mode-5 Risks ............................................................................ 49
6.2.3 Effects of Mode-5 Constants on Ship-Hit Contours ..................................... 51 I
6.2.4 Range Distributions of Theoretical and Simulated Impacts........................ 58
6.3 Shaping Constants for Delta-GEM .......................................................................... 60
6.3.1 Optimum Mode-5 Shaping Constants ........................................................... 61
6.3.2 Launch-Area Mode-5 Risks ............................................................................ 64
6.4 Shaping Constants for Titan IV................................................................................ 65
6.5 Shaping Constants for LLVl .................................................................................... 69
6.6 Shaping Constants for Other Launch Vehicles ....................................................... 72

7. Potential Future Investigations ......................................................................................... 73

8. Summarv:
., ............................................................................................................................ 74

9/10/96 ii RTI
Appendix A. Failure Response Modes in Program DAMP ............................................... 79

Appendix B. Shaping-Constant Effects on Mode-5 Impact Distributions ........................ 81

Appendix C. Filter Characteristics ....................................................................................... 90

Appendix D. Launch and Performance Histories .............................................................. 96
D.1 Basic Data ................................................................................................................. 96
D.1.1 Data Sources ................................................................................................................................................................... 96
D.1.2 Assignment of Failure-Response Modes...................................................... 98
D.1.3 Assignment of Flight Phase.......................................... ~ ....................................................................... 98
D.1.4 Representative Configurations ................................................................... 100
D.2 Atlas Launch and Performance History .............................................................. 101
D.2.1 A'tlas Launch History ..................................................................................................... 103
D.2.2 Atlas Failure Narratives ........... ~ .................................................................... 115
D.3 Delta Launch and Performance History .............................................................. 133
D.3.1 Delta Launch History................................................................................... 136
D.3.2 Delta Failure Narratives .............................................................................. 142
D.4 Titan Launch and Performance History .............................................................. 146
D.4.1 Titan Launch History ................................................................................... 149
D.4.2 Titan Failure Narratives .............................................................................. 157
D.5 Thor Launch and Performance History (Not Including Delta) ......................... 164
D.5.1 Thor and Thor-Boosted Launch History .................................................... 164
D.5.2 Thor and Thor-Boosted Failure Narratives ............................................... 167

References ............................................................................................................................. 171

9/10/96 iii RTI
Table of Figures
Figure 1. Joust Impact Trace Showing a Mode-5 Failure Response ....................................6
Figure 2. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.0.............................. 11
Figure 3. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.5.............................. 12
Figure 4. Filter Factor Results for Representative Configurations of Atlas ...................... 23
Figure 5. Combined Random-Attitude and Slow-Tum Results ........................................ 36
Figure 6. Atlas IIAS Breakup Percentages for Random-Attitude Tums ........................... 37
Figure 7. Atlas HAS Impacts with No Breakup ........................................................ ~ ........ 39
Figure 8. Atlas IIAS Impacts with Breakup ......................................................................... 40
Figure 9. Atlas IIAS Simulation Results with B = 1,000 ..................................................... 42
Figure 10. Atlas IIAS Simulation Results with B = 50,000.................................................. 44
Figure 11. Atlas HAS Simulation Results with B = 100,000................................................ 45
Figure 12. Atlas HAS Simulation Results with B = 500,000................................................ 46
Figure 13. Atlas HAS Simulation·Results with B = 5,000,000............................................. 47
Figure 14. Effects of Breakup q-alpha on A for Atlas IIAS ................................................ 49
Figure 15. Mode-5 Density-Function Values at Three Miles ............................................. 51
Figure 16. Atlas IIAS Mode-5 Ship-Hit Contours with A= 3.00 ....................................... 53
Figure 17. Atlas IIAS All-Mode Ship-Hit Contours with A = 3.00.................................... 54
Figure 18. Atlas IIAS Mode-5 Ship-Hit Contours with A= 3.45 ....................................... 55
Figure 19. Atlas IIAS All-Mode Ship-Hit Contours with A= 3.45.................................... 56
Figure 20. Atlas IIAS Mode-5 Ship-Hit Contours with A = 6.30 ....................................... 57
Figure 21. Atlas IIAS All-Mode Ship-Hit Contours with A = 6.30.................................... 58
Figure 22. Impact-Range Distributions .................................................................................. 59
Figure 23. Delta-GEM Breakup· Percentages ....................................................................... 61
Figure 24. Delta-GEM Simulation Results with B ==-1,000.................................................. 62
Figure 25. Delta-GEM Simulation Results with Best-Fit Shaping Constants ................... 63
Figure 26. Titctn·IV Breakup Percentages ................................................................................ 65
Figure 27. Titan·Simulation Results with B = 1,000 ............................................................ 66
Figure 28. Titan Simulation Results with Best-Fit Shaping Constants.............................. 67
Figure 29. LLVl Breakup Percentages ..................................................................................................................... 69
Figure 30. LLVl Simulation Results with B = l,000............................................................ 70

9/10/96 iv RTI
Figure 31. LLVl Simulation Results with Best-Fit Shaping Constants ............................. 71
Figure 32. £-Ratios for Ranges from 1 to 25 Miles .............................................................. 86
Figure 33. Percentage of Impacts Between Flight Line and Any Radial .......................... 87
Figure 34. Percentage of Impacts in 5-Degree Sectors ........................................................ 88
Figure 35. Exponential Weights for Fading-Memory Filters ............................................. 93
Figure 36. Recursive Filter Factor for Last Data Point........................................................ 94
Figure 37, Atlas Launch Summary..................................................................................... 102
Figure 38. Delta Launch Summary." ................................................................................... 135
Figure 39. Titan Launch Summary..................................................................................... 148
Figure 40. Thor Launch Summary ..................................................................................... 164

Table of Tables
Table 1. Effects of Mode-5 Shaping Constant A on Atlas IIA Risks .................................. 10
Table 2. Predicted Failure Probabilities for Representative Configurations .................... 17
Table 3. Predicted Failure Probabilities for All Configurations ........................................ 18
Table 4. Comparison of Weighting Percentages ................................................................. 19
Table 5. Filter Factor Influence on Weighting Percentages ................................................ 21
Table 6. Failure Probabilities for Atlas, Delta, and Titan ................................................... 24
Table 7. Number of Atlas Failures - All Configurations (532 Flights) .............................. 25
Table 8. Number of Delta Failures-All Configurations (232 Flights).............................. 25
Table 9. Number of Titan Failures - All Configurations (337 Flights) .............................. 25
Table 10. Number of Eastern-Range Thor Failures (85 Flights) ........................................ 25
Table 11. Number of Failures for All Vehicles (1186 Flights)............................................ 26
Table 12. Date of Most Recent Failure ................................................................................. 26
Table 13. Percentage Weighting for Sample of 1186 Launches ......................................... 27
Table 14. Response-Mode Occurrence Percentages ............................................................ 27
Table 15. Recommended Response-Mode Percentages for Flight Phases O- 2................ 28
Table 16. Recommended Response-Mode Percentages for Flight Phases O- 1................ 29
Table 17. Absolute Failure Probabilities for Response Modes 1 - 5 .................................. 29
Table 18. Percent of Response Modes 3 and 4 That Tumble .............................................. 30

9/10/96 V
Table 19. Sample Impact Distribution for Atlas IIAS- with No Breakup .......................... 41
Table 20. Shaping Constants for Atlas IIAS......................................................................... 48
Table 21. Shaping Constants and Related Risks for Atlas HAS-......................................... 50
Table 22. Best-Fit Conditions for Atlas IIAS............................................. :.......................... 52
Table 23. Shaping Constants and Related Risks for Delta-GEM ....................................... 64
Table 24. Shaping Consta.nts for Titan IV ............................................................................ 68
Table 25. Shaping Constants for LLVl ................................................................................. 72
Table 26. Summary of A Values for B = 1,000................. ;................................................... 72-
Table 27. Failure Probabilities for Atlas, Delta, and Titan ................................................. 75
Table 28. Recommended Response-Mode Percentages for Flight Phases O-2 ................. 75~
Table 29. Recommended Response-Mode Percentages for Flight Phases O- 1................ 75
Table 30. Absolute Failure Probabilities for Response Modes 1 - 5 .................................. 76
Table 31. Summary of A Values for B = 1,000..................................................................•... 77
Table 32. Summary of Optimum·Mode-5 Shaping Constants ........................................... 77
Table 33. Effect on £-Ratio-of Varying Mode-5 Constant A {B = 1000) - Part 1 ................ 82
Table 34. Effect on £-Ratio-of Varying Mode-5 Constant A {B = 1000) - Part 2 ................ 83
Table 35. Effect on £-Ratio-of Varying Mode-5 Constant B {A = 3) - Part 1 ...................... 84
Table 36. Effect on £-Ratio-of Varying Mode-5 Constant B {A= 3) - Part 2 ...................... 85
Table 37. Filter Application for Failure Probability............................................................ 95
Table 38. Flight-Phase Defi°:,itions........................................................................................ 99
Table 39. Flight Phases by Launch Vehicle ......................................................................... 99
Table 40. Summary of Atlas Vehicle Configurations ....................................................... 101
Table 41. Atlas Launch History ...........................................................•............................... 103
•Table 42. Summary of Delta Vehicle Configurations ....................................................... 133
Table 43. Delta Launch History .......................................................................................... 136
Table 44. Summary of Titan Vehicle Configurations ....................................................... 147 .
Table 45. Titan Launch History .......................................................................................... 149
Table 46. Thor Launch History ........................................................................................... 165

9/10/96 Vl RTI
1. Introduction
The debris from most launch vehicles that fail catastrophically tend to impact close to the
intended flight line. Typical failures that produce such results are premature thrust
termination, stage ignition failure, tank rupture or explosion, or rapid out-of-control
tumble. Less likely malfunctions may cause a vehicle to execute a sustained turn away
from the flight line. Examples are control failures that cause the rocket engine to lock in a
fixed position near null, or failures leading to erroneous orientation of the guidance
platform. Such failures should not be ignored, since they may produce nearly all or a
significant part of the risks to population centers that are more than a mile or so uprange or
many miles away from the flight line. Consequently, RTI has been tasked to estimate the
probabilities of occurrence of these less-likely failures, and to determine optimum values
for the shaping constants of the associated impact-density function

RTI has developed a prototype risk-analysis program (1) to analyze the level of risk in the
launch area when ballistic missiles and space vehicles are launched, and (2) to provide
guidelines for launch operations and launch-area risk management. This program, "facility
DAMage and Personnel injury" (DAMP), uses information about the launch vehicle, its
trajectory and failure responses, and facilities and populations in the launch area to estimate
hit probabilities and casualty expectations. When a missile or space vehicle malfunctions,
people and facilities may be subjected to significant risks from falling inert debris, or from
overpressures and secondary debris produced by a stage, component, or large propellant
chunk that explodes on impact. Although fire, toxic materials, and radiation may also
subject personnel to significant danger, these hazards are not addressed in program DAMP.
Hazards are greatest in the launch area and along the intended flight line, but lesser
hazards exist throughout the area inside the impact limit lines. Small hazards exist even
outside these lines if the flight termination system fails or other unlikely events occur.

In computing launch-area risks, DAMP makes no attempt to model vehicle failures per
se. A list of possible failures for any vehicle would be extensive, and variations in
failures from vehicle to vehicle would complicate the modeling process. Instead,
DAMP models failure responses. Regardless of the exact nature of the failures that can
occur, there are only six possible response modes that affect risks on the ground, five
for failure responses, and one to model the behavior of a normal vehicle. The six
modes are described in Appendix A. It can be seen from the descriptions that impacts
resulting from failure-response Modes 1, 2, and 3 occur at most a mile or two from the
launch point, while those from Mode 4 can only occur near the flight line, even though the
vehicle may tumble before breakup or destruct. Although the hazards outside the launch
area and away from the flight line may be small, vehicle flight tests through the years have
demonstrated that finite hazards do exist in these areas. Such hazards are due almost
entirely to Mode-5 failure responses, even through the probability of a Mode-5 failure may
be only a small part of the total failure probability. The Mode-5 failure-response,
theoretical though it is, was developed to reflect the facts that: (1) unlikely vehicle failures

9/10/96 1 RTI
can cause impacts uprange or well away from the intended flight line, and (2) some vehicle
failures cannot logically be classified as Response Modes 1, 2, 3, or 4.

In- keeping with the above, the Mode-5 impact-density function was developed with the
characteristics listed below. The function, which fills the void left by Modes 1 through 4, is
sufficiently robust to include all possible impacts, yet seemingly comports with observed
test results.

(1) Impacts can occur in any direction from the launch point and at any range within
the vehicle's energy capabilities.

(2) At any given impact range from the launch point, the likelihood of impact
decreases as the angular deviation from the flight line increases, becoming least.
likely in the uprange direction. For any fixed angular deviation from the flight
line, the likelihood of impact decreases as the impact range increases.

(3) At fixed impact ranges near the launch point, the impact density function changes
gradually as the impact direction swings 180° from downrange to uprange. As
the impact range increases, the decrease in the density function becomes
progressively more and more rapid with change in impact direction. In other
words, the greater the impact range, the more rapidly the density function
changes with angular deviation from the flight line. •

As modeled in DAMP, the effects of destruct action on the Mode-5 density function are
accounted for in the launch area by supplementing impacts inside the impact limit lines
with those that would occur outside the impact limit lines if no destruct action were taken.
The Mode-5 failure-response methodology was fully developed in an earlier RTI report111•
As pointed ·out there, the shape of the impact density function can be controlled somewhat
through the selection of shaping constants that appear in the defining equation Intuition
suggests that the constants should be vehicle dependent, since (1) ruggedly built missiles
would, after a malfunction, be more likely to impact well away from the flight line than
would a fragile space vehicle that tends to break up before deviating significantly; and
.(2) certain vehicles, after a malfunction, tend to stabilize and •continue thrusting at large
angles of attack, while other vehicles that experience similar malfunctions tend to tumble.
Hit probabilities computed by-program DAMP for targets located more than two miles or
so uprange from the pad or more than a few miles from the flight line, are due almost
entirely to the Mode-5 impact-density function Thus, the assumed probability of
occurrence of a Mode-5 response as well as the selected Mode-5 constants are of
considerable importance.

The tasking for this. study is set _forth as Task No. 10/95-77, Paragraph 2.0, of Contract
FO4703-91-C-0112. The primary purpose of the tasking is: "Perform a study to
determine the best values for Mode-5 failure probability and the Mode-5 density-
function shaping constant A." Although not explicitly included in the statement of work,
the study also develops absolute failure probabilities for Atlas, Delta, and Titan, and

9/10/% 2 RTI
relative probabilities of occurrence for all failure-response modes for these vehicles, LLVl,
and other new launch systems.

Although it may be reasonable to establish the relative probability of occurrence of a
Mode-5 failure response by empirical means, the number of Mode-5 failures is too small to
have any hope of establishing accurate values for the shaping constants from this sample
alone. Inadequate descriptions of vehicle behavior in the available historical records and
uncertainty in impact location following a malfunction add to the difficulty of classifying
failure responses. In view of the limited data available for vehicles that have experienced
Mode-5 failures, the values chosen for the Mode-5 constants must depend on simulations of
vehicle behavior following failure.

2. Examples Showing Need for Mode 5
The need for a Mode-5 response or some similar response mode (or a multiplicity of other
response modes) can be seen from the following vehicle performance descriptions extracted
from Appendix D:

(1) Atlas BE, 24 Jan 61. Missile stability was lost at about 161 seconds, some 30
seconds after BECO, probably due to failure of the servo-amplifier power supply.
The sustainer engine shut down at 248 seconds, and the vernier engines about 10
seconds later. Impact occurred 1316 miles downrange and 215 miles crossrange. •

(2) Titan M-4, 6 Oct 61. A one-bit error in the W velocity accumulation caused impact
86 miles short and 14 miles right of target.
(3) Atlas 145D (Mariner R-1), 22 July 62. Booster stage and flight appeared normal
until after booster staging at guidance enable at about 157 seconds. Operation of
guidance rate beacon was intermittent. Due to this and faulty guidance equations,
erroneous guidance commands were given based on invalid rate data. Vehicle
deviations became evident at 172 seconds and continued throughout flight with a
maximum yaw deviation of 60° and pitch deviation of 28° occurring at 270
seconds. The vehicle deviated grossly from the planned trajectory in azimuth and
velocity, and executed abnormal maneuvers in pitch and yaw. The missile was
destroyed by the RSO at 293.5 seconds, some 12 seconds after SECO.
(4) Atlas SLV-3 (GTA-9), 17 May 66. Vehicle became unstable when B2 pitch control
was lost at 121 seconds. Loss of pitch control resulted in a pitch-down maneuver
much greater than 90°. Guidance control was lost at 132 seconds. After BECO,
the vehicle stabilized in an abnormal attitude. Although the vehicle did not
follow the planned trajectory, SECO (at 280 seconds), VECO (at 298 seconds), and
Agena separation occurred normally from programmer commands.

(5) Atlas 95F (ABRES/AFSC), 3 May 68. Immediately after liftoff the telemetered roll
and yaw rates indicated that the missile was erratic. During the first 10 seconds of
flight the missile yawed hard to the left. It then began a hard yaw to the right,

9/10/96 3 RTI
crossed over the flight line and continued toward the right destruct line. Shortly
thereafter the missile apparently pitched up violently and the HP began moving
back toward the beach. The missile was destructed at about 45 seconds when the
altitude was about 14,000 feet and the downrange distance about 9 miles. Major
pieces impacted less than a mile offshore, indicating uprange movement of the
impact point during the last part of thrusting flight.
(6) Delta Intelsat III, 18 Sep·68. Due to loss of rate gyro, undamped pitch oscillations
began at 20 seconds. A series of violent maneuvers followed at 59 seconds.
During the 13-second period while these maneuvers continued, the vehicle
pitched down some 270°, then up 210°, and then made a large yaw to the left. At
72 seconds the vehicle regained control and flew stably in a down and leftward
direction until 100 seconds. At this time, with the main engine against the pitch
and yaw stops, the destabilizing aerodynamic forces became so· large that quasi-
control could no longer be maintained. The first stage broke up at 103 seconds.
The second stage was destroyed by the RSO at 110.6 seconds. Major pieces
impacted about 12 miles downrange and 2 miles left of the flight line.
(7) Delta Pioneer E, 27 Aug 69. First-stage hydraulics system failed a few seconds
before first-~tage burnout (MECO). The vehicle pitched down, yawed left, rolled
counterclockwise driving all gyros off limits, and then tumbled. Second-stage
separation and ignition occurred while the vehicle was out of control. After about
20 seconds, the second stage regained control in a yaw-right, pitch-up attitude. It
flew stably in this attitude for about 240 seconds until destroyed by the safety
officer at T+484 seconds.
(8) Atlas 68E, 8 Dec 80. Flight appeared normal until 102.7 seconds when the lube oil
pressure on the B2 booster engine suddenly dropped. At 120.1 seconds, the
engine shut down, followed 385 msec later by guidance shutdown of the Bl
engine. The asymmetric thrust during shutdown caused yaw and roll rates that
the flight-control system could not correct. As a result, attitude control was lost
and the thrusting sustainer pivoted the missile to a retrofire attitude before the
vehicle could be stabilized: After the booster package was jettisoned, the missile
was stabilized and decelerating in the retrofire mode by 148 seconds. The
sustainer continued thrusting in this attitude until 282.9 seconds when reentry
heating apparently caused sustainer shutdown and vehicle.breakup.

9/10/96 4 RTI
It is obvious from the response-mode definitions in Appendix A that none of the described
vehicle failures can be considered as a Mode 1, 2, or 3 response, or a Mode-4 on-trajectory
failure.• Except possibly for (2), it also seems apparent that none can be modeled as either a
rapid tumble or a slow tum.

• Although prompt destruct action during any of the described flights might have resulted in a Mode-4
classification, the safety officer typically needs several seconds to evaluate data after a malfunction.
Quick action is contrary to safety philosophy if impact limit lines are not threatened and the destruct •
system is not at risk, since additional flight time enhances the user's opportunity to pinpoint the
nature of the problem.

9/10/96 5 RTI
A good illustration of a Mode-5 failure response occurred during launch of Prospector
(Joust) on the Eastern Range in-June 1991. The Joust consists of a single-stage Castor IV-A
solid-propellant rocket motor and a payload module. The "vehicle made a radical pitch-up
maneuver due to· aft-skirt structural failure at approximately T+14 Seconds." 121 The
vacuum instantaneous impact trace from the RSO console is shown in Figure 1. If the
safety officer had taken destruct action during the time interval from 18 to 25 seconds,
impact would have been well away from the flight line.

CYIER A
UNCLRSSIFIED IP "AP 1 JOUST1761-R
r20SEC.
+ 3 □ .a + 3 □.□
RLTEP. .. PP.rttE
I. 17B CNH!AVE53
SKIN
ON TRRCK ...
. . . ..... ..._._:,.--25SEC. ON TRACK
1. D DELAY ~• 1 .II DELAY
',• r1BSEC. .::---,---

+· 12 CHEV ..
\"·./
t •
.
~ - • • • •30SEC.
•
15 CHEV
■

19.7 5LO
\
'\
•
....
. . . . . . ~-.

16.3 !iLO
32.2 SltT !II .1 5HT
a. 1 RGT 15SEC. Q.7 LFT
~-2 LOIi ~ 1 LOU
\
\ 78 HDG
625 VEL
2 ALT

l
!
....... -- ..
D. I 1l
. --/ . --, ·- --•-=--.-,,,•' CNTRAVE'i!
SKIN . i ·;
I
ON TRRU
0 5 DELAY I
0 .
I
'
ON TRACK
0.5 DELAY
I f i
i

+ 4 GREEN

Figure 1. Joust Impact Trace Showing a Mode-5 Failure Response

As still another example of a Mode-5 failure response, a guided Red Tigress sounding
rocket was launched from Pad 20 at Cape Canaveral on 20 Aug 91. Within a second or
two after clearing the launcher, the rocket made a near 90° right tum, and flew stably in
this direction until destroyed by the safety officer at 23.3 seconds. Pieces impacted
some two or three miles from the launch pad. This failure might have been classified
as a Mode-2 response if destruct action had been taken·shortly after launch.

9/10/96 6 RTI
3. Understanding the Mode-5 Failure Response
Unlike failure response Modes 3 and 4, response Mode 5 (and also Mode 2) is not a direct
function of time from launch. For Modes 3 and 4, the mean point of impact (MPI) for each
debris class is fixed, once the failure time is established. At each instant there is only one
possible location for the :MPI for each debris class. On the other hand, the Mod~S impact-
density function for each debris class consists of a primary part and a secondary
superimposed part. The primary impact-density function accounts for impact variability
due to the erratic flight of the vehicle. It is used to determine the probability that the mean
piece in a debris class resulting from vehicle breakup falls in a given area (say on a building
or open field). The secondary density function accounts for debris dispersion due to
vehicle breakup and to aerodynamic effects during free fall. It is used to determine the
probability that fragments from the class actually hit a building or field. In other words, the
primary impact-density function is used to compute the probability that the secondary
function is centered in some specified area; the secondary function, which describes the
distribution of class pieces about the mean point, is then used to compute the probability
that one or more class pieces impacts on the specified population center or area.
The primary part of the Mod~S impact density function, which was presented as Eq. (9.5)
in Ref. [1], is reproduced here as Eq. (1):

(1)

where R is the range from the launch point in miles, ~ is the angle in radians between the
uprange direction and a line fro:r,n the pad through the impact point, R is the impact-range
rate in miles per second. A and C are dimensionless shaping constants, and shaping-
constant D is in miles. For a Mod~S response, there is by definition an earliest time of
occurrence TP (pitch-over time) and a latest time of occurrence T5 (burnout, orbital injection,
or some other specified termination time). The specific time in this span at which a Mode-5
response manifests itself is of no consequence, although the duration of the span must be
considered in assigning a probability of occurrence for a Mod~S response.
Given that a Mod~S response has occurred, the probability that the center of the secondary
function lies in some region or on some building (population center) is determined by
integrating the primary impact-density function for the class over the region or building.
The primary function depends on range (R) and direction (q>) from the launch point to the
population center, but not directly on time from launch. The primary function does,

"' As an aid to understanding, the supplement of (j), designated as 0, is used in plots and tables in this
report.

9/10/96 RTI
however, involve the quantity R which is expressed explicitly as a function of R and only
implicitly as a function·of time. Values of R from the nominal trajectory are differenced to
computeR.

The secondary Mode-5 impact-density function is circular normal in form and expressed by
the equation

(2)

where d is the distance from the impact point of the mean piece to the center of the target,
and oc is the standard deviation (dispersion) for the debris class. The fact that the center of
the secondary impact-density function (or secondary MPI for a debris class) lies Off some
population center does not necessarily mean that pieces in the class hit the center. The
probability that one or more pieces actually hits the pop center is determined by integrating
the secondaryimpact-density function over the center and combining results for all pieces
in the class. The dispersions for the secondary function are computed by root-sum-
squaring individual dispersions• arising from the effects of winds, vehicle-breakup
velocities, and drag uncertainties for the class. They are computed from the nominal
trajectory, and cari be explicitly expressed as a function· of impact range. Since the pop
center can also be hit if the MPI of the secondary density function lies outside the pop
center, all possible mutually-exclusive locations of the secondary function that can result in
impact on the pop center must be considered. For each mutually-exclusive location, the
probability that one or more class pieces impacts on the pop center is calculated, and the
results combined to obtain the total hit probability for the class.
The Mode-5 primary impact-density function is modeled so· it is independent of how the
impact point arrives at a particular location For example, there are myriad paths that a
vehicle can travel to impact at a location two miles crossrange left from the launch pad.
Figure 1 shows one such way for a Joust vehicle that failed at 15 seconds, but four seconds
later had moved the impact point uprange and CTO$!ange to a position two miles
crossrange left from the launch point. Another way to place the impact point two- miles
•crossrange left is for the vehicle to fly in the wrong direction (north instead of east) from
liftoff.

Although numerous failure mechanisms and vehicle behaviors can lead to a Mode-5
response and impact in a particular area, the exact mechanism and behavior are irrelevant
All such possibilities are assumed to be accounted for by Eq. (1). Four specific failures that
produce Mode-5 responses are easily- described: (1) a re-orientation of the guidance
platform, (2) insertion of an erroneous spatial target into the guidance system, (3) locking of
the engine nozzle in a fixed position near null thus producing a near-constant angular

* These dispersions are a subset of the Mode-4 impact dispersions.

9/10/96 8 RTI
acceleration of the vehicle body and a slow turn of the velocity vector, (4) erroneous
accumulation of velocity bits by the guidance system. Many other Mode-5 responses are so
convoluted that they defy description or categorization

3.1 Effects of Mode-5 Shaping Constants
The primary part of the Mode-5 impact-density function was presented previously as
Eq. (1). As originally formulated, the function contained three shaping constants. If both
numerator and denominator of the equation are divided by the constant C, and B is
substituted for D/C, one unnecessary constant disappears so that the function may be
expressed as follows:

(3)

The values chosen for the shaping constants A and B that appear in Eq. (3) influence, but do
not change, the basic nature of the Mode-5 impact-density function For many years values
of A = 2.5 and B = 1000 were used in the Eastern Range ship-hit computations, although in
more recent risk studies the value of A has been increased to 3.0. This increase resulted .
from the observation that, in recent years, vehicles that experience Mode-5 failure responses
seem less likely than earlier developmental vehicles to deviate significantly from the
intended flight line. To see how A and B affect the distribution of Mode-5 impacts, and to
further understanding of the function, the results of choosing various values of A and B are
provided in Appendix B.

3.2 Effects of Shaping Constant on DAMP Results
As pointed out in the Introduction, two important types of constant parameters
required by DAMP for risk estimations must be determined. They are: (1) probability
of a Mode-5 failure response, and (2) valqes of the Mode-5 shaping constants A and B,
currently set at 3.0 and 1000, respectively. As will be demonstrated later, DAMP
results are far more sensitive to changes in A than in B.

The following cases illustrate the effects that constant A has on calculated risks.

Case 1: Baseline Risks for Atlas IIA

In the baseline risk analysis for Atlas IIAm, the probability of a Modew5 failure response
was estimated at 12.5% of the total failure probability during the first 120 seconds of
flight. Even so, risks resulting from Mode-5 responses accounted for about 90% of the
total risks for people inside the impact limit lines (ILL). Table 1 indicates the range of
risks inside the ILLs for day launches from Pad A using various estimates of the
shaping constant A and a value of B = 1000.

9/10/96 9 RTI
Table 1. Effects of Mode-5 Shaping Constant A on Atlas IIA Risks
B = 1,000 Percent of Mode-5 Casualty Expectancv (x 10°') inside ILLs
Constant A IPs Uprange Modes Total for all Modes
2.5 28.6 246 259.9
3.0 20.7 136 149.4
3.5 14.6 58.9 72.7
4.0 10.0 30.5 44.3

The results in·the third column are directly proportional to the probability that a Mode-
5 failure occurs. For the Atlas IIA analysis, a value of 1/200 = 0.005 was assumed.

Case 2: Risk Contours for Atlas IIAS

Definitions of Flight Hazard Area and Flight Caution Area may be based on the risk
contours for inner-ear injury. Constant A can have a significant effect on the location of
the 10-6 contour, as illustrated in Figure 2 and Figure 3 for the Atlas IIAS. For these
figures, the Mode-5 absolute probability of occurrence was 0.005, constant A was 3.0
and 3.5, and constant B was 1000.

9/10/96 10 RTI
>i
Lo
~
-~
- '°
I
0
lf)
I "q""
I
...---f 0
C ...---f 0
1--1 II ..--t
(/.I
<[ L<[
1--1 d
1--1wLn
l/l L I
d a., a.,
_, C "ZS
.p C Q
<I:1--1L

Figure 2. Atlas HAS Risk Contours for Inner-Ear Injury with A= 3.0

9/10/96 11 RTI
-
0
-4

Figure 3. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.5

9/10/96 12 RTI
4. Methodology for Assessing Failure Probabilities
A primary purpose of this study is to develop estimates of the relative probabilities of
occurrence of a Mode-5 failure response for Atlas, Delta, Ti~ and as a by-product, for
other launch vehicles as well. Natural fallouts of this effort are the relative probabilities of
occurrence of other failure-response modes used in program PAMP as well as overall
vehicle failure probabilities. There are at least two approaches commonly used in
estimating launch-vehicle failure probabilities: (1) a so-called parts-analysis or engineering
approach, involving an engineering assessment of the reliability of various parts and
components comprising each missile subsystem, and the effects of a part, component or
subsystem failure; and (2) an empirical statistical approach based on actual launch results.
There are serious problems with both approaches.

4.1 The Parts-Analysis Approach
A description of this approach, its difficulties and shortcomings, are discussed in some
detail in a draft report by Booz• Allen & Hamilton, Inc. 141 prepared in 1992 for the Air Force
Space Command. Since we cannot improve on the ideas and words expressed by
Booz• Allen, we quote the following from that report:

"The engineering approach for calculation of launch vehicle success rates is based
on measurement/estimation of piece-part reliabilities and their combination into
reliability block models of the launch system. These block models . .. include
consideration of the criticality of individual components, the presence (or absence)
of redundant capabilities, the likelihood that one component failure might cause a
failure in another component, as well as other needed data. By combining the
individual piece-part reliabilities in this model, the engineering approach produces
an overall reliability estimate for the launch system.

"The engin~ng approach has several significant limitations that tend to reduce
confidence in its results. First, the approach assumes that the interrelationships
among and between sub-systems are understood sufficiently to enable
development of a reliability block diagram. This assumption is highly
questionable in complex systems, such as space launch vehicles, whose operational
histories include many anecdotes regarding unexpected relationships between
'independenf sub-systems.

"The second drawback of the engineering approach is that it assesses the reliability
of the system in a perfectly assembled condition. As a result, it assesses reliability
without regard to manufacturing, processing, or operations variations and errors."

Effects typically overlooked or ignored include:

a. Improper installation of components
b. Erroneous computer programs

9/10/96 13 RTI
c. Insertion of improper computer programs
d. Support-personnel fatigue
A third limitation of the parts-analysis approach discussed in Ref. [4] deals with the
subjectivity and invalid assumptions often used to· estimate piece/component reliabilities.
Here Booz•Allen quotes from a reporf1 by the Office of Technology Assessment, and we
do likewise:

"The design reliability of proposed vehicles is generally estimated using:

Data from laboratory tests of vehicle systems (e.g., engines and avionics) and
components that have already been built;

Engineer's judgments about the reliability- achievable in systems and
components that have not been built;

Analyses of whether a failure in one system or component would cause other
systems and components, or the vehicle to fail; and

Assumptions (often tacit) that:

the laboratory conditions under which systems were tested precisely
duplicate the conditions under which the systems will operate,
the conditions under which the system will operate are those under which
theywere designed to operate,

the engineer's judgments about reliability are correct, and
the failure analyses considered all circumstances and details that influence
reliability:

Such engineering estimates of design·reliability are incomplete and subjective...".

Effects influencing reliability that the analyst may fail to consider include:

a. Lightning strikes
b. Aging effects, particularly for solid propellants
c. Corrosion
d. Insufficient heat or cold insulation for critical components
e.Idng
f. Erroneous antennae patterns or instrumentation

Booz• Allen concludes as follows:·

''Finally, due to its nature, the engineering approach can not account for
undetected design flaws. (If these flaws were detected, and could be modeled,

9/10/96 14 RTI
they would be corrected.) However, experience has shown that design flaws do
cause failures in operational launch systems, and will likely do so in the future."

The major objection to the parts-analysis approach, hinted at above but not actually
expressed, is that all such approaches involve either explicitly or implicitly a so-called K-
factor. The K-factor is included in the reliability calculations in an attempt to compensate
for the fact that the environment in which a part or system is tested is not the same as the
flight environment. Since the K-factor is surely not the same for all components and
systems, multiple values must be assumed and the entire process becomes highly
subjective.

In view of the objections and limitations just presented, in this report the parts-analysis
approach is not considered in assessing vehicle reliability or in estimating the relative
probabilities of occurrence of the various failure-response modes.

4.2 The Empirical Approach
A seemingly more objective way to evaluate vehicle reliability (or conversely, vehicle
failure probabilities) is by examining the actual performance of flight-tested vehicles. In
support of this approach, the following is quoted from the Office of Technology
Assessment1 report previously referenced:

"The only completely objective method of estimating a vehicle's probability of
failure is by statistical analysis of number of failures observed in identical vehicles
under conditions representative of those under which future launches will be
attempted."

Although we agree with the Office of Technology Assessment statement, the obvious
difficulty with this approach is that no such sample of identical vehicles exists or is ever
likely to exist.

In their report'41 previously referenced, Booz• Allen makes the same point in different words
by stating that "the empirical approach has one significant drawback in that it can not
project the effects of changes in the launch systems". The effects of such changes can only
be assessed objectively by further flight testing.

The difficulty in projecting success rates (or failure rates) from past tests to future tests is
clearly recognized. Nevertheless, RTI has relied exclusively on this method to estimate the
relative probabilities of occurrence for the various failure-response modes. Even so, total
objectivity cannot be claimed since, as will be seen later, the answers depend to a large
extent on how the performance data are filtered, and how big a risk one wants to take that
the true failure probability is underestimated.

9/10/96 15 RTI
5. Computation of Failure Probabilities
The test results for Atlas, Delta, and Titan in the tables of Appendix D have been used
for three primary purposes:
(1) To predict or estimate the overall probability that each vehicle will fail during the
various phases of flight (see Table 39, Appendix D, for flight-phase definitions).

(2) To establish the relative and overall probabilities for Response Modes 1 through 5..
(3) To establish the relative frequency of tumble for Response Modes 3 and 4.

5.1 Overall Failure Probat>ility

To- predict failure probabilities for Atlas, Delta, and Titan, the test results in
Appendix D for representative configurations (i.e., "l" in last column) have been
filtered using three different weighting techniques described in Appendix C:
(1) Equal weighting
(2) Index-count .weighting
(3) Exponential weighting
In computing filtered or weighted failure probabilities, a test is assigned a score of one
to indicate the occurrence of a failure or some anomalous behavior, and a score of zero
if no failure occurred. Admittedly, there may be disagreements about the classification
of a few flights, since the launch agency may consider as successful or partially
successful some flights that are shown as failures in· Appendix D. To avoid such
disagreements, it is better to- think of some non-normal events, particularly those
occurring late in flight, as anomalies rather than failures. The flight phases, as shown
in column 2 of Table 2 and defined in Appendix D.1.3, are inclusive; e.g., flight phase
"0 - 3" includes phases 0, 1, 1.5, 2, 2.5, and 3. An 'NA' in the response-mode column in
the tables of Appendix D indicates that some failure or anomalous behavior has had an
.effect on the final orbit or impact point without producing additional risks to people on
the ground or necessarily failing the mission. In the failure-probability calculations of
Table 2 and Table 3, an 'NA' has been- considered as a success for all flight phases
except "0 - 5", irrespective of the phase in which the failure or anomalous behavior took
place. Only in flight phase "0- 5" is an 'NA' response considered a failure. The
filtered results for representative configurations (defined in Appendix D.1.4) are given
in Table 2 for six flight phases. For flights with multiple entries in the Response-Mode
and Flight-Phase columns (e.g., see Appendix D.2.1, No. 257), the first listed value was
used in the filtering process.

9/10/96 16 RTI
Table 2. Predicted Failure Probabilities for Representative Configurations
Filter Technic ue Sample
Flight Equal Index Expon. Expon. Expon Failures
Vehicle Phase Weight Count F =0.99 F = 0.98 F = 0.97 /Total
Atlas 0 0 0 0 0 0 0/7
0-1 0.0256 0.0253 0.0245 0.0219 0.0186 4/156
0-2 0.0449 0.0385 0.0387 0.0313 0.0243 7/156
0-3 0.0769 0.0715 0.0714 0.0643 0.0568 12/156
0-4 0.0833 0.0811 0.0801 0.0740 0.0663 13/156
0-5* 0.1090 0.1100 0.1078 0~1019 0.0929 17/156
Delta 0 0 0 0 0 0 0/125
0-1 0.0160 . 0.0126 0.0134 0.0104 0.0075 2/125
0-2 0.0160 0.0126 0.0134 0.0104 0.0075 2/125
0-3 0.0160 0.0126 ·o.0134 0.0104 0.0075 2/125
0-4 0.0160 0.0126 0.0134 0.0104 0.0075 2/125
0-5* 0.0640 0.0447 0.0535 0.0469 0.0442 8/125
Titan 0 0.0306 0.0210 0.0225 0.0292 0.0352 3/98
0-1 0.0234 0.0305 0.0314 0.0403 0.0470 4/171
0-2 0.0409 0.0496 0.0514 0.0642 0.0750 7/171
0-3 0.0526 0.0581 0.0597 0.0689 0.0773 9/171
0-4 0.0526 0.0581 0.0597 0.0689 0.0773 9/171
0-5* 0.1111 0.1167 0.1188 0.1284 0.1358 19/171
* Includes response mode 'NA'
It is apparent from the data in Table 2 that estimates of future vehicle reliability depend
on the filtering (i.e., weighting) technique applied. Since there are many ways to
perform the filtering, all generally producing slightly different results, the choice of
method to use in deriving empirical failure probabilities cannot be totally objective.
Subjective decisions must also be made about which past configurations to consider as
representative of future vehicles, which flight tests to include_ in the sample, how to
weight the individual flights, and, in unusual cases, whether to consider a flight a
success or a failure, and to which flight phase to attribute a failure. Except for data
weighting (i.e., choice of filter), these decisions were made for Atlas, Delta, and Titan
before computing the failure probabilities shown in Table 2. •

For Atlas and Delta, it can be seen from Table 2 that the predicted failure probabilities
computed. with the exponential filter decrease as the value of F decreases. Since a
decreasing F means more emphasis on recent data and less emphasis on the old, the
launch reliability for these vehicles is apparently improving. The reverse seems to be
true for Titan, suggesting either that Titan reliability is not improving or, possibly, that
improvements that have been or are being made to the vehicle are not yet fully
reflected in the test· results. For Atlas and Delta, the computed failure probabilities
based on equal weighting are higher than for all other filters, and the predicted failure

9/10/96 17 RTI
probabilities using index-count filtering are larger than those for exponential filtering.
For Titan, the results are mixed, further suggesting that Titan reliability has not
improved in recent years.

For comparison purposes, the same filtering techniques have been applied to all flight
tests shown in the tables of Appendix D, regardless of configuration. The results are
presented in Table 3.

Table 3. Predicted Failure Probabilities for All Configurations
Filter Technic ue Sample
Flight Equal Index Expon. Expon Expon Failures
Vehicle Phase Weight Count F =0.99 F=0.98 F =0.97 /Total
Atlas 0 0 0 0 0 0 0/7
0-1 0.1053 0.0641 0.0422 0.0273 0.0190 56/532
0-2 0.1711 0.0990 0.0555 0.0311 0.0204 91/532
0-3 0.2086 0.1261 0.0802 0.0559 0.0455 111/532
0-4 0.2143 0.1330 0.0873 0.0627 0.0511 114/532
0-5 • 0.2575 0.1671 0.1150 0.0866 0.0725 137/532
Delta 0 0 0 0 0 0 0/196
0-1. 0.0172 0.0164 0.0148 0.0110 0.0077 4/232
0-2 0.0259 0.0232 0.0201 0.0133 0.0085 6/232
0-3 0.0431 0.0279 0.0263 0.0150 0.0089 10/232
0-4 0.0431 0.0279 0.0263 0.0150 0.0089 10/232
0-5* 0.1078 0.0766 0.0740 0.0536 0.0459 25/232
Titan 0 0.0306 0.0137 0.0187 0.0281 0.0349 3/98
0-1 0.0534 0.0319 0.0351 0.0399 0.0467 18/337
0-2 0.1424 0.0771 0.0719 0.0662 0.0750 48/337
0-3 0.1632 0.0924 0.0830 0.0711 0.0770 55/337
0-4 0.1662 0.0942 0.0840 0.0712 0.0771 56/337
0-5· 0.1958· 0.1369 0.1326 0.1277 0.1346 66/337
• Includes response mode 'NA'

.A comparison of Table 2 and Table 3 shows that in most cases, but not all, exponential
filtering produces failure probabilities for the representative configuration samples that
are smaller than the corresponding probabilities for the all-configuration samples. The
fact that most differences between corresponding samples are relatively small attests to
the effectiveness of the exponential filter in down-weighting early launch failures. This
is not the case for equal weighting of tests, where the predicted failure probabilities
based on all configurations are up to 3.6 times as large.

With respect to- the weighting of missile and space-vehicle performance data, RTI
favors an exponential filter over either the equal-weight or index-count filters.
Weighting percentages for the three filters are given in Table 4 for sample sizes of 4 to
1,000. Except for small samples, the percentages produced by equal weighting place
too much emphasis on old data, thus failing to account for the learning process and

9/10/96 18 RTI
hardware improvements that have taken place through the years. For samples
approaching 100 or so, it seriously over-weights the old data and under-weights the
more recent events. Although equal weighting does not seem suitable for this
application, it could be appropriate in other large-sample situations, for example,
predicting the failure probability of devices that are all manufactured at the same time
by the same process, and tested to the same standards.

Table 4. Comparison of Weicllting Percentages
Sample Last+ Last5 Last 10 Last 25 !Last 50 Last
Size Filter* Point Points Points Points Points Half
4 Expon. 25.8 - - - - 51.0
Index 40.0 - - - - 70.0
Equal 25.0 - - - - 50.0
10 Expon. 10.9 52.5 100.0 - - 52.5
Index 18.2 72.7 100.0 - - 72.5
Equal 10.0 50.0 100.0 - - 50.0
20 Expon. 6.0 28.9 55.0 - - 55.0
Index 9.5 42.9 73.8 - - 73.8
Equal 5.0 25.0 50.0 - - 50.0
100 Expon. · 2.3 11.1 21.1 45.7 73.3 73.3
Index 2.0 9.7 18.9 43.6 74.8 74.8
Equal 1.0 5.0 10.0 25.0 50.0 50.0
200 Expon. 2.0 9.8 18.6 40.4 64.7 88.3
Index 1.0 4.9 9.7 23.4 43.7 74.9
Equal 0.5 2.5 5.0 12.5 25.0 50.0
500 Expon. 2.0 9.6 18.3 39.7 63.6 99.4
Index 0.4 2.0 4.0 9.7 19.0 75.0
Equal 0.2 1.0 2.0 5.0 10.0 50.0
1000 Expon. 2.0 9.6 18.3 39.7 63.6 99.996
Index 0.1 1.0 2.0 4.9 9.7 75.0
Equal 0.1 0.5 1.0 2.5 5.0 50.0
* F = 0.98 for exponential filter
+ "Last" refers to the most recent data point
The index-count filter has serious deficiencies when applied to either small or large
samples of missiles and space vehicles. For small samples, too much emphasis is
placed on recent data. For a sample of four, 40% of the total weight is given to the last
test, and 70% to the last two tests. For a sample of ten, 18.2% of the total weight is
given to the last test and 72.7% to the last five tests. The reliability improvement rate
implied by these weightings seems too optimistic unless there were serious design
flaws in the early configurations that were discovered and corrected. Since many types
of failures surely exist that occur only once in 50 or once in 100 or more launches, the
tenth launch may be no better than the first for predicting the probability of occurrence
of such failures. For large samples, the index-count filter under-weights current data

9/10/96 19 RTI
more and more as the sample size increases. For samples of 200, 500, and 1000, the
weighting of the last 50 tests are, in each case, 43.7%, 19.0%, and 9.7% of the total
weight. For samples of 100 or more, no matter how large, the index-count filter assigns
25% of the data weight to the oldest half of the data sample - too much in RTI's
opinion.
For missiles and space vehicles, the data weightings imposed by the exponential filter
(F = 0.98) appear reasonable. For small samples less than 20 or so, there is little
difference between equal and exponential weightings. For sample sizes near 80, the
index-count and exponential filters produce similar results. For sample sizes of 200
and more, the weights assigned to the most recent 5, 10, 25, and 50 tests are essentially
constant, showing the fading-memory nature of the exponential filter.
The denominator of the exponential-filter equation [Eq. (18), Appendix CJ is a
geometric series that asymptotically approaches a limit of [1/(1- F)] as n approaches
infinity. For F = 0.98, that limit is 50. Thus, the last data point, which is always given a
weight of one, can never be weighted less than 2% of the total, no· matter how large the
sample. For samples of 200 and 300, the oldest half of the data receives only 11.7% and
5% of the total weight. For samples of 500 and larger, the oldest half of the data sample
is essentially o~tted altogether. The exponential filter is clearly a fading-memory
filter, as it should be for space-vehicle performance data.
Having decided upon the exponential filter as the best method for weighting missile
and space-vehicle performance data, a filter constant F must be chosen. To see how
data weighting varies with filter-factor value, weighting percentages for various
samples were computed for representative configurations of Atlas, Delta, and Titan
using values of F from 0.96 to 0.995. The results are shown in Table 5.

9/10/96 20 RTI
Table 5. Filter Factor Influence on Weig hting Percentages
Vehicle Filter • Last Last 10 Last 50 Last Lastl00 Pt. Ratio
(sample) Cons't Point Points Points Half* Points last: first
Atlas 0.96 4.01 33.6 87.2 96.0 98.5 560
(156) 0.97 3.03 26.5 78.9 91.5 96.1 112
0.98 2.09 19.1 66.4 82.9 90.6 22.9
0.99 1.26 12.1 49.9 68.7 80.1 4.7
0.995 0.92 9.0 40.9 59.7 72.7 2.2
Delta 0.% 4.02 33.5 87.5 92.9 98.9 158
(125) 0.97 3.07 26.9 80.0 87.3 97.4 43.7
0.98 2.17 19.9 69.1 78.3 94.3 12.2
0.99 1.40 13.4 55.2 65.6 88.6 3.5
0.995 1.07 10.5 47.6 58.2 84.7 1.9
Titan 0.96 4.00 33.5 87.1 97.1 98.4 1030
(171) 0.97 3.02 26.4 78.6 93.2 95.8 177
0.98 2.07 18.9 65.7 85.1 89.6 31.0
0.99 1.22 11.7 48.1 70.5 77.2 5.5
0.995 0.87 8.5 38.5 60.8 68.5 2.3
* Last half + 1 if sample size is odd

Although the choice of a filter constant cannot be completely objective, use of a value
less than 0.97 or greater than 0.99 produces undesirable weightings. For F = 0.96, for
example, the most recent test result for Titan is weighted 1030 times that for the oldest
test; the last 50 data points receive 87.1 % of the total weighting, leaving only 12.9% for
the first 121 flights; the last 100 flights receive 98.4% of the total weighting thus, in
effect, omitting the oldest 71 flights from the solution.
At the high end of the F spectrum, a value of 0.995 fails to down-weight the old test
•results sufficiently. Using Atlas as an example, the most recent data point (1/31/96) is
weighted only 2.2 times that of the oldest data point (8/14/64). The oldest half of the
data, stretching from 8/14/64 to 3/06/73, receives 40% of the total weight, and the
earliest 56 launches, comprising 36% of the data, receive 27% (100 - 73) of the total
weight. This is not too different from equal weighting of tests, a procedure that fails to
acknowledge the improvements in Atlas reliability that have taken place over a period
of 32 years.

In choosing a value of F, an attempt is made to strike a suitable balance between two
contrary objectives:

(1) to down-weight substantially those failures for which the probability of
occurrence has been greatly reduced through redesign and replacement of
components, improved test procedures, and the like;

9/10/96 21 RTI
(2) to down-weight only slightly, or not at all, those failures that are random in
nature, that can still occur in replacement components, or that occur only once in
100 or several hundred launches in components that have not yet failed.
No matter what technique is employed, filtering is at best a compromise. The perfect
filter would somehow down-weight to some extent or entirely those failures that have
been "fixed" or made less likely, without down-weighting those random failures with
unknown causes. The filters considered in this study have no such capabilities; they
produce a result based solely on the launch sequence, and where in the sequence
failures have occurred.
In predicting vehicle failure probabilities from empirical data, large representative
samples are essential for a good estimate, and the more reliable the vehicle, the greater
the need for a large sample. For example, if some characteristic exists in exactly 1% of a
population, the probability is 0.37 that it will not appear in a random sample of 100,
and 0.61 that it will not appear if the sample size is 50. If the characteristic exists in 2%
of the population, it fails to- appear about 36% of the time in a random sample of 50.

For reasons presented above, the data samples for Atlas, Delta, and Titan have been
made as large as possible consistent with the notion of representative configurations, as
set forth in Ref. [4]. In RTI's judgment, the value of F that best weights the performance
data is 0.98, although a value anywhere in the interval 0.97 to 0.99 cannot be ruled out.
For consistency in data weighting, the same values of F have been used for all vehicle
programs. The differences in predicted failure probability that result from these three
F's are illustrated in Figure 4 for Atlas. The plots show the inverse relationship
between filter volatility and the value of F. For F = 0.97 vis-a-vis larger values, it can be
seen that the filtered failure probability jumps higher with each failure and drops at a
faster rate with each successful launch that follows.

9/10/96 22 RTI
0.12
0.11 ..............i.................!................J................. L...............!...-.-.J. F.=..o.97.....
: i i i i :F i
1 11 i i i i - =0~98
0.10 ••••• ······1· ··············1·················1·················1·················j···-----i••F·=··~~99 ·····

0.09
>-
~ 0.08
:aca
.c 0.07
e
a.. 0.06
(l)
lo...
::J 0.05
'ffi
u.. i \\ i i ! \; \ ;',,,
"C
0.04
(l)
lo...
(l) 0.03
=
u:: r,,~-
0.02 .............L I '~:-~:t-1-1········---1' ..............
0.01 . . . . . . . . . . . . . ;OOOOOOOppO&aOOOOO; •••••••••••••••••;••ooOOOOOOOOOOOOO ;OOOOOO ■ OOOOOOOHO; . . • • • • • • • • • • • • • • • ; OOOOO ■ OHHOOOOOO ; ■ --600000000 . .

I ! ! l i ! i
0.00
0 20 40 60 80 100 120 140 160
Sample Index (newer->)
Figure 4. Filter Factor Results for Representative Configurations of Atlas

In summary, it must be recognized that there is no "correct'' value for F, and that it is
even difficult to argue generally that one value of F is better than another. In RTI's
view, values of F below 0.97 place too much emphasis on a relatively small sample of
recent launches. Values above 0.99 extend the sample so far back in time that too little
emphasis is placed on improvements in design, materials, and operational procedures.
In any event, the value chosen for F is crucial in arriving at a predicted failure
probability. For the more conservative, a value of 0.99 can be chosen; the optimistic
might chose 0.97.

Since most risk-analysis studies that RTI makes are concerned with the launch area,
failure probabilities beyond flight-phase 2 are of minor interest. The overall failure
probabilities shown in Table 6 have, with one exception, been extracted from Table 2
for F = 0.98. Where a best estimate is called for, RTI plans to use these probabilities in
future launch-area risk analyses for the 45 SW/SE unless directed otherwise, or until
additions to the data samples in Appendix D justify changes.

9/10/96 23 RTI
Table 6. Failure Probabilities for Atlas, Delta, and Titan
Predicted Failure Probability*
Flight Phase Flight Phase
Vehicle 0-1 0-2
Atlas 0.022 0.031
Delta 0.010 0.013
Titan 0.040 0.064
* Exponential filter with F = 0.98
For Delta, the predicted failure probabilities shown in Table 2 for flight-phases O- 1
and O- 2 are the same, since no second-stage failure has occurred in the 125 flights
included in the representative sample. Obviously, this does not mean that the
probability of a Delta second-stage failure is zero. As stated earlier, the choice of F is a
judgment matter with the most reasonable range for F considered to be 0.97 SF S 0.99. j
To- show a difference in failure probabilities between Delta flight phases, a value of
F = 0.98 has been used for flight phases O-1, and 0.99 for flight phases O- 2. It is an
interesting coincidence that the same value of 0.013 is obtained using F = 0.98 and all
Delta configurations (see Table 3). Another way to estimate the Delta second-stage
II
failure probability is to calculate an upper confidence limit at some suitable level for an
event that has occurred zero times in 125 trials. At the 80% confidence level, the
reliability is at least 0.987, so- the failure probability during second-stage bum (flight
I
phases 1.5 - 2) is no bigger than 0.013.

5.2 Relative and Absolute Probabllltles for Response Modes I
I

For Atlas, Delta, and Titan vehicles, failure-response Modes 1, 2, and 3 are much less I
likely to- occur than Modes 4 and 5. Since the probabilities of occurrence for the less-
likely modes may be only one in a thousand or less, such responses may not have
occurred at all in the flight tests of representative configurations. •In fact, in· the I
combined samples for Atlas, Delta, and Titan, only 16 failures have occurred during
flights phases O- 2. None of the 16 resulted in response-modes 1, 2, or 3. Because of
. the small number of failures in the representative configuration samples, the relative
probabilities of occurrence for Modes 1 through 5 have been estimated using results
from all vehicle configurations and launches shown in Appendix D. The rationale for
this approach is that, except for obvious problems that have been corrected, other
changes made through the years to improve vehicle reliability have reduced the
probabilities of occurrence of all response modes more or less proportionally. The
greater significance of more recent vehicle modifications and test results is. accounted
for by using an exponential filter to estimate overall failure probabilities. Thus, if
Mode-1 failures occurred more frequently in the distant past than in recent years, the
weighting process reduces the significance of the earlier Mode-1 responses in the
relative probability-of-occurrence calculations. As tabulated from Appendix D, the
number (count) of failures by response mode and flight phase for Atlas, Delta, Titan,
and Eastern-Range Thor launches are given in Table 7 through Table 10. Thor launches

9/10/96 24 RTI
from the Western Range were not included since available performance records were
incomplete. The results for the four vehicles are combined in Table 11. Table 12 gives
last-occurrence dates by' response mode for each launch vehicle.

Table 7. Number of Atlas Failures - All Confisrurations (532 Flights)
Flight Failure-Res :,onse Mode 3&4
Phase 1 2 3 4 5 'NA' Tumble
0 0 0 0 0 0 0 0
0-1 7 1 2 38 8 4 11
0-2 7 1 2 66 15 13 19
0-3 7 1 2 86 15 18 25
0-4 7 1 2 89 15 21 27
0-5 7 1 2 89 15 23 27

Table 8. Number of Delta Failures - All Configurations (232 Flights)
Flight Failure-Res oonse Mode 3&4
Phase 1 2 3 4 5 'NA' Tumble
0 0 0 0 0 0 0 0
0-1 0 0 0 ·2 2 5 0
0-2 0 0 0 4 2 10 1
0-3 0 0 0 7 3 12 1
0-4 0 0 0 7 3 13 1
0-5 0 0 0 7 3 15 1

Table 9. Number of Titan Failures - All Configurations (337 Flights)
Flight Failure-Res oonse Mode 3&4
Phase 1 2 3 4 5 'NA' Tumble
0 0 0 0 3 0 0 1
0-1 2 2 0 13 1 0 5
0-2 2 2 0 39 5 3 10
0-3 2 2 0 46 5 5 11
0-4 2 2 0 47 5 7 11
0-5 2 2 0 47 5 10 11

Table 10. Number of Eastern-Range Thor Failures (85 Flights)
Flight Failure-Res oonse Mode 3&4
Phase 1 2 3 4 5 'NA' Tumble
0 0 0 0 0 0 0 0
0-1 4 1 1 15 4 1 3
0-2 4 1 1 20 5 3 3
0-3 4 1 1 22 5 3 3
0-4 4 1 1 22 5 4 3
0-5 4 1 1 22 5 5 3

9/10/% 25 RTI
Table 11. Number of Failures for All Vehicles (1186 Flights)
Flight Failure-Res oonse Mode 3&4
Phase 1 2 3 4 5 'NA' Tumble
0 0 0 0 3 0 0 1
0-1 13 4 3- 68 15 11 19
0-2 13 4 3 129 27 29 33
0-3 13 4 3 161 28 38 40
0-4 13 4 3 165 28 45 42
0-5 13 4 3 165 28 53 42

Table 12. Date of Most Recent Failure
Response Vehicle
Mode Atlas Delta Titan Thor*
1 03/02/65 none 12/12/59 04/19/58
2 12/18/81 none 05/01/63 12/30/58
3 .04/25/61 none none 07/21/59
4 08/22/92 05/03/86 10/05/93 03/24//64
5 12/08/80 08/27/69 11/30/65 01/24/62
*

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