AD (03,3

USAARU REPORT NO. 66-7

EXPECTED INJURY RATES FOREXPERIMENTAL AIRBORNE OPERATIONS

By

R. A. Avner, 1st Lt., MSC

JUNE 1966

U. S. ARMY AEROMEDICAL RESEARCH UNITFort Rucker, Alabama

U. S. Army Medical Research and Development Command

Distribution Statement. Distribution of this document is unlimited. Citationof names of commercial equipment or materials does not constitute an officialendorsement or approval of the use of such items.

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L

AD

USAARU REPORT NO. 66-7

EXPECTED INJURY RATES FOREXPERIMENTAL AIRBORNE OPERATIONS

By

R. A. Avner, 1st Lt., MSC

JUNE 1966

U. S. ARMY AEROMEDICAL RESEARCH UNITFort Rucker, Alabama

U. S. Army Medical Research and Development Command

Distribution Statement. Distribution of this document is unlimited. Citationof names of commercial equipment or materials does not constitute an officialendorsement or approval of the use of such items.

ABSTRACT

Probability of injury for Army paratroopers under conditionsof full combat load and unprepared drop zone was estimated to be.006 (standard error = .002, N = 5,253). Tables were computed toallow tests of departure from this rate under experimental conditionsinvolving up to 50 jumpers.

APPROVED: __________-.____.__ __

WILLIAM P. SCHANELt Colonel, MCActing Commander

TABLE OF CONTENTS

Introduction and Purpose 1

Testing departures from standard injury rates 2

Use of table 2

Production of table 3

Table "Probability of "n" injuries among "N"jumpers (P = .006)" 4

References 6

Distribution List

DD Form 1473

EXPECTED INJURY RATES FOR EXPERIMENTAL AIRBORNEOPERATIONS

INTRODUCTION AND PURPOSE

Superior equipment and training have led to an extremely low injury ratefor U. S. Army parachutists. Under general unit training conditions about 1.7injuries would be expected for every 1,000 jumps (P=.0017, standard error = .0002,N = 137,966). Under conditions of full combat load and unprepared drop zone thisrate increases to about 6 injuries per 1,000 jumps (P = .006, standard error = .002,N = 5,253)*. The latter rate is probably typical of what can be expected underthese more severe conditions. Both British Army parachutists (Whittingham) andU. S. Forest Service "smokejumpers" (King) are also reported to have an injuryrote of about .005 under similar severe conditions.

Base injury experience has several uses in development of new airborneequipment or techniques. In the case of innovations intended to increase safety,it serves as a basis for measurement of improvement. In the case of inn,'ationsintended to rriet situations which are more hazardous than usual, it can serve asa basis for measure of the "loss" or "payment" exacted (i.e., increased injury rate)for the "gain" attained (the ability to meet the new situation).

In either case, it is usually not economically feasible to evaluate newdevelopments by use of samples of the size upon which the base rate has beendetermined. Use of smalle- samples (e.g., 50 or fewer jumps) leads however to aless precise estimate of the injury rate. With small samples the injury or non-injuryof a single man can make relatively enormous changes in the observed injury rate.If one out of a group of ten men is injured the observed injury rate for this group is10% (or 100 per 1,000). Yet, if this is the only injury in ten groups of ten meneach the observed rate is only 1% for this larger group of 100 men. Thus, there isa possibility that even for low general injury rates some small samples will occasionallyshow much higher observed rates. It is the purpose of this report to show with exactlywhat probability relatively large observed rates of injuries might occur in smallsamples from a population in which the true injury rate is relatively small. Themajor use of such information is in evnluation of ongoing programs. It is undesirableto terminate an experiment because of an "excessive" injury rate when in fact the

Almost exactly half of these injuries were severe enough to require evacuation to

permanent medical facilities and subsequent hospitalization. There were no fatalities.

injury rate is not significantly different from that expected by chance varin•ion inthe base rate. It is even more undesirable not to terminate an experimer t simplybecause the actual number of injuries is smolTwhen this number indicates an injuryrate significantly in excess of the acceptable rate.

TESTING DEPARTURES FROM STANDARD INJURY RATES

If production of injuries is assumed to occur at random with a fixed probabilityin a given sample group, the number of injured in this sample group will follow thebinomial distribution. Normal approximations to the binomial unfortunotely haverelatively large errors when P approaches zero or unity even for reasonably "large"samples of N = 100. It is therefore necessary to perform any lasts by ue of theappropriate exact binomial distribution.

The most efficient manner in which such tests could be run is probably someform of sequential analysis (Wald) in which small samples are observed in sequenceuntil the hypothesis of "no departure from standard rates" is either accepted orrejected. Unfortunately one of the conditions of military parachuting is usuallythat jumping is performed in moderately sized groups (20 to 50 men). Jumps madeby smaller groups coadid probably not be used for a valid estimate of the results ofjumps made under more typical conditions. Thus decisions must usually be based onone or two independent jumps by groups totalling less than fifty men.

The inclosed binomial table gives the expected probability of varying numbersof injuries for groups of up to 50 himpers when the true injury rate is 6 per 1,000.

USE OF TABLE

The major use of the table is in determining if an observed injury rate issignificantly higher than the expected combat-load injury rate. If it has been de-cided that the presence of a significantly higher rate is unacceptable, such a findingwould support the termination of the test.

The procedure to be used consists of two steps. First a probability value ischmsen which corresponds to how frequently the experimenter is willing to mistakenlyhalt the experiment when the injury rate is actually no more than normal. This iscalled the "alpha level" in statistical terminology. An alpha level of .01 wouldindicate that the experimenter is willing to have this error happen once in every 100tests, a level of .001 indicates once in every 1000 tests, and so forth. Second,following a jump, the number of injuries is counted and the tabled probability for

2

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"his many or more injuries in a group of the size used is determined. If this probabilitys less than the alpha level the exoeriment is halted, if it is more, there is no signifi-:ant difference (at the level tabled) between the observed and "standard" injury rate.

If more than one group jumps (up t( 50 total) the total injuries and size of thegroups may be combined for a more reliable test. This combination is valid only ifeach of the men jump only once (the same man must not be a member of more than oneDf the groups).

Choice of alpha level will depend on the objective of the tests. If safety isof first importance the alpha level will be hi,'n (e.g., .15 or even .20). If safetyis of importance secondary to another objective, the alpha level will be low (e.g.,.01, .001, or even .0001).

Examples: 1. (a) alpha level chosen to be .01

(b) Observation: 26 men jump, 2 are injured (probabilityof 2 or more injuries when the true injury rote is .006 is .010633, as given by thetable).

(c) Conclusion: do riot halt experiment - .010633 is greater

than .01

2. (a) alpha level chosen to be .001

(b) Observation:. 12 men jump, 3 are injured (this many ormore injuries would occur only 46 times in a million when the true injury rate is.006).

(c) Conclusion: halt experiment - .000046 is less than .001.

PRODUCTION OF TABLE

Individual binomial probabilities for P = .006; r =•0, 1,7; n = 1, 1,50were computed on a Monroe Epic 2000 electronic calculator. An iterative procedurewas used which, coupleldwith a biased roundoff in this machine, produced a maximumerror of about .5 x 10"1 for r = 0. The error for all other valoes of r was less thanthis amount. Individual probabilities to 8 significant d~gits were then summed foreach n to verify that this summation was equal to unity. The printed terms of thesummation were then used to produce the inclosed 6 place table of cumulated binomialprobabilities for p = .006; r = 0, 1,6; n = 1,1,50. The table was subsequently proof-read twice (independently) against the original printouts of the summations.

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References

1. Data for inijury rates were provided by:

a. Safety Director, US Army Mobility Command, Warren, Mich.

b. Commanding General, 82nd Airborne Division, Ft Bragg, N. C.

c. Commanding Officer, 428th Medical Bn., Fort Benning, Georgia.

2. King, Robert D. FAA Aviation News. p 11, Vol 4, No. 11, March 1966.

3. Wald, A. Sequential Analysis, 1947, Wiley, N. Y.

4. Whittingham; cited in Bergin, K. G., Aviation Medicine, 1949, John Wrightand Sons, Ltd, Bristol.

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I ORIGINATIN I ACTIVITY IC., ,ntpoe -thor) a P RCPoiT SICUP' T C LASIWICA TION

US Army Aeromedical Research Unit 1 Unclassified

Fort Rucker, Alabama

3 n1PORT TITLE

EXPECTED INJURY RATES FOR EXPERIMENTAL AIRBORNE OPERATIONS

4 DESCRIPTIVE NO-IS rTvp. of . ePort and A ncdmt,# dat*#)

5 AUTNOAS() cL..t n.-o. ftft O e. -t(,teal)

Avner, R. A., 1st Lt., MSC

6 OttRPORT OATE 1 70 TOVAL NO OF PAG'S 7b N4 or stews

June 1966 600 4so CONTRACT OR GRANT NO 94 ORIGINAtOR*S 1NTPORt NUMOFIS)

R..JFCT No 3AO 2560 ]A 819 USAARU Report No. 66-7

S Task No. 036 (FY 66) OR O,,. -nn ON" NOM3, (Any, h.p n h.... b .. d..

d

10 AVA ILABILITY LIMITATION NOTICES

Distribution of this document is unlimited. Citation of names of commercial equi.pment ormaterials does not constitute an official endorsement or approval of the use of such items.

I1 SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

US Army Medical Research and DevelopmentCommand, Washington, D. C. 20315

13 ABSTRACT

Probability of injury for Army paratroopers under conditions of full combatload and unprepared drop zone was estimated to be .006 (standard error = .002,

N = 5,253). Tables were computed to allow tests of departure from this rate under

experimental conditions involving up to 50 jumpers.

DD I ,0s 1473 UnclassifiedSecurity Classification

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