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NAVAL POSTGRADUATE SCHOOLv Monterey, Califolrna C) / THESIS ANALYSIS OF U.S. NAVY AIRCRAFT ACCIDENT RATES IN MAJOR AVIATION COMMANDS by Lawrence Charles Bucher September 1976 Thesis Advisor: G. K. Poock Approved for public release; distribution unlimited.

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NAVAL POSTGRADUATE SCHOOLv

Monterey, Califolrna C) /

THESISANALYSIS OF U.S. NAVY AIRCRAFT

ACCIDENT RATES IN MAJOR AVIATION COMMANDS

by

Lawrence Charles Bucher

September 1976

Thesis Advisor: G. K. Poock

Approved for public release; distribution unlimited.

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Analysis of U.S. Navy Aircraft Accident Master's ThesisRates in Major Aviation Commandsi Rantamhbi' M&I~4~ 0. R OrnuGOG. RE6PORT NuMOER

7. AUfleOW4 CNRATBE=M

Lawrence Charl er 9' ,U

9. PRmOmuFWIN ORGANIZATION NARE AND ADDRSS AAP NSwwmNaval Postgi'aduate School kAa ! ' T"1UwtMonterey, California 93940

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Naval Postgraduate School 1076Monterey, California 93940 _____________

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Naval Postgraduate School UnclassifiedMonterey, California 93940 ,* ~&~iC~~I@NRON

16. CISTRIGUTION STATEENT (oel s.Rpse)

**Approved for public release; stribution unlimited.

17. OISTRIOUTION STATE[MENT (of M 08oh. abetedM slaoo n l ItW If Eftm u11000)

IS. SUPPLONENTARY MOTIES

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X~imedep3ndent variable measures were obtained for allmajor aircraft accidents between July 1971 and July 1974.Using these time dependent variables and functional formsof these variables, a regression analysis was performed foreach of eight major aviation commands. By using thesefunctional forms of the variables, a relatively high amountof variance in aircraft accident rate was accounted for at

DO ,JAIN,1473 EIINO O6 SOSLT P5~ i/~'2(Page 1) SIX 0102-034-11"01 SECURITY CLASSIFICATION OF TWIS PAGE[ (Us..Dal

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a high confidence level in some commands. When reviewingthe results of the eight major commands considered, it wasparticularly noted that the variables most instrumentalin explaining the variance in aircraft accident rate werenot all pilot oriented but were variables interpreted as4 being related either to pilot experience level, pilotproficiency or aircraft cniin

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* Analysis of U.*S. Navy AircraftAccident Rates in Major Aviation Commands

by

Lawrence Charles BucherLieutenant Commander, United States Navy

B.S.E.E., Purdue University, 1966

_ - ubmitted in partial fulfillment of -the

requirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOLSeptember-1976

Auth or

Approved by:Tesis dvisor

econd Reader

Ctirman, Department of perations .esigrc

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ABSTRACT

Time dependent variable neasures were obtained for all

major aircraft accidents between July 1971 and July 1974.

Using these time dependent variables and functional forms

of these variables, a regression analysis was performed

for each of eight major aviation commands. By using these

functional forms of the variables, a relatively high amount

of variance in aircraft accident rate was accounted for at

a high confidence level in some commands. When reviewing

the results of the eight major commands considered, it was

particularly noted that the variables most instrumental

in explaining the variance in aircraft accident rate were

not all pilot oriented but were variables interpreted as

being related either to pilot experience level, pilot

proficiency or aircraft condition.

Ii

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TABLE OF CONTNTS

I. IM UTO1NCTION -- eeeeee---------------------------- 7

II. PROBLEM DEFINITION ------------------------------ 11

III. ANALYTICAL PROCEDURES ---------------------------- 13

A. DATA SOURCE ---------------------------------- 13

B. DATA SELECTION ........- -------------------- 13

C. PRELIMINARY DATA PREPARATION ------------------ 17

D. THE ANALYSIS TECHNIQUE ---------------------- 18

IV, RESULTS ------------------------------------------ 23

A, COMNAVAIRLANT --------------------- 23

B, MARLANT -------------------------------------- 26

C. COMNAVAIRPAC --------------------------------- 30

D. MARPAC eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 33

E, CNATRA eeeeeeeeeeeeeeeeeeeeeeee---------- 36

F. NAVAL RESERVES ------------------------------- 39

G, MARTC ---------------------------------------- 42

H. RDT&E/NASC ----------------------------------- 45

V. DISCUSSION --------------------------------------- 48

VI. RECOMMENDATIONS ---------------------------------- 52

APPENDIX As Average Monthly Data Point Values forMajor Commands ------------------------- 53

APPENDIX Bt Aircraft Accidents by Month and byCommand ----------------------------- 64

APPENDIX Cc Forward (Stepwise) Multiple Regression -- 66

APPENDIX D, Statiatical Tests for Significance ------- 69

LIST OF REFERENCES ----------------------------------- 71

INITIAL DISTRIBUTION LIST ---------------------------- 72

5

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LIST OF TABLES

I. DATA SET INCLUDED IN CURRENT STUDY ------------ 16

II. CONSTRUCTED VARIABLES ------------- U......--------- 20

III. CONNAVAIRLANT MATRIX OF SIMPLE CORRELATION

COEFFICINTS ------- - ------------------------ 25

IV. COTWAVAIRLANT REGRESSION OUTPUT SUMMARY ---------- 25

V. MARLANT MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------- 29

VI. MARLANT REGRESSION OUTPUT SUMMARY ---------------- 29

VII. COMNAVAIRPAC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS -------------------------------------- 32

VIII. COMNAVAIRPAC REGRESSION OUTPUT SUMMARY ...........- 32

IX. MARPAC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------- 35

X. MARPAC REGRESSION OUTPUT SUMMARY ----------------- 35

XI. CNATRA MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------ 38

XII. CNATRA REGRESSION OUTPUT SUMMARY ----------------- 38

XIII. NAVAL RESERVES MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------

XIV. NAVAL RESERVES REGRESSION OUTPUT SUMMARY --------- 41

XV. M.ARTC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS -----------------------------------

XVI. MARTC REGRESSION OUTPUT SUMMARY ------------------ 44

XVII. RDT&E/NASC MATRIX OF SIMPLE CORRELATION 47COEFFICIENTS -------------------------------------

XVIII. RDT&E/NASC REGRESSION OUTPUT SUMMARY -------------- 47

XIX. SIGNS OF CORRELATION COEFFICIENTS ---------------- 49

6

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I. INTRODUCTION

Aviation safety is one of the major tools used to obtain

J Navy goal of fleet readiness. The reports necessary to

provide the Naval Safety Center with a means by which to

judge the Navy's progress in aviation safety are delineated

in OPNAVINST 3750.6 (Series). Through analysis of reported

mishaps, the safety center has the ability to determine

correctable material and personnel deficiencies, Through

the administrative effort expended in submitting reports,

the Navy can be repaid many times in the savings of lives

and material.

Due to extensive post aircraft accident analysis by

accident investigation teams, aircraft accidents have been

broadly categorized in terms of causal factors. Causal

factors are not to be confused with environmental factors

but are any event, act, failure/malfunction, circumstance

or occurrence, the presence or absence of which caused the

accident. Contributing to accidents are poorly designed

equipment, supervisory error, improper aircrew training,

failure of a facility to provide adequate runway drainage,

maintenance induced equipment malfunctions, etc.

An accident is designated as a major accident if:

(1) loss of life occurs; (2) complete loss of an aircraft

is involvedi or (3) substantial damage occurs to any

K 7

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aircraft involved where substantial damap is defined in

Appendix A of OPAVINST 3750.6 (Series). The most common

cause cited in the literature on aircraft accidents is

pilot error. In a study by Brictson, et al. Z-1969-7,

approximately seventy-eight percent of the accidents stud-

ied attributed pilot error as being the primary causal

factor, with only eight percent being attributed to

support personnel errors, and the remaining thirteen per-

cent being attributed to aircraft failure, equipment failure

and/or weather.

A study conducted for the Royal Air Force by Goorney

E19651, concluded Viat fatigue, personal worries, com-

placency, emotional stress and lack of current flying expe-

rience, directly contributed to pilot error. Goorney's

study states that excessive ground duties prior to flying

attributed to fatigue and that personal worries concerning

marriages, dating, housing, financial and work problems

attributed to emotional stress.

Collicot, et al. Z-1972_ categorized accident causal

factors into pilot error, material failure, maintenance

error, and miscellaneous other causes. The authors compared

Air Force F-4 accidents with Navy-Marine F-4 accidents and

attributed maintenance error disparities to the fact that

Air Force F-4 aircraft only realized one-tenth of the can-

nibalization of parts that Navy-Marine aircraft realized.

The authors also singled out that the Navy-Marine c ricer

job rotational policies resulted in lower in-type flight

8

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hours for Navy-Marine aviAtors and thus adversely affectedtheir pilot proficiency. The authors also noted that, in

comparing dual piloted to single piloted aircraft, the dual

piloted aircraft had fewer accidents per ten thousand hours

than the single piloted aircraft. The authors conclusion

was that pilot mental overload was critical in the determina-

tion of a prime factor in pilot error.

As a result of the Collicot study and a study by Kowalsky,

et al. ZE1974J,. the emphasis that pilot induced accidents

were caused by lack of pilot proficiency was shifted to

implications that pilot error accidents may be attributed

to a state of temporary mental overload where the pilots

incorrectly evaluated information inputed to them during the

overload period.

Sinc. the advent of the Naval Safety Center, a great deal

of effort has been expended in maintaining extensive data

banks of accident related information. Statistical Analysis

of available data shnuld enable predictive mathematical

models to be constructed, as much of the data available can

be construed as measuies of pilot proficiency. Myers Z-1974 7

attempted such a statistical analysis, hypothesizing that

measures of pilot proficiency and experience would suffice

to form an adequate foundation for accident rate analysis.

He applied statistical techniques of principle component

analysis and cluster analysis to ten variables obtained from

the Individual Flight Activity Reporting System (IFARS) which

are submi'tted to the Safety Center. Comparing two groups of

9

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pilots--one group being involved in aircraft accidents and

the other group being accident free--his. results were not

as pronounced as desired. The fact that each group con-

tained only fifty subjects is reason to believe that this

small sample size suppressed his accident predictivo results.

Maxwell and Stucki Z-1975,J applied regression analysis

techniques to an all Navy study of aircraft accidents for

the period July 1968 to June 1974. Their analysis indicated

that 46.6% of the total accident rate variability is explained

by pilot related variable measures if one wishes to accept

a statistical confidence level of 75% as meaningful. Results

of their study corroborated with the previous studies cited,

that pilot error of one sort or another is the single largest

cause of aircraft accidents.

The author of this Writing agrees with Maxwell and Stucki

that sufficient data should be currently available, from

which predictive capability is extractable. The variable

nature of the monthly accident rate suggests underlying

factors, causal and thus definable in their role of accident

perpetration. Using statistical analysis to isolate variable

measures associated with pilot proficiency and aircraft

maintenance which vary either directly or indirectly with

accident rate, then predictive and thus preventive know-

ledge can assist in lowering the loss of human life and

the dollar loss resulting from aircraft accidents.

10

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II. PROBLEM DEFINITION

The Naval Safety Center (NSC), Norfolk, Virginia, has

provided the author with major accident rates computed for

aircraft accidents for eight major commands: (1) Commander

Naval Air Forces Atlantic (COMNAVAIRIANT); (2) Fleet Marine

Forces Atlantic (MARLANT); (3) Commander Naval Air Forces

Pacific (COMNAVAIRPAC); (4) Fleet Mariae Forces Pacific

(MARPAC); (5) Commander Naval Air Training Command (CNATRA),

(6) Commander Marine Training Command (MARTC); (7) Naval

Reserves; (8) Commander Research Development Test and

Evaluation/Naval Air Systems Command (RDT&E/NASC); for

fiscal years 1969 through 1974. The accident rate is defined

as the total number of accidents in a given month multiplied

by a constant factor of ten thousand and then divided by

the total monthly hours flown for a given command. Major

accidents by definition, as delineated in OPNAVINST 3750.6

(Series), are characterized by loss of life, loss of aircraft,

or extensive aircraft damage measured in necessary man-hours

to effect repair.

A variety of approaches to look for consistent trends

or cyclic phenomena in aircraft accident rate of Navy-Marine

accidents was undertaken by Poock [-19762. None were found

that could pass any statistical tests to verify their

existence beyond reasonable elements of chance.

11

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The purpose of this paper is to further explore accident

rate dependence on time related variable measures for the

eight major commands listed above in hopes that one or more

of these measures can be identified for later use in the

reduction of accident rates and thus the reduction in the

loss of lives and money.

12

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III. ANALYTICAL PROCEDURES

A. DATA SOURCE

OPNAVINST 3750.6 (Series) promulgates the requirements

and procedures for the reporting of each aircraft accident

or incident involving all Navy and Marine aircraft. This

establishes control over accident data with the goal of

increasing aviation safety. The reports are forwarded

to the Naval Safety Center (NSC) for inclusion in their

master data bank. Accident data currently available from

NSC can provide approximately eighty variable measures for

each accident.

B. DATA SELECTION

The NSC data bank provides a ready source of data for

each accident or data set. However, as this is a continuation

of the work of Maxwell and Stucki, the 2110 computer data

cards obtained from NSC for their study were also used in

this study.

The initial step in the conduct of the current accident

rate analysis was to select appropriate variable measures or

data points. A data point for an accident was considered

to be any suitable variable measure associated with the

accident- and a data set consisted of data points for a

L13

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specific accident. Specific measures were chosen in mutual

discussions with NSC personnel.

Selection of appropriate data points required that each

point be time dependent. Data point time dependency and

subsequent selection was based on the variable descriptions

contained in the anual of Code Classification for Navy

Aircraft Accident, Incident and Ground Accident Reporting

(Code Manual) promulgated by NSC.

A sufficient number of data sets had to be incorporated

into the analysis to facilitate viable statistical results,

but the span of time defined by the data sets had to be

chosen with care. Unfortunately, of the six fiscal years

of data available to the author, only fiscal years 1972,

1973, and 1974 were used in this study. Fiscal years 1969,

1970, and 1971 were eliminated primarily because some data

sets were either incomplete or entirely void of information.

A change in reporting procedures during 1972 alleviated this

problem. Also, in the fiscal years chosen for the analysis,

a particular accident too often had to be disregarded due to

incomplete data or to the fact that the particular occurrence

involved another aircraft and the other aircraft was deemed

at fault. Therefore, either due to insufficient data or

to an occurrence and not an accident, a total of 636 of

the original 2110 data sets available were used. Data for

each variable of these 636 data sets were complete and there

is absolutely no data missing in the data sets used in

the analysis.

14

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Ten data points from each set of the original thirty

data points requested ty" Maxwell and Stucki were selected

for inclusion in the current analysis. Nine of these data

points are the same data points used in the Maxwell and

Stucki study with the addition of the data point "Years

Experience as a Designated Naval Aviation" and the data

point "Flight Purpose Code" deleted. In addition, the data

points selected also allowed the author to construct four

additional variables deemed as measures of experience and

pilot proficiency. Table I lists the basic variables used

in the study. The first ten variables listed are from the

Naval Safety Center and variables eleven through fourteen

are the constructed variables.

Pilot age, years experience as a designated Naval aviator,

experience, age at designation as a Naval aviator and total

flight ti-ne in the aircraft involved in the reported accident

have b'4en considered as measures of pilot experience. If

these variables are true measures of experience they should

exhibit negative correlation with accident rate, assuming

a relationship exists.

There is the age old adage of "practice makes perfect"

which this author construes as a measure of pilot proficiency.

Included in the category of pilot proficiency were totalflight time during the preceding ninety days, total night

flight time during the preceding ninety nights, total day

flight time during the preceding ninety days, the number

of carrier landings in the last thirty days, the number of

carrier landings in the last thirty nights, and the ratio

15

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TABLE I

DATA SET INCLUDED IN CURRENT STUDY

1. Accident rate by month (RATE)

2. Pilot's age (AGE)

3. Years experience as a designated Naval aviator (rA)

4. Total flight time in accident involved aircraft model

(TTINE)

5. Total flight time during preceding ninety days (TOT9)

6. Total night flight time during preceding ninety nights(NITE90)

7. Daylight carrier 1-ndings during preceding thirty days(CLDAY)

8. Night carrier land ngs during preceding thirty nights(CIIIT)

9. Number of aircraft tours (ACTOUR)

10. Aircraft flight hours since last major or minorinspection (ACHRS)

11. The ratio of years experience as a designated Navalaviator and total flight time in the accident involvedaircraft model (EXPER=DNA/TTIME)

12. Age at designation as a Naval aviator (WINGS=AGE-DNA)

13. Total flight time during preceding ninety days minustotal night flight time during preceding ninety nights(DAY90=TOT90-NITE90)

14. The ratio of total night flight time during the pre-ceding ninety nights to total day flight time duringthe preceding ninety days (NITEDAY=NITE90/DAY9O)

_16

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of night flight time to day flight time during the preceding

ninety days and nights.

To measure airframe age and general condition, two var-

iables were selected. All Navy/%arine aircraft are required

to undergo a Periodic Aircraft Rework (PAR) cycle for analysis

and repair after having accumulated a specific number of

flight hours. Thus, the number of aircraft tours was chosen

as one variable. As a measure of aircraft condition, the

aircraft flight hours since the last major or minor inspection

was also selected as a variab!3.

C. PRELIMINARY DATA PREPARATION

A common theoretical proposition in parametric statistics

states that changes in one variable can be explained by

reference to changes in several other variables. Such a

relationship is described in a simple way by a multiple

linear regression equation as described in Appendix C. To

use this statistical method the relationships between the

variables require the following assumptionst (1) normality;

(2) data must be in the interval measurement scale;

(3) the number of observations exceeds tht number of coef-

ficients to be estimated; and (4) no exact linear relation-

ships exist between any of the explanatory variables.

Normality was assumed by invoking the Central Limit Theorem'

and the technique of averaging by month was used to transform

the data into interval data.

17

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Raw data for each of the first ten variables of Table I

was averaged by month for each of the thirty-six months within

the time span selected and was also used to compute the values

for the remairtng variables of Table I.

D. 7E ANALYSIS TECHNIQUE

To conduct the statistical analysis of the data set the

author selected the forward (stepwise) multiple regression

computer program package developed by Jae-On Kim and Frank

J. Kahout at the University of Iowa. The program is included

in the Statistical Package for the Social Sciences (SPSS)

compiled and edited by Nie, et al. Z-1975-7.

Multiple regression may be viewed as a descriptive tool

whereby the linear dependence of one variable on other var-

iables is summarized and decomposed. Kim and Kahout state

that the most important uses of the technique as a descriptive

tool aret

(1) to find the best linear prediction equationand evaluate its prediction accuracy; (2) tocontrol for other confounding factors in orderto evaluate the contribution of a specificvariable or set of variables; and (3) to findstructural relations and provide explanationsfor seemingly complex multivariate relation-ships, such as is done in path analysis.

However, the primary purpose is to evaluate and measure over-

all dependence of a specified (dependent) variable on a set

of other variables (independent). The dependent variable

used for the current study was accident rate and tie inde-

pendent variables consisted of those variables listed as 2

through 14 in Table I and all the variables listed in Table II.

18

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To explain the variables listed in Table II it must

again be stated that regression analysis assumes the under-

lying relationships among the variables are linear and addi-

tive. There are man occasions for which such simple linear

models are inadequate. Early efforts by the author dealt

entirely with first order variables but examination of

scatterplots of.the residuals, which are conceived as meas-

ures of the error component, indicated lack of linearity and

the presence of curvilinearity. Therefore, functional terms

were added to the variable list as suggested by Kim and Kahout.

These additional variables are listed in Table II.

The SPSS computer program is designed to provide the user

with a considerable number of control options. The listwise

deletion option was chosen for use by the author as it is

the most conservative and accurate of the options.

The forward (stepwise) multiple regression technique

(Appendix C) is particularly useful in studies of the current

type. Tt is appropriate to enter independent variables one

by one on the basis of a pre-determined statistical ,riteria.

This procedure is used when a researcher desires to isolate

a subset of available predictor variables that will yield an

optimal prediction equation with as few terms as possible.

Draper and Smith [-1966J conclude the following in their

discussion of various regression procedures, "We believe

this (stepwise regression) to be the best of the variable

selection procedures discussed and recommend its use."

The percentage of the accident rate variability explained

19

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* TABIR 11

4CONSTRUCTED VAXBES

1. AG32 (AGE)2 20. CLAIa 10CD

k2. TTI32 =(TTIR)2 21 WT = 1.O/Cdt4IT2

3. T0T902 m(TOT90)2 22. ACTCRJRI =1.O/ACTOUR2

4. WINGS2 a (WINGS)2 23. ACHRSI 1.0/ACHRS2

5. DhY902 = (DAY90)2 24. IXIAI = 1.O/DNA2

6. CLDAY2 = (CLDAY) 2 25. EXPERI = 1.0/tExPE2

7. CI&NIT2 = (CLNIT)2 26. WINGSI =1.OAVINGS2

8. ACHRS2 = (ACHRS) 2 27. RTAGE = (AGE) 1

9. EXPER2 = (EXpER)2 28. RTDNA w(DNA)*

10. flNA2 = (DNA)2 29. RTTTU = (TTII )i

*11. NITE902 = (NITE9O) 2 30. RTTOT9O = (TOT9O)i

12. ACTOUR2 = (ACTOUR) 2 31. RTDAY9Or = (DAY90)i13. NITEDAY2 = (NITEDAY)2 32. RTCLDAY = (CLDAY)i

L.14. NITEDAYI = 1.0/NITEDAY2 33. RTCILVIT = (CLNIT)1

15. AGEI = 1.O/AGE2 34. RTACI{RS = (ACHRS)i

16. TTIPMI = 1.0/TTIME2 35. RTEXPER = (EXPER)i

17. TOT90I =1.0/T0T902 36. RTWINGS = (WINGS) 1

18. NITE90I =1.0/AIITE9O2 37. RTNITE90 = (NITE9O)i

19. DAY90I =1.O/DAY902 38. RTACTOUR w(ACTOUR)t

39. RTNITEDAY =(NITEDAY)1

20

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by the time related independent variables entered is exactly

the type of statistical output required to ascertain the

causal factors responsible for that variability.

Thirteen separate regression calculations were attempted

for each of the eight couands considered. Each of the

separate regression calculations were permutations of the

variables listed in Table I and the variables listed in

Table I. Regression calculations using only the first

eight variables of Table I or regression calculations using

the first ten variablest of Table I led to the suspicion of

curvilinearity in the data as a result of an inspection of the

residual scatter plots. Therefore, the author attempted

various regression calculations using combinations of the

variables of Table I with either the squares of those var-

iables, the inverse squares of those variables, the square

roots of those variables or any combinations thereof.

There is no unique procedure for selecting the best

criteria and personal judgement is a necessary part of any

decision reached by the analyst. The author set up guide-

lines to choose the "best" equation as follows, (1) the

regression equation would be limited to five or six inde-

pendent variables; (2) the regression equation chosen should

accotut for the highest amount of the variance in aircraft

accident rate; (3) the residual plots would be examined

for the best indication of minimum residuals; and (4) the

statistical significance of each regression would be cal-

culated as outlined in Appendix D and the regression equation

21

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* yielding the greatest amount of accountable variance with

the highest confidence level would be the equation selected.

22

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IV. RESULTS

A. COWIAVAIRLANT

Early efforts at regression analysis by the author used

only the variables listed in Table I. These efforts led to

the suspicion of curvilinearity as a result of examination of

the residual plots. The order of variable inclusion at the

early stage was, (1) total flight time during the ninety

days preceding the accident (TOT9O)g and (2) aircraft flight

hours since the last major or minor inspection (ACHRS). In

equation form the regression became,

RATE = 0.35295 + o.o0658(TOT9O) + O.O0163(ACHRS)

This equation accounted for 19.5% of the variance in aircraft

accident rate at a 95% confidence level.

Final regression results using functional forms of the

variables indicated that the hierarchical order of variable

inclusion as governed by the individual variable contributions

towards explaining accident rate variance was, (1) the square

root of aircraft flight hours since the lasti major or minor

inspection (RTACHRS)i (2) the square of aircraft flight

hours since the last major or minor inspection (ACHRS2)i

(3) the inverse square of the total flight time during the

ninety days preceding the accident (TOT9OI)i (4) the inverse

square of the quotient years experience as a designated

Naval aviator and total flight time in the accident involved

23

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aircraft model (EXPERI)i and (5) the square root of the

quotient years experience as a designated Naval aviator

and total flight time in the accident involved aircraft

model (RTEXPER). Table III lists the simple correlation

coefficients and Table IV is a sumary listing of computer

output provided by the SPSS package. In equation form the

regression becames

RATE = 0.89771 + 0.11823(RTACHRS) - 0.00002(ACHRS2)

- 464 .21653(TOT90I) - 0.00002(EXPRI)

- 4.76996(RTEXPER)

or in terms of Table I variables

RATE = 0.89771 + 0.11823(ACHRS)* - 0.00002(ACHRS) 2

- 464.21653(TOT90)2 ,- 0.00002(TTInE/DINA) 2

4.76996(DNA/TTImE)*

These equations account for 42.9% of the variance in aircraft

accident rate at a 99% confidence level. Therefore, by

using functional forms of the variables, an additional

23.4% of the variance was accounted for--a substantial

improvement in the results.

The net effect of the functional forms of hours since

the last major or minor inspection is positive. The remain-

ing variables are interpreted as being measures of either

pilot experience or pilot proficiency and they have a net

effect of reducing aircraft accident rate.

24

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0 r-400N C- h

A 100 li M

0000 4 J4 .

4

oI 0 O+l 0 IAOO%Go5 4r- W 0 tm7

'ii ; III 0'00M0004

Cm r- W N0 11 04 MW

hI 00 C~J~ -4 0N WC

4 0 0'%n%4D 0 $40 (0 0 O -

0 o00N00 0U U 000

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B. MARLANT

Using the same early methods as those used for COMNAVAIRLANT

the order of variable inclusion at the early stage was:

(1) years experience as a designated Naval aviator (DJA)l

(2) daylight carrier landings during the preceding thirty

days (CLDAY), (3) the quotient of years experience as a

designated Naval aviator and total flight time in the accident

involved aircraft model (EXPER); (4) the quotient of night

flight hours to day flight hours during the preceding ninety

days (NITEDAY); and (5) total flight time in accident

involved aircraft model. In equation form the regression

became:

RATE = 0.96753 + 0.09865(DNA) + o.o8248(CLDAY)

- 20.27987(EXPER) + 1.41098(NITEDAY)

- 0.oo048(TTME)

This equation accounted for 32.6% of the variance in air-

craft accident rate at a 75% confidence level.

Final regression results using functions of the var-

iables indicated that the hierarchical order of variable

inclusion as governed by the individual variable contri-

butions towars explaining accident rate variance was:

(1) the square root of years experience as a designated

Naval aviator (RTI14A); (2) the square root of total

night flight time during the preceding ninety nights

(RTNITE90); (3) total night flight time during the

26

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preceding ninety nights (NITE90); (4) the quotient of

years experience as a designated Naval aviator and total

flight time in the accident involved aircraft model (EXPER)l

(5) total flight time in the accident involved aircraft

model (TTDbE); and (6) the square of night carrier land-

ings during the preceding thirty nights (CINIT2). Table V

lists the simple correlation coefficients and Table VI is a

summary listing of computer output provided by the SPSS

package. In equation form the regression became:

RATE = -0.17128 + 0.88657(RTDNA) + 0.52634(RTNITEgo)

-O.06351(NITE9O) - 57.37027(EV.ER) - 0.00115(TTIME)

+ 0.21877(CLNIT2)

or in terms of Table I variables

RATE = -0.17128 + 0.88657(DNA)i + 0.52634(NITE90)*

- 0.06351(NITE90) - 57.37027(DNA/TTIME)

2- 0.00115(TTIME) + 0.21877(CLNIT)

These equations account for 56.5% of the variance in air-

craft accident rate at a 99% confidence level versus the

32.6% accounted for initially. A substantial improvement

was again observed when using functional forms of the

variables in the regression analysis.

When reviewing the correlation matrix (Table V) it is

noted that every variable present in the equation is posi-

tively correlated with accident rate except for EXPER (a

measure of pilot experience) and the square of night

carrier'landings in the last thirty days (a measure of pilot

27

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proficiency). The net affect of the functional forms of

night flight hours during the last ninety nights is positive,

an indication that night flying may be a hazardous evolution

and add to accident rate.

28

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O04 -* *0,10 0

H 0C'V'WW'0 441 NI0 0c o

a-Im 0)P C40

~OCO4 N~4W %n 0 0a-'C*0

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C. CMUAVAIRPAC

Initial efforts yielded the following order of variable

inclusions (1) total flight time during the preceding

ninety days (DAY9O); (2) the number of aircraft tours

(ACTOUR)i and (3) years experience as a designated Naval

aviator. In equation form the regression becames

RATE = -0.07944 + 0.01289(DAY90) + 0.10561(ACTOUR)

+ o.04137?(DNA)

This equation accounted for 33.8% of the variance in air-

craft accident rate at a 99% confidence level.

Final regression results using functions of the var-

iables indicated that the hierarchical order of variable

inclusion as governed by the individual variable contri-

butions towards explaining accident rate variance was a

(1) the inverse square of total day flight time during

the preceding ninety days (DAY90I); (2) the square of

the age of the pilot at designation as a Naval aviator

(WINGS2); (3) the number of aircraft tours (ACTOUR);

(4) the inverse square of aircraft hours since the last

major or minor inspection (ACHRSI); and (5) the square

of the hours since the last major or minor inspection

(ACHRS2). Table VII lists the simple correlation coef-

ficients and Table VIII is a sunary listing of computer

output provided by the SPSS package. In equation form the

regression became,

30

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RATE = 1.47J4?79 - 670.77272(DAY90I) - O.Ool34(WNMGS2)

+ O.15733(ACTOUR) + 30,.94442(ACHRSI)

+ 0.00001(ACMRS2)

or in terms of Table I variables

RATE = l.474.79 - 670.77272/(DAY90)2 - 0.0013(AGE - tiA)2

+ O.15733(ACTOVR) + 30.944.42(ACHRS) 2

+ 0.0000l(ACHS) 2

These equations account for 45.7% of the variance in air-

craft aocdent rate at a 99.5% confidence level, an increase

of 11.9% in accounting for variance.

It is noted in these equations that the number of

aircraft tours and functional forms of hours since the

last major or minor inspection have a positive effect on

accident rate. Conversely, variables interpreted as

measures of pilot proficiency and experience level have

a negative effect.

31

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mCM~' M~%N 0 Y%0-C l

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~E-

32

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D. MARPAC

Initial efforts at regression analysis yielded very poor

results for this command. The only variable to be included

in the equation was the quotient of night flight hours to

day flight hours during the preceding ninety days. In

equation form the regression becames

RATE = 1.75337 - 2.47720(NIE90/DAY90)

This equation accounted for 9.2% of the variance in air-

craft accident rate at a 75% confidence level.

Further regression efforts using functions of the var-

iables led to much better results with the hierarchical

order of variable inclusion being: (1) the square of

the number of aircraft tours (ACTOUR2)i (2) the number

of aircraft tours (ACTOUR); (3) the square of total

night flight time during the preceding ninety nights

(NITE902); (4) the square of the quotient total night

flight hours to total day flight hours during the preceding

ninety days (NITEDAY2); (5) aircraft flight hours since

the last major or minor inspection (ACHRS); and (6) the

square of age at designation as a Naval aviator (WINGS2).

Table IX lists the simple correlation coefficients and

Table X is a summary listing of computer output provided

by the SPSS package. In equation form the regression

became:

33

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RATE - 1.26335 - 0.32047(ACTOUR2) + 2.2.178(ACTUR)

+ 0.0102(NITR902) - 19.20769(NITEDAY2)

- 0.00565(ACHRS) - 0.00462(uINGS2)

or in terms of Table I variables

RATE = 1.26335 - 0.32O47(ACTOOR)2 + 2.2.178(ACT0IJR)

+ 0.01042(NITE90) 2 _ 19.20769(NITE90/DAY90) 2

- 0.00565(ACHRS) - 0.00462(AGE-DIKA) 2

Either equation accounts for 39.2% of the variance in air-

craft accident rate at a 95% confidence level, a substantial

improvement over the 9.2% of variance accounted for initially.

Reviewing the correlation matrix it is noted that every

variable present in the equation is negatively correlated

with accident rate. However, the intercorrelations of the

variables has the affect of causing some of the signs of

the coefficients in the equation to change, with the net

effect of the functional forms of aircraft tours being

positive.

434

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I r~v~cjcri' 0 M"* MroM M -O 'i 0 0 HW 0%

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1. ONATRA

All attempts at regression analysis for this coumand

yielded essentially the same results. Early efforts using

only the variables listed in Table I yielded the following

order of variable inclusion: (1) the quotient of total

night flight hours to total day flight hours during the

preceding ninety days (NITEDAY); (2) total flight time

in accident involved aircraft model (TTIME); (3) the

quotient of total flight time in accident involved aircraft

model to years experience as a designated Naval aviator

(TTD1/ A), (4) aircraft flight hours since the last

major or minor inspection (ACHRS)i and (5) the quotient

of years experience as a designated Naval aviator to total

flight time in accident involved aircraft model. In equation

form the regression became,

RATE = 5.22976 + 51.98496(NITE9O/DAY9O) + 0.00955(TTIME)

- 0.01973(TTIME/DNA) - 0.04198(ACHRS)

- 216.41848(DNA/TTIME)

This equation accounted for 32.3% of the variance in air-

craft accident rate at a 90% confidence level.

Later regression results using functions of the variables

yielded: (1) the square root of aircraft flight hours since

the last major or minor accident (RTACHRS)i (2) the square

of aircraft hours since the last major or minor inspection

36

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* (ACmRS), (3) the square of the total day flight hours

flown during the preceding ninety days (DAY902)1 (4) the

square root of the quotient of total flight time in the

accident involved aircraft model to years experience as a

designated Naval aviator (l.O/RTUPER); and (5) the

quotient of total flight time in accident involved air-

craft model and years experience as a designated Naval

aviator. Table XI lists the simple correlation coefficients

and Table XII is a summary listing of computer output pro-

vided by the SPSS package. In equation form the regression

became s

RAT = -0.31346 + 0.11248(RTACHRS) - 0.00003(ACHRS2)

- 0.00002(DAY902) + 0.03J482(l.0/RTEXPER)

- 0.00092(1.0/EXPER)

or in terms of Table I variables

RATE = - 0.31346 + 0.11248(ACHRS)' - 0.00003(ACHRS) 2

- 0.00002(DAY9) 2 + 0.03482(TTIME/DNA)"

- 0.00092(TTIE/DNA)

Either equation accounts for 33.0% of the variance in air-

craft rate at a confidence level of 90%1 representing no

significant change in the results. The functional forms

of aircraft hours since the last major or minor inspection

and the reciprocal forms of EXPER have a net positive

effect while the square of day flight time during the last

ninety days has a negative affect.

37

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. I .J P - ' - . . .. -..... . ... --- ' . .. ... W

F. NAVAL J VSW V

Initial efforts yielded the following order of variable

inclusione (1) total night flight time during the preceding

ninety nights (NITB90)s (2) the quotient of total night

flight time and total day flight time during the preceding

ninety days and nights (NITE90/AY90)1 (3) total flight

time during the ninety days preceding the accident (TOT9O)g

and (4) the number of daylight carrier landings during the

preceding thirty days. In equation form the regression

became:

RATE 0.97395 + o.o6986(NITE90) - 1.2294(NiT9o/DAYgO)

- 0.00777(TOT90) - 0.03343(CLDAY)

This equation accounted for 71.4% of the variance in air-

craft accident rate at a 99% confidence level.

Final regression results using functions of the variables

indicated that the hierarchical order of variable inclusion

as governed by the individual variable contributions towards

explaining aircraft accident rate variance was, (1) the

square of total night flight time during the preceding

ninety nights (NITE902); (2) the square of the quotient

of total night flight time and total day flight time during

the preceding ninety days (NITEDAY2); (3) the inverse

square of aircraft flight hours since the last major or

minor inspection (ACHSI); (4) the square root of daylight

carrier landings during the preceding thirty days; and

39

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(5) the inverse square of the quotient of years experience

as a designated Naval avia+or and total flight time in the

accident involved aircraft model (EXPRI). Table XIII lists

the simple correlation coefficients and Table XIV is a summary

listing of computer output provided by the SPSS package. In

equation form the regression became:

RATE = 0.83553 + O.00084(NITE902) - 0.56367(NITEDAY2)

-311.23233(ACHRSI) - 0. 22889(RTCLDAY)

+ 0.00002(EXPERI)

or in terms of Table I variables

RATE = 0.83553 + O.00084(NITE90)2 _ 0.56367(NITE90/DAY9O)2

- 311.23233(I.0/ACHRS)2 _ 0.22889(CLDAY)}

+ 0.00002(TTIME/DNA) 2

Either equation accounts for 81.3% of the variance in air-

craft accident rate at a 99.9% confidence level, a 9.9%

increase of accountable variance over initial efforts. The

net effect of the square of night flight hours during the

preceding ninety nights and the quotient of night flight

hours and day flight hours during the preceding ninety

nights and days is negative. This may indicate that the

higher the ratio of night flight hours to day flight hours

(a measure of pilot proficiency), the lower the accident

rate.

4o

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G. KARTC

Initial efforts using only the variables of Table I

yielded the following order of variable inclusions (1) the

quotient of total night flight hours and total day flight

hours during the preceding ninety days (NITEDAY); (2) total

flight time in accident involved aircraft model (TTIN);

(3) the quotient of total flight time in accident involved

aircraft model and years designated as a Naval aviator

(TTU/M A); (4) age at designation as a Naval aviator

(WINGS); and (5) number of aircraft tours (ACTOUR). In

equation form the regression became:

RATE- - 45.84436 + 2.23927(NITEDAY) + 0.02707(TTIME)

- 0.15004(1.0/EXPER) + 2.20096(WINGS)

- O.75295(ACTOUR)

This equation accounted for 68.0% of the variance in air-

craft accident rate at a 95% confidence level.

Final regression results using functions of the variables

indicated that the hierarchical order of variable inclusion

as governed by the individual variable contributions towards

explaining aircraft accident rate variance was: (1) the

square of the quotient total night flight time and total

day flight time during the preceding ninety days (NITEDAY2);

(2) total flight time in accident involved aircraft model

(TTIME); (3) the inverse square of the quotient years expe-

rience as a designated Naval aviator and total flight time in

* 42

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the accident involved aircraft model (EII)i (4) total

night flight time during the preceding ninety nights (NITE9O)l

and (5) the square of age at designation as a Naval aviator

(INGS2). Table XV lists the simple correlation coefficients

and Table XVI is a summary listing of computer output provided

by the SPSS package. In equation form the regression becames

RATE - - 0.36132 + 65.28325(NITEDAY2) + 0.00328(TTINE)

- .O0008(EXPRI) - 0.41913(NITE90)

+ 0.00385(WINGS2)

or in terms of Table I variables

RATE = - 0.36132 + 65.28325(NITE90/DAY90)2 + 0.00328(TTIME)

- 0.00008(TTIME/DNA) 2 _ 0.1+9I3(NITE90)

+ 0.00385(AGE-DNA)2

Either equation accounts for 79.9% of the variance in air-

craft accident rate at a 95% confidence level, a 10.9% increase

of accountable variance over initial efforts.

It should be noted for this command that only one variable

interpreted as a measure of experience (EXPERI) is negatively

correlated with accident rate. Another measure of experience

(WINGS2) and three variables interpreted as measures of pilot

proficiency are all positively correlated with accident rate.

This positive correlation of pilot proficiency and experience

variables is contrary to what the author hypothesized. The

study by Poock Z-1976J also concluded that this command

produced unusual results.

£43

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0% fO MVNO 0 Q "M-4CM

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H. RDY&Z/ASC

These two conands were grouped together due to the factthat neither command had enough data points to be analyzed

if considered as individual commands. Initial efforts using

only the variables of Table I yielded the following order of

variable inclusions (1) total night flight hours during the

preceding ninety nights (NITB90); (2) the quotient of

years experience as a designated Naval aviator and total

flight time in accident involved aircraft model (EXPER);

and (3) pilot's age. In equation form the regression

became.

RATE = 0.93622 - 0.08430(NITE90) + 0.31653(EXPER)

- 0.01623(AGE)

This equation accounted for 56.5% of the variance in air-

craft accident rate at a 95% confidence level.Final regression results using functions of the variables

indicated that the hierarchical order of variable inclusion

as governed by the individual variable contributions towards

explaining aircraft accident rate variance was, (1) the

square of total night flight during the preceding ninety

nights (NITE902); (2) the square root of total flight

-time in accident involved aircraft model (RTTTIME)i (3) the

inverse square of years experience as a designated Naval

aviator (DNAI); (4) the square root of the inverse quotient

45

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of years experience as a designated Naval aviator and

total flight time in the accident involved aircraft model

(1.O )TZXu)i (5) the inverse square of total flighttime during the preceding ninety days (TOT90I) and (6) the

square root of total flight time during the preceding ninety

days (RTTOT90). Table XVII lists the simple correlation

coefficients and Table XVIII is a summary listing of com-

puter output provided by the SPSS package. In equation

form the regression became:

RATE = - 1.21331 + 0.71262(NITE902) + 0.23598(RTTTIME)

+ 19.68521(DNAI) - 0.642I(1.0/RTEXPER)

+ 182.91525(TOT90I) + 0.38527(RTTOT90)

or in terms of Table I variables

RATE = - 1.21331 + 0.71262(NITE90) 2 + 0.23598(TTIME)*

+ 19.68521(1.0/DNA) - o.61421(TTImE/DNA)'

+ 182.91525(1.O/TOT9O) 2 + 0.38527(TOT90)i

Either equation accounts for 80.8% of the varianoe in air-

craft accident rate at a 95% confidence level, a 25.3%

increase o-3r initial efforts.

46

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V. DISCUSSION

Reviewing the results it can be seen that as functional

forms of the variables were introduced into the regression

analysis that more variance in aircraft accident rate was

accounted for at a higher confidence level. This was true

for all eight commands considered.

Observing the signs of the correlation coefficients

listed in Table XIX, it can be seen that the variable EXMPR,

which is the ratio of years experience as a designated

Naval aviator and total flight time in accident involved

aircraft model, was negatively correlated with accident

rate in all cases. This indicates that the more flight

time in a particular aircraft model that a pilot possesses

per year of designated Naval aviator service that he will

become more safe and thus have fewer accidents. This could

suggest that the more experienced a pilot becomes the larger

a repertoire of near tragedies he has to draw from and thus

the more reminders or analogies he has to compare with

current situations.

Conversely, the variable CLNIT, which is the number of

night carrier landings a pilot has during the last thirty

nights, showed positive correlation with aircraft accident

rate in the three commands where the variable was present

(COMNAVAIRLANT, MARLANT, COMNAVAIRPAC). This may indicate

48

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E4 +++1+

4-

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4E-

0

* E04

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* 09

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that night, carrier landings are more taxing evolutions

and tend to add to aircraft accident rate.

It has been common belief that pilot proficiency lessens

aircraft accident rate. However, when again reviewing the

correlation coefficients, it is observed that the correlation

of total flight time during the preceding ninety days (TOT90)

and day flight time during the preceding ninety days (DAY90)

is positively correlated with aircraft accident rate except

in the cases of CNATRA and MARTC (both training commands).

It is also observed that the variable night flight time

during the preceding ninety nights is positively correlated

with aircraft accident rate in all commands except CNATRA.

Considering that the training commands are on a schedule

where the pilot should not experience fatigue, the positive

correlation of these variables with aircraft accident rate

would tend to indicate that if flight time is not uniformly

spread out that practice does not necessarily make perfect

and that a possible fatigue factor may be causing an increase

in aircraft accident rate. Fatigue could be construed as

having the majority of flight time during the preceding

ninety days massed into a short period of time instead of

being distributed uniformly over the ninety day period. (It

is understood that data for a thirty day period is now being

recorded.) Another explanation would support Goorney's

supposition that pilot complacency may increase directly

as the number of hours flown and thus contribute to aircraft

accidents. In this case, new pilots in the training command

50

L K ..... ... ... ..... ... . . ... . . .. . ...... . .. . . ...... ...

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most likely will not become complacent or they will not

receive their wings.

The rem variables listed in Table XIX did not

indicate a dominant sign of the correlation coefficient

common to all commands. Therefore, the author will not

attempt to explain the rem variables individually.

When reviewing the results of the major commands con-

sidered, it should be noted that the variables most instru-

mental in explaining the variance in aircraft accident

rate are not all pilot oriented variables as was shown in

the Maxwell and Stucki study which was an overall Navy/

Marine study. The overall results don't seem to apply

when taking a more microscopic look at individual commands.

COMNAVAIRLANT, COMNAVAIRPAC, MARPAC, CNATRA and Naval Reseirves

regression equations all contain variables interpreted as

being either related to experience level, pilot proficiency,

or aircraft condition. Only MARIANT, MARTC, and RDT&E/NASC

account for the variance in aircraft accident rate by

variables interpreted as being pilot oriented variables

in their respective regression equations. Condition of

the aircraft must therefore also be considered when attempt-

ing to account for the variance in aircraft accident rate.

51

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VI. RECWUKDTCI

The current study includes eight major commands in its

treatment of aircraft accident rate. Functional forms of

the variables produced the best results. For this type of

study however, the author recommends that the distributions

for each variable be ascertained and that these distributions

whether they be gamma, beta, exponential, etc. be used in

an attempt to analyze aircraft accident rate.

This study was limited to consideration of only accident

involved pilots and accident involved aircraft. A future

study could be done comparing these pilots and aircraft

to accident free pilots and aircraft in order to ascertaiA

whether these groups are from the same distribution. It

would then be possible to ascertain critical points in a

pilot's career or the life of an aircraft.

A more microscopic study than this study may seem appro-

priate. However, subdividing the data any further into

Airwings may limit the analyst to only a small number of

data points.

52

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AflWIX C

ee FOWR (SUPWISZ) NULTIPLU RZEGRSSION

The basic principles of regression analysis may be

extended to situations involving two or more independent

variables. The general mathematical form of the (unstand-

ardited) regression is

YO = A+ Bj1X + 2 . +BAC

where Y' represents the estimated value of the dependent

variable, A is the Y intercept, the Bi are regression

coefficients, and the X, are the independent variables.

It is assumed that this is a aomplete set of variables

from which the equation is to be chopen and includes any

functions such as squares and inverse squares thought to

be desirable and necessary.

The A and Bi coefficients are selected in such a way as

to minimize the sum of squared residuals, y-y,)2.By

minimizing the squared residuals, the regression technique

maximizes the correlation between the actual dependent

variable (Y) and the estimated dependent variable (Y')

while the correlation between the independent variables

and the residual values (Y-Y') are reduced.

The proportion of variance of Y explained, i.e., the

goodness of fit of the regression equation can be evaluated

by examining the square of the multiple correlation (R2),

where R2 is calculated by,

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= - 2

ssy -sr ssre;y

or

variation In Y explained by the combined

R2 linear influence of the independent variablestotal variation in Y

where SSy is the total variation or sum of squares in Y,

SSr is the sum of squared residuals, and SSreg is the

regression of squares.

The forward (stepwise) selection procedure available in

the Statistical Package for the Social Sciences (SPSS ver-sion 6) used for this study inserts variables in turn until

the regression equation is satisfactory. Independent var-

iables are entered only if they meet certain statistical

ctiteria. The order of inclusion is determined by the

respective contribuvion of each variable that explains the

greatest amount of variance previously unexplained by the

variables already in the equation. Th, variable that does

this is the next variable to be entered.

This order of insertion is determined by using the

partial correlation coefficient as a measure of the impor-

tance of variables not yet in the equation. The,basic

procedure is as follows. First select the X most correlated

with Y (suppose it is XI) and find the linear regression

equatiorr Y = f(X1 ). Next find the partial correlation

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coefficient of X (ijl) and Y (after allowance for Xl),

i.e., find the correlation between the residuals from the

Aregression Y = f(X1 ) and the residuals from another regres-

sion X =f(X). The X. with the highest partial correlation

with Y is now selected and the process continues. As each

variable ib entered into the regression, the following

values are examined,

1. R2, the multiple correlation coefficient;

2. The partial F-test value for the variable most

recently entered, which shows whether the variable

has taken up a significant amount of variation

over that removed by variables previously entered

in the regression.

As soon as the partial F value related to the most recently

entered variable becomes nonsignificant the process is

terminated.

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APPENDIX D

STATISTICAL TESTS FOR SIGNIFICANCE

Regression procedures per se may be categorized as de-

scriptive statistics. Regression analysis is commonly per-

formed on sample data from which the researcher is either

interested in estimating population parameters from sample

regression statistics or to testing statistical hypothesis

about the population parameters and determining confidence

limits for estimates in testirng the hypothesis.

The overall test for goodness of fit of the regression

equation uses statistical inference procedures to test the

null hypothesis that the sample of observations being analyzed

has been drawn from a population in which the multiple cor-

relation is equal to zero. An equivalent way of stating

the null hypothesis, Ho, is that the next variable to be

added in a forward regression would not add significantly

to the explained variance in the dependent variable, Y,

already accounted for by variables included in the regression

equation. The alternate hypothesis, Hi, directly contradicts

the null hypothesis.The test statistic employed for the overall test is

SSreg/ R2/

-SSres (6-K') (1-R2)/(N-K- )

'" 69

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where SS ini the sum of squares explained by the entireregregression equation, SSres is the residual (unexplained)

sum of squares, K is the number of independent variables

in the equation and N is the sample size. The F ratio is

distributed approxiuately as the F distribution with degrees

of freedom K and (N-K-i).

Adjusted R2 is an R2 statistic adjusted for the num-

ber of independent variables in the equation and the number

of cases. It is a more conservative estimate of the percent

of variance explained, especially when the sample size is

small. The adjusted R2 formula uses unbiasec estimates

of the error variance and the total variance of Y in the

population. The formula used by SPSS is:

R2 2K1Adjusted R= R - (1-R)

Becaused Adjusted R2 is a conservative estimate of the per-

cent of variance explained, the author used the following

F statistic to determine confidence levels for the regression

equations obtained for each command considered:

(Adjusted R2 )/K

(1-Adjusted R2 )/(N-K-I)

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LIST OF FmmCEES

Brictson, C. A., Pitrela, F. D., and Wulfeck, J. W., &-alysisof Aircraft Carrier Land Accidents (1265 to 1969).Dunlap and Associates, CNR, Washingon, D. C., November1969.

Collicott, C. R., Muir, D. Z., and Dell, A. H., U. S. NavalAviation Safety, ORG Study 766, October 1972.

Draper, N. R., and Smith, H., Applied Resreslion Analysis,John Wiley and Sons, Inc., New York, 1966.

Goorney, A. I , The Human Factor in Aircraft Accidents-Investigation of Background Factors of Pilot Error-Related Aircraft Accidents. Flying Personnel ResearchCommittee, Ministry of Defense, Great Britain, July1965.

Kowalseky, N. B., Masters, R. L., Stone, R. B., Bubcock, G.L., and Rypka, E. W., An Analysis of Pilot Error-RelatedAircraft Accidents, NASA Contractor Report 2444, June197T.

Manual of Code Classification for Navy Aircraft Accident,Incident, and Ground Accident Reportin , Records Div-ision, Records and Data Processing Department, NavalSafety Center, 1 July 1972.

Maxwell, J. S., and Stucki, L. V., nalysis of the VariableBehavior Manifested in All Navy/Marine Major AircraftAccident Rates, Unpublished Master's Thesis, NavalPostgraduate School, Monterey, California, September1975.

Myers, H. B., Jr., Pilot Accident Potential as Related toTotal Fliht EZaience and Recency and Frequency ofFlying, Unpublished Master's Thesis, Naval PostgraduateSchool, Monterey, California, September 1974.

Navy Aircraft Accident, Incident and Ground Accident Report-ing Procedures, OPNAVINST 3750.6J of 13 December 1973.

Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K.,and Bent, D. H., Statigtical Package for the SocialSciences, Second Editin, McGraw-Hill, New York, 1975.

Poock, G. K., Trends in Major Aircraft Accident Rates, NavalPostgraduate School Report #NPS55Pk76061, Monterey, Cali-fornia, June 1976.

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INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2Cameron StationAlexandria, Virginia 22314

2. Chief of Naval Personnel 1

Pero lbDepartment of the NavyWashington, D. C. 20370

3. Library, Code 0212 2Naval Postgraduate SchoolMonterey, California 93940

4. Department Chairman, Code 55 2Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940

5. Associate Professor G. K. Poock, Code 55Pk 3Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940

6. Assistant Professor D. E. Neil, Code 55Ni 1Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940

7. Director, Aviation Safety Programs 1Naval Postgraduate SchoolMonterey, California 93940

8. Naval Safety Center 1Naval Air StationNorfolk, Virginia 23511

9. LCDR R. W. Mister Code 1155 1Naval Safety CenterNaval Air StationNorfolk, Virginia 23511

10. LCDR L. C. Bucher 119 Arbor AvenueTopsham, Maine 04086

72