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UNCLASSIFIEDNOLTR 71-31

MATHEMATICAL EVALUATION3 FOR CONTROLLING HAZARDS

By:William T. Fine

ABSTRACT: To facilitate expedi t ious cont ro l o f hazards fo raccident prevention purposes, two grea t needs have been rec-ognized. These are for 1) a method to determine the r e l a t i veser iousness of all hazards for guidance in assigning prioritiesfor prevent ive e ffo r t ; and (2) a method to give a de f in i t edeterminat ion as to whether the estimated cost of the contem-plated correct ive act ion to el iminate a hazard is j u s t i f i ed .

To supply these needs, a formula has been devised which weighsthe cont ro l l ing fac to rs and ca lcu la tes the r i sk of a hazardous

si tuat ion, , giving a numerical evaluat ion to the urgency forremedial a t ten t ion to the hazard. Calcula ted Risk Scores are

then used to es tab i i sh priorities for cor rec t ive effor t . Anaddi t iona l formula weighs the estimated cos t and effect ivenessof any contemplated correct ive act ion aga ins t the Risk Scoreand gives a determinat ion as to whether the cost is j u s t i f i ed .

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PUBLISHED 8 MARCH 1971

NAVAL ORDNANCE LABORATORYWHITE OAK, MARYLAND

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MATHEMTICAL EVALUATIONS FOR CONTROLLING HAZARDS

The methods described in this report were conceived and developedby the author in recognition of needs for a method of determiningre la t ive urgencies for attention to hazards, and for a simplesystem to give guidance as to whether the estimated cost of anengineering project to eliminate a hazard is just i f ied. Theseneeds are sat isf ied by the use of formulae which weigh the vary-ing degrees of the controlling factors.

In a few months of actual use a t the Naval Ordnance Laboratory,these formulae have furnished solid foundation for safety recom-rendations for engineering action; they have saved many thousandsof dollars by cancelling costly projects which the r isks did notjust i fy; and they have given bet ter direction to the ent i re safetyprogram by indicating the relat ive potent ia l seriousness of a llhazards.

Since weights or values assigned to the various factors of th eformulae are empirical, extended experience may indicate advis-abi l i ty of raising or lowering some of the cri ter ia . Howeversince resul ts are primarily for comparative purposes, re la t iveevaluations will be valid within any organization as long asstandards of judgment are consistent.

These methods are promulgated for information and for any usedesired by addressees. It is believed they have universal appli-cation and should provide advancement in the sta te of the art ofthe safety engineering profession.

GEORGE G. BALLCaptain, USN

ROBERT ENNISBy direct ion

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CONTENTS

Chapter I

INTRODUCTION

Section Page1 General .......................... ........... 12 efinitions ........................ . . . . . . . . . . .. . . 2

Chapter IIFORMULA FOR EVALUATING THE SERIOUSNESS

OF A RISK DUE TO A HAZARD

1 Genera l ............. -* . o . o ...... o....... ... 42 The Formula...... .......................... 43 Examples ...... ...... o........ .......... 64 Summarizing Risk Scores ................. 155 Resul t s and Uses of Summary of Risk Scores ...... 17

Chapter IIIFORMULA TO DETERMINE JUSTIFICATIONFOR RECOMMENDEDCORRECTIVE ACTION

I Genera l ...................... .................. 182 The Formula ................. o.. . . . . .o. . . . . . . .o. . . . . . . 18

3 Cri ter ia for Just i f icat io n...................... 194 Examples . . .... o............ - 205 Recommended Procedure for Using the J Formula .. 256 Exception to Reliance on the J Formula .......... 26

Appendix A. J Formula Worksheet . . . . . . . . . . . . . . 27

Appendix B. Rating Summary Sheet ......................... 28Table 1. Risk Score Summary and Action Sheet .......... 16

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Chapter 1

INTRODUCTION

GENERAL. The purpose of this chapter _s to i l lustrate th eneed for quantitative evaluations to aid in the control of haz-ards and to explain the general plan of this report.

A problem frequently facing the head of any (f ield type)safety organization is to determine just how serious each knownhazard is, and to decide to what extent he should concentratehis resources and str ive to get each situation corrected.Normal safety routines such as inspections and investigationsusually produce varying list of hazards which cannot all becorrected a t once. Decisions must be made as to which ones arethe most urgent. On costly projects, management often askswhether the r isk due to the hazard just i f ies the cost of th ework required to eliminate it. Since budgets are l imited,there is necessity to assign pr ior i t i es for costly projects toeliminate hazards.

The question of whether a costly engineering project isjust i f ied is usually answered by a general opinion which maybe little bet ter than guesswork. Unfortunately in many cases,the decision to undertake any costly correction of a hazarddepends to a great extent on the salesmanship of safety personnel.As a result, due to insuff ic ient information, the cost of cor-recting a very serious hazard may be considered prohibitive bymanagement, and the project postponed; or due to excellentselling jobs by Safety, highly expensive engineering or construc-t ion jobs may be approved when the r isks involved real ly do notjust i fy them.

In Chapter 2 of this report , a formula is presented to calculate the r isk due to a hazard, or to quantitativelyevaluate the potential severity of a hazardous situation. Useof this formula will provide a logical system for safety andmanagement to determine priori t ies for attention to hazardoussituations, and guidance for safety personnel in determiningthe areas where their efforts should be concentrated.


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In Chap te r 3 o f this report a fo rmula is p r e s e n t e d fo rde te rmin ing whethe r o r n o t the cost o f e l i m i n a t i n g a hazard is

just i f ied. Use of the formula will provide a solid foundationupon which safety personnel may base their recommendations forengineering-type corrective action. It will assure that proj-ects which are not just i f ied will not be recc.mended.

This report deals with just i f icat ion of costs to eliminatehazards. This does not inply in any way that a cost, no matterhow great, is not worthwhile if it will prevent an accident andsave a human l i fe . However we must also consider accident pre-vention with reason and judgment. Budgets are not unlimited.Therefore the maximum possible benefi t for safety must be derivedfrom any expenditure for safety. When an analysis resul ts in adecision that the cost of cer ta in measures to eliminate a hazard is not just i f ied, we do not say or suggest that the hazard isnot serious and may be ignored. We do say that, based on evalu-ation of the controlling factors, the return on the investment,or in other words, the amount of accident prevention benefit , isbelow the standards we have established. The amount of moneyinvolved will no doubt provide greater safety benefi t if used toal leviate other higher-risk hazards which this system will iden-t i fy. As for the hazard in question, less costly preventivemeasures should be sought.

DEFINITIONS. For the purpose of this presentation, threefactors are defined as follows.

a. HAZARD: Any unsafe condition or potent ia l source of anaccident. Examples are: an unguarded hole in the ground; defec-t ive brakes on a vehicle; a deteriorated wood ladder; a slipperyroad.

b. HAZARD-EVENT: An undesirable occurrence; the combinationof a hazard with some act ivi ty or person which could s tar t asequence of events to end in an accident. Examples of hazard-events are: a person walking through a f ie ld which contains ahazard such as an unguarded well opening; a person not wearingeye protection while in an eye hazardous area; a person drivinga vehicle that has defective brakes; a man climbing up a defec-t ive ladder; a vehicle being driven on a slippery road.

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c. ACCIDENT SEQUENCE: The chain of events or occurrenceswhich take place star t ing with a hazard-event and ending withthe consequences of an accident.

d. Additional defini t ions will be provided in la ter pagesas needed.

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Chapter 2

FORMULA FOR EVALUATING THE SERIOUSNESSOF THE RISK DUE TO A HAZARD

GENERAL. The purpose of th i s chapter is to present a completeexplanation of the method for quant i ta t ively evaluating the seri-ousness of hazards, and some of the benefi ts that may be derivedfrom such analyses.

The expression a calculated r isk is often used as a catch-al l for any case when work is to be done without proper safetymeasures being taken. But usually such work is done without anyactual calculation. By means of th i s formula, the r isk is calcu-lated. The seriousness of the r isk due to a hazard is evaluatedby considering the potent ia l conse&uences of an accident, th eexposure or frequency of occurrence of the hazard-event that couldlead to the accident, and the probability that the hazard-event

will resul t in the accident and consequences.

THE FORMULA is as follows:

Risk Score = Consequences x Exposure x Probabi l i ty

Abbreviated: R = C x E x P

Definitions of the elements of the formula and numerical ratingsfor the varying degrees of the elements are given below.

a. CONSEQUENCES C: The most probable resul ts of a potentialaccident, including injur ies and property damage. This i3 basedupon an appraisal of the ent i re s i tuat ion surrounding the hazard,and accident experience. Classifications and ra t ings are:

Description Rating

1) Catastrophe: numerous fa ta l i t ies ; extensivedamage (over $1,000,000); major disruption of act ivi t ieso f nat ional s igni f icance ................................... 100

(2) Multiple fa ta l i t ies ; damage $500,000 to$1,000,000 .............................................. 50

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Description Rating

(3) Fatal i ty, damage $100,000 to $500.000 ...... 25

(4) Extremely serious injury (amputation,permanent disabil i ty); damage $1000 to $100,000 ......... 15

(5) DisablinC injur ies; damage up to $1000 . . . . . 5

(6) Minor cuts, bruises, bumps; minor damage... 1

b. EXPOSURE E: Frequencv of occurrence of the hazard-event(the undesired event which could s tar t the accident-sequence).Classif icat ions are below. Selection is based on observation,experience and knowledge of the act ivi ty concerned.

Description Rating

The hazard-event occurs:

(1) Continuously (or many times daily) ......... 10

(2) Frequently (approximately once daily) ...... 6

(3) Occasionally (from once per week to onceper month) .............................................. 3

(4) Unusually (from once per month to onceper year) ...................................... 2

(5) Rarely (it has been known to occur) ........ 1

(6) Very rarely (not known to have occurred,but considered remotely possible)...................... 0.5

c. PROBABILITY P: This is the l ikelihood that, once th ehazard-event occurs, the conylete accident-seauence of eventswill follow with the necessary timing and coincidence to resultin the accident and conseczuences. This is determined by carefulconsideration of each step in the accident sequence all the wayto the consequences, and based upon experience and knowledge ofthe act ivi ty, plus personal observation. Classif icat ions andratings are:

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DESCRIPTION RatingThe accident-sequence, including the consequences:

(1) Is the most l ikely and expected resul t ifthe hazard-event takes place ........................... 10

(2) Is quite possible, would not be unusual,has an even 50/50 chance ..................................... 6

(3) Would be an unusual sequence or coincidence 3

(4) Would be a remotely possible coincidence.

(It h a s happened here . .................................. 1(5) Extremely remote but conceivably possible.

(Has never happened after many years of exposure.) . . . . . 0.5

(6) Practically impossible sequence orcoincidence; a one in a million possibi l i ty. (Hasnever happened in spite of exposure over many years.). . 0.1

EXAMPLES. The use of this formula is demonstrated by actualexamples. Six widely different types of situations have beenselected to i l lustrate the broad appl icabi l i ty of the formulaand method of computation.

a. Example No. 1 (Actual case)

(1) Problem. There is a quarter-mile stretch of two-laneroad used frequently by both vehicles and pedestrians departingor entering the grounds. There is no sidewalk, so pedestriansfrequently walk in the road, especially when the grass is wet orsnow covered. There is little hazard to pedestrians when al l th et ra ff ic is going in one direction only; but when vehicles aregoing in both directions and passing by each other, the vehiclesrequire the ent i re width of the road, and pedestrians must thenwalk on the grass alongside the road. It is considered that anaccidental fatal i ty could occur if a pedestrian steps into th eroad, or remains in the road a t a point where two vehicles ar epassing.

(2) Steps to Use the Risk Score Formula:

(a) Step 1. List the accident-sequence of eventsthat could resul t in the undesired consequences.

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1 It is a wet or snowy day, making the grassalong the road wet and uninviting to walk on.

2 At quit t ing time, a l ine of vehicles, andsome pedestrians are leaving the grounds, using this road.

3 One pedestrian walks on the right side ofthis road, and he has an at t i tude which makes him oblivious tothe t raff ic . (This is the hazard-event.)

4 Although traffic is one way out a t thistime, one vehicle comes from the opposing direction causing th eoutgoing t raff ic l ine to move to the r ight edge of the road.

5 The pedestrian on the right side of th eroad fai ls to observe the vehicles, and he remains in the road.

6 The driver of one vehicle fai ls to noticethe pedestrian and st r ikes him from the rear.

7 Pedestrian is kil led.

(b) Step 2. Determine values for elements offormula:

1 Conseauences: A fatal i ty. Therefore C = 25.

2 Exposure: The hazard-event is event 3above, the pedestrian remaining in road and refusing to noticethe line of t raff ic . It is considered that this type individualappears or is created by conditions occasionally. ThereforeE = 3.

3 Probabili ty of al l events of the accident-sequence following the hazard-event is: conceivably possible,although it has never happened in many years. Reasoning is asfollows: events 4, 5, 6 and 7 are individually unlikely, so th ecombination of their occurring simultaneously is extremely remote.Event 4 is unlikely because t ra ff ic is one way a t qui t t ing time.Event 5 is unlikely because a number of drivers would undoubtedlysound their horns and force the pedestrian's attention. Event 6

is unlikely because most drivers are not deliberately reckless.Event 7, a fatality, is unlikely because vehicle speeds are notgreat on the road, and the most l ikely case would be a glancingblow and minor injury. Not even a minor injury has ever beenreported here. In view of the above Probabili ty P = 0.5.

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(c) Step 3. Substitute into formula and determinethe Risk Score.R = C x E x P = 25 x 3 x 0.5 = 37.5

(NOTE: The Risk Score of one case alone is meaningless. addi-t ional hazardous situations must also be calculated for compar-ative purposes and a definite pattern. Five additional casesare similarly calculated below.)

b. Example No. 2 (Actual situation several years ago.Hypothetical case now.)

(1) Problem. Fifty (50) compressed air hoses are in

use for general cleaning purposes in a machine shop, being usedwithout proper pressure-reduction nozzles a t various pressuressome up to 90 pounds per square inch. This causes potentialeye hazards, although eye protection is worn by most men. Th emost probable consequence of this hazard is a serious eye injury.

(2) Using the Risk Score Formula:

(a) Step 1. List the sequence of events to causean eye injury accident:

1 Many machine operators use compressed a irstreams to blow metal chips from work.

2 Most employees occasionally remove theirsafety glasses while still in the hazardous area. (This is th ehazard-event.)

3 One employee who is not wearing eye protectionwalks past a machine while an air hose is being used.

4 A metal chip blows into the employee's eye.

5 A serious eye injury resul ts .

(b) Step 2.

1 Consequence: A disabling eye injury. C = 5.

2 Exposure: The hazard-event (an employeeremoving his eye protection while still in an eye hazardous area)is considered to occur many times daily. E = 10.

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3 Probabili ty: The total accident-sequenceis considered quite possible. P = 6.

(c) Step 3. Substitute into formula and determinethe Risk Score.

R = C x E x P = 5 x 10 x 6 = 300

c. Example No. 3 (Actual case)

(1) Problem. A 12,000 gallon propane storage tank issubject to two hazards. One hazard is the fact that the tankis located alongside a well-traveled road. The road slopes, andis occasionally slippery due to rain, snow or ice. It is con-sidered possible that a vehicle (par t icular ly a truck) could goout of control, leave the road, str ike and rupture the tank, andcause a propane gas explosion and f i re that could destroy severalbuildings, with consequences amounting to damage costing $200,000,plus a fatal i ty. The second hazard is the tank 's location closeto ultra-highly conmressed air l ines and equipment. A highpressure pipeline explosion could resul t from a malfunctioningsafety valve, a human error in operating the equipment, damageto a pipeline, or from other causes. Blast or flying debriscould conceivably st r ike the propane storage tank, rupture itand cause it to explode with the same consequences as for a run-away vehicle.

(2) Using the Risk Score formula: (NOTE: In this casethere are two hazards, so the evaluation is done in two parts,one for each of the hazards, and the total scores are added.)

(a) Step 1. Consider just the f i rs t hazard, thatdue to a vehicle. List the sequence of events that would resultin an accident:

1 Many vehicles are driven down the h i l lalongside the storage tank.

2 The road has suddenly become slippery due toan unexpected freezing rain.

3 One truck star ts to slide on the slipperyroad as it goes down this hill. (NOTE: This is the hazard-event that star ts the accident sequence.)

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4 The driver loses his steering control ata point when he is uphil l from and approaching the tank.

5 Brakes fa i l to stop the vehicle from sliding.

6 Vehicle heads out of control toward the tank.

7 Vehicle str ikes the tank with enough forceto rupture it and permit the propane gas to leak out.

8 A spark ignites the propane.

9 Explosion and conflagration occur.

10 Building and equipment damage is $200,000,and one man is kil led.

(b) Step 2. Substitute numerical values into formula:

1 Conseauences: One fa ta l i ty and Damage lossof $200,000. Therefore C = 25.

2 Exposure: The hazard-event that wouldstart the accident sequence is event No. 3, the truck star t ingto sl ide on this road. This has happened rarely.Therefoe E = 1.

-3 Probability: To decide on the l ikelihoodthat the complete accident-sequence will follow the occurrenceof the hazard-event, we consider the probability of each event:

a Consider event 4: Loss of steer ingcontrol to occur a t the precise point in the road approachingthe tank is possible but would be a coincidence.

b Consider event 5: failure of brakes.Once the vehicle star ted to slide, if the road were ice covered,it would be expected that the brakes would fa i l to stop the slide.

c Consider event 6: the vehicle headingtoward the tank. This is highly unlikely. Momentum would causethe vehicle to continue straight down the road.

_ Consider event 7 the vehicle str ikingthe tank with great force, and squarely. Extremely unlikely.

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If a vehicle were sliding on an ice covered surface toward th etank, it would be easily diverted from its direction of travel

by a number of obstructions between the road and the tank.When roads are slippery, t ravel is curtailed and drivers arecautioned to drive slow. A slow rate of speed would be unlikelyto produce enough force to damage the tank. The shape andposition of the tank are such that a vehicle would tend toglance off it.

e Events 8 through 10 are l ikely to followif event 7 took place.

f In summary, the highly unlikely natureof most of the events from 4 through 2 gives a net Probabi l i tyof almost a one in a million possibi l i ty. It has never

happened, but it is conceivable. Therefore P = 0.5.

4 R = 25 x 1 x 0.5 = 12.5

(c) Step 3. Repeat the entire above process for th esecond hazard (location near the high pressure air l ines andequipment): List the sequence of events:

1 Normal daily act ivi t ies involve operation ofequipment and pressurizing of pipelines some of which are in th evicini ty of the propane storage tank.

2 A pipeline containing ai r compressed to 3000

pounds per square inch, approximately 50 feet away from th estorage tank, has become deteriorated or damaged. (:This is th ehazard-event.)

3 The pipeline bursts.

4 Metal debris is thrown by the blast in a lldirections, several pieces flying and st r iking the propane tankwith such force that the tank is ruptured.

5 Propane starts to leak out of the tank.

6 A spark ignites the propane fumes.

7 The propane and air mixture explodes.

8 Building damage is $200,000, and one manis kil led.

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(d) Step 4. Determine values and subst i tute in

formula. 1 Consequences: One fatal i ty and damage lossof $200,000. C = 25.

2 Exposure: High pressure air l ines have beenknown to have been neglected or damaged. Frequency of suchoccurrences is considered unusual. Therefore E = 2.

-3 Probability: Now we estimate the likelihoodthat a damaged pipeline will explode and the explosion will occurclose enough and with enough blas t to throw debris and str ikethe propane tank with such force as to couplete the accidentsequence. Several bursts have occurred in past years, but none

have damaged the propane tank. Few of the pipelines are closeenough to endanger the tank. After careful observation, th eaccident sequence is considered very remotely possible. Theclassif icat ion is placed a t P = 0.5.

4 Substituting into the formula:

R = 25 x 2 x 0.5 = 25

Tota l R = 12.5 + 25 = 37.5

d. Exanyle No. 4

1) Problem. Building 303 contains a number of ovenswhich are ,sed for environmental tes t ing (heating) of explosives,in quant i t ies up to five pounds of explosive material per ovena t one time. One side of the building is made of blowout panelsso thaL in case of an accidental detonation of explosives, mostof the blast will be expended out the blowout wall with lessdemolishment of the ent i re building. This type of oven has beenknown to run away or heat excessively due to faulty heat controldevices, and thereby cause the explosives in the oven to detonate.The potent ia l hazard considered here is the endangering of personswho occasionally walk past the building on its blowout side. Suchpersons could be severely injured if an explosion occurred whilethey were passing by.

(2) Potent ia l sequence of events:

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(a) Several ovens are in use, each containingfive pounds of explosives undergoing tes t .

(b) Persons are usually present in the area outsidethe building on the blowout side. This is a normal and acceptedcondition.

(c) The thermostatic controls of one oven in use* become defective and the oven temperature r ises above safe

operating range (the hazard event).

(d) The secondary emergency shutoff control fa i l sto function.

(e) The oven overheats.

(f) The explosive content of the oven explodes.

(g) A passerby near the building is fa ta l ly injuredby the blas t and flying debris.

(3) Formula use:

(a) Consequence: A fatal i ty. C = 25.

(b) Exposure: The hazard-event, the malfunctioningof the oven heat controls, has happened before, but very rarely.E -1.

(c) Probabili ty of the complete accident sequencefollowing the hazard event: al l ovens have been equipped withsecondary emergency shutoff controls. Monthly maintenance pro-cedures have now been established to ensure their proper function-ing. Failure of the secondary shutoff if it should be needed isconsidered highly unlikely. It would be a remotely possiblecoincidence if the secondary failure occurred at the same timeand on the same oven on which a thermostatic control failed.Therefore the Probabili ty rating P = 1.

(d) Substituting in the formula:

R = 25 x 1 x 1 = 25

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e. Example No. 5 (Actual case)

1) Problem. There are approximately 100 household-type refr igerators in use in which various kinds of chemicalsare stored. Many of these refr igerators are not sparkproofFlanmuable volat i le solvents stored in nonsparkproof refr ig-erators could leak, vaporize, contact electr ical sparks andresul t in an explosion or fire. Most l ikely resul ts would beminor injur ies and possible damage estimated a t $200.00.

(2) Necessary sequence of events for an accident:

(a) Various kinds of chemicals are placed andstored in approximately 100 refr igerators (normal practice).

(b) Occasionally flaxruable volat i le solvents areplaced in a nonsparkproof refr igerator (a violation of safepractice. This is the hazard-event).

(c) A solvent container leaks (or the cover isnot on t ight) .

(d) Fumes reach an electr ic spark.

(e) Fumes explode and cause $200.00 damage.

(3) Formula use:

(a) Consequence: Damage is $200.00. C = 5.

(b) Exposure: The hazard-event, the violation inevent (b) above, is believed to occur frequently. E = 6.

(c) Probability: The probability of the accidentsequence following the violation and resulting in the accidentis considered remotely possible. Therefore P = 1.


R = 5 x 6 x 1 = 30

f. Example No. 6 (Actual case)

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(1) Problem. The hallways of Shop Bui ld ing 25 aresubjec ted to cons iderable traffic by pedes t r ians and shop-car tsor wagons. A hazardous t ra ff ic si tuat ion a t one blind cornercould resul t in col l is ions between persons walking and materialson carts, and cause minor injur ies .

(2) Necessary sequence of events:

(a) One employee walking and one employee pushinga cart approach the blind corner from different directions atexactly the same time. (This is the hazard-event.)

(b) Both employees approaching the intersect ionare unwary and somewhat in a hurry.

(c) One or both employees on the col l is ion coursefa i l to react and stop in time to avoid a col l is ion.

(d) A minor injury resul ts .

(3) Formula use:

a) Consecuencet Minor injury. C = 1.

(b) ExPosure: The hazard-event occurs many timesdai ly. E = 10.

(c) Probability: The complete accident-sequenceis quite possible, not unusual. P = 6.

(d) Risk Score R = 1 x 10 x 6 = 60

SUMbkRIZING RISK SCORES. As demonstrated above, the RiskScores for 20 additional hazardous si tuat ions have been calculated.These 26 cases are now listed in order of the magnitude of theirRisk Scores, or we can say - in order of the relat ive seriousnessof their risks. See Table 1: Risk Score Summary and Action Sheet.The cr i t ica l (dotted) l ines are drawn where best judgment dictatesto signify urgency for corrective action in accordance with th eRisk Scores.

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Table 1

RISK SCORE SUMl, RY AND ACTION SHEETHAZARD DESCRIPTION RISACTION

Window washer on third floor, without safety bel t ,Ahangs on with one hand and leans out.............. 1500

Men working in ditch six feet deep, ditch not shored,di r t is soft, subject to sliding.................. 75 0

Painters on scaffold without handrail, 30 feet high,not using safety belts............................ 75 0

Benzene used for cleaning floor of shop, a busy area, Ismmediate correctionmen smoke, other spark sources nearby .............. 450 required. Activityshould be discon-

Compressed flammable gas cylinders standing unsecured snue tiscazr

on pal let , along busy ais le , caps on.............. 375 is reduced.Uncontrolled compressed air used in machine shop, up

to 90 psi, for general cleaning ................... 300Men smoking in flammiable storage warehouse, no sprin-

kler system, highly flammable material ............ 270Portable electr ic dr i l l in use without ground wire,

getting rough usage by several people ............. 200Conpressed air receiver without safety rel ief valve,

automatic shut-off a t 200 psi, old equipment.. . . . . 180People walking past deep unguarded ditch, considerable

t raff ic , poor lighting ............................ 150 Urgent. Requires

Heavy instruments unstable on seven foot high shelf attention as sooncase, subject to bumping by employees ............. 150 (as possible.

Trucks rounding blind corner without stopping,opposing traff ic and pedestrians, 10 MPH l im it . . . . 13 5

Steps of main building slippery whenever wet, nohandrail, many pedestrians daily .................. 90

Compressed oxygen cylinder standing unsecured nearwall, little t raff ic or m ov em ent . . . . . .. . . .. . . .. . . . 85

Pedestrian and hand-cart t raff ica t blind corner

in hallway of shop building ....................... 60Oxygen and acetylene cylinders stored together, caps

on, good ventilation, fireproof surroundings ...... 45Inadequate handrailing along outside stairway,

occasional use every day .......................... 40Large propane storage tank in busy area: vehicle

t raff ic , and high pressure air operations ......... 37.5Both pedeccrians and vehicles using same road. Road Hazard should be

not always wide enough for both ................... 37.5 eliminated withoutChemicals stored in nonsparkproof refr igerators , delay, but situation

occasionally including flammable volatile liquids. 30 is not an emergency.

Broken sidewalk, occasional pedestrian t raff ic , holesand loose concrete 30

Persons near explosives building, within range ofpossible missiles: safe procedures in building .... 25

Portable vacuum pump lacking bel t guard. Pump movedaround occasionally by several employees .......... 18

Machinist using heavy f i le without f i le handle, indaily use ......................................... 18

Workman using hammer with loose head, in use dailyfor odd jobs ...................................... s18

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RESULTS ND USES OF SUMb1IRY OF RISK SCORES.

a. The Risk Score Summary and Action Sheet on Table 1 isnow a very useful device. If necessary or advisable, the listshould be presented to management for top level concurrenceand approval of the ACTION column.

b. Beneficial uses of this list are as follows:

(1) Establishes pr ior i t ies for at tent ion by both Safetyand Management. Hazardous si tuat ions are l i s ted in the orderof their importance. The position on the list of any item canbe lowered by corrective action which will decrease its possibleConsequences, Exposure, or Probability.

(2) It provides guidance to indicate urgency of newlydiscovered hazards. For each new hazardous si tuat ion, computethe Risk Score. I ts urgency is indicated by the ACTION areain which its Risk Score fal ls . In part icular, it would serveas guidance as to whether a job must be stopped when a highlyhazardous si tuat ion is noted in a highly essent ia l operation.If the Risk Score is above the upper cr i t ica l line, job mustbe stopped unti l some corrective action can be taken to, a t th eleast , lower any one of the three factors to get the Score intoa less urgent category.

(3) It would provide a means of set t ing goals and

objectives for the Safety Program, other than or in ad~dition tothe use of accident s ta t i s t ics . For example, a safety programcan be rated, or safety accomplishment can be demonstrated bythe number of cases for which corrective action has been takenand caused the cases to be placed in less urgent categories.A goal could be to have no hazardous si tuat ions above th elowest category. The safety sta tus of an organization can beindicated by the number of items in each category a t any time.

NOTE: With reference to Table 1, the author hastens to pointout that very few of the l is ted hazardous si tuat ions presentlyexist a t the Naval Ordnance Laboratory, the locale where thisprogram originates. Most of the severe cases were selected forexpediency from previous years' experience, are hypothetical, orcombine experience and hypothesis. It is recommended to poten-tial users of this system, that they also compile workable listsas soon as possible from their past experience and hypotheses,to be used as guidance for co.parative evaluation of hazardoussi tuat ions as they occur or are discovered.

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NOLTR 71-31

Chapter 3

FORMULA TO DETERMINE JUSTIFICATIONFOR RECOMMENDEDCORRECTIVE ACTION

GENERAL. The purpose of this chapter is to describe th emethod of determining whether the cost of corrective actionto alleviate a hazard is justified. Once a hazard has beenrecognized, appropriate corrective action must be tentat ively

decided upon and i t s cost estimated. Now the Justificationformula can be used to determine whether the estimated costis just i f ied.

THE FORMULA, is as follows:

Consequences x Exposure x Probabili tyJust i f icat ion = Cost Factor x Degree of Correction

Elements are abbreviated:

CxExPCF xD C

It should be noted that the elements of the numerator of thisformula are the same as in the Risk Score formula describedin Chapter 2. W e have simply added a denominator made up oftwo additional elements which are as follows:

a. COST FACTOR CF: A measure of the estimated dollarcost of the proposed corrective action. Classifications andratings are:

Cost Rating

1) Over $50,000 ........................ 10

(2) $25 ,000 to $50,000 ............... 6

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NOLTR 71- 31

Cost Rating

(3) $10,000 to $25,000 .............. 4

(4) $1,000 to $10,000 ............... 3

(5) $100 to $1,000 .................. 2

(6) $25.00 to $100 .................. 1

(7) Under $25.00 .................... 0.5

b. DEGREE OF CORRECTION DC: An est imate o f the deg-reeto which the proposed corrective action will eliminate oral leviate the hazard, forestal l the hazard-event, or inter-rupt the accident sequence. This wil l be an opinion basedon e•perience and knowledge of the act ivi ty concerned.Classifications and ratings are:

Description Rating

(1) Hazard positively eliminated, 100 1

(2) Hazard reduced a t l eas t 75%, butnot conpletely ................................. 0 2

(3) Hazard reduced by 50 to 75% ...... 3

(4) Hazard reduced by 25 to 50%... . . . . 4

(5) Slight effect on hazard (lessthan 25%....................................... 6

CRITERIA FOR JUSTIFICATION. Values are subst i tu ted in tothe formula to determine the numerical value for Jus t i f i ca t ion .The Crit ical Just i f icat ion Rating is 10. For any rating over10, the expenditure will be considered just i f ied. For ascore less than 10, the cost of the contermlated correctiveaction is not just i f ied.

NOTE: The cr i t ica l Just i f icat ion Rating has been arbitrari ly

se t a t 10, based on experience, judgment and the currentbudgetary s i tuat ion. After extended experience a t any indi -vidual organization, based on accident experience, budgetarysituations, and appraisals of the safety status, it may befound desirable to raise or lower the cr i t ica l score.

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NOLTR 71- 31

EXAMPLES. The use of the Just i f icat ion formula willbe i l lustrated by

the useof

the same six examples discussedin Chapter 2.

a. Example No. 1: The hazard of pedestrians and vehiclesusing the same road. To reduce this risk, the correctiveaction being considered is to construct a sidewalk alongsidethe road, a t an estimated cost of 1500.00. The J formulais now used to determine whether this contemplated expenditureis just i f ied.

1) Substitute values in the J formula

C x E xP

CF x DC

(a) C. E. and P, for this situation werediscussed as Example No. 1 in Chapter 2 of this report anddetermined to be 25, 3 and 0.5, respectively.

(b) Cost Factor. The estimated cost is $1500.00.Therefore CF = 3.

(c) Degree of Correction. The probability ofthe hazard-event occurring is considered to be reduced atleast 75 percent, but not 100 percent, by the constructionof a sidewalk. Therefore DC - 2.

(d) Jus t i f i ca t ion Rating.

2 5 3 x 0 5 3.J = 3 X 2 0.6 = 6 . 2 5

(2) Conclusion. J is less than 10. Therefore th ecost of construction of the sidewalk is not just i f ied.

NOTE: This lack of sufficient just i f icat ion evaluates th esituation from the safety viewpoint only. Management couldfeel there is added just i f icat ion for morale or other purposes.

(3) Additional consideration. Since the Risk Scoreis still a substantial 37.5, other (less costly) correctivemeasures should be sought. This includes improved administrative

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NOLTR 71-31

controls to enforce one-way t ra ff ic measures, reduce speed,

and encourage pedestrians to use another exi t gate. Thiswill reduce the Risk Score by reducing both Exposure andProbability.

b. ExamPle No. 2: The hazard due to compressed a irbeing used in a shop without proper pressure reduction nozzles.The proposedcorrective action is instal lat ion of proper pres-sure reducing nozzles on the 50 air hoses, a t a cost of $8.00each, or $400.00. To determine just i f icat ion for the expenditure:

1) Determine values for the elements of the J formula:

(a) C. E. and P, were discussed in Example No. 2

of Chapter 2 and evaluated a t 5, 10 and 6 respectively.

(b) Cost Factor. The cost of the correctiveaction is $400,00, so CF = 2.

(c) Degree of Correction. The corrective actionwill reduce the hazard by a t least 50 percent, so DC = 3.


_5 x 10 X 6 _ 300 .J- 2 x 3 - 6

(2) Conclusion. J is well above 10. The cost ofinstal l ing pressure reduction nozzles is strongly just i f ied.

c. Example No. 3: The hazardous location of the 12,000gallon propane storage tank. The proposed corrective actionis to relocate the tank to a place where it will be lessl ikely to be damaged by any external source, a t an estimatedcost of $16,000.

1) Determine values for elements of the formula:

(a) C, E, and P, were determined in Example No. 3

of Chapter 2, to be 25, 1 and 1.5 (the two hazards combined).(b) Cost Factor. Cost of relocation is $16,000.

CF 4.

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NOLTR 71-31

(c) Degree of Correction. In the very bestlocation available, there still remains a remote possibi l i tyof damage to the tank, so DC = 2.


J 2 5 • 1.5 37.54x2 8 4.7

(2) Conclusion. Based on the established cr i te r ia ,the cost of relocation of the tank is not just i f ied.

(3) It is emphasized that the conclusion in this case

that the proposed corrective action is not just i f ied, does notmean that the hazard is of little or no significance. TheRisk Score is still 37.5, and this remains of appreciableconcern. Since the potent ia l consequences of an accident arequite severe, effort should be expended to reduce the r isk, byreducing ei ther the Exposure or the Probability, or devisingother less costly corrective action. In this case it is con-sidered that an additional steel plate barr ier could be erectedto protect the tank from the compressed air act ivi t ies , and oneor two strong posts in the ground could minimize danger fromthe road. Thus the Probability of serious damage to the truck,and the Risk Score, would be considerably lessened a t a verynominal cost.

d. Example No. 4: The hazard to persons near a buildingin which explosives are processed. The proposed correctiveaction is the construction of a barricade along the outside ofthe building to protect passersby in event of an explosion within,a t an estimated cost of 5000.00. Using the J formula:


(a) C. E. and P, as discussed in Example No. 4of Chapter 2 were evaluated a t 25, 1, and 1, respectively.

(b) Cost Factor. Estimated cost is 5000.00.

CF = 3.

(c) Degree of Correction (to protect passersby)is considered over 75 percent. DC = 2.

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NOLTR 71-331

(2) Substituting values in the formula:

j = 25 x 1 x 1 = 25 = 4.203 x 2 6

(3) Conclusion. The expenditure of $5000.00 toconstruct a barricade to protect passersby is not just i f ied.

(4) Further consideration. Review of this problemrevealed that although the Probability of the complete acci-dent sequence occurring was adjudged to be remote, it couldbe made much more remote (and the Risk Score halved) byadministrative controls such as portable barr iers and warningsigns, to reduce or eliminate the presence of passersby inthe danger zone. Further, the type of solution that was pro-posed for this problem (extensive barricading) does not geta t the source of the problem. It would fa i l to protectproperty and persons inside the barricad e. It is consideredpreferable to concentrate on more extensive measures to preventan explosion such as by instal lat ion of additional fai l -safemechanisms on the ovens.

e. Example No. 5: The hazard of household type refr ig-erators (nonsparkproof) being used to store chemicals. Theproposed corrective action is to place warning signs (decals)on al l nonsparkproof refrigerators, cautioning against theiruse for volat i le solvents, plus administrative controls.

Cost of signs for the 100 boxes is $87.00.


(a) C. E. and P, as discussed in Example No. 5of Chapter 2 were evaluated a t 5, 6 and 3, respectively.

(b) Cost Factor. Cost is $87.00 CF = 1.

(c) Degree of Correction. The proposed actionof placing warning signs is considered to have an effect ofreducing the violation by 50 percent to 75 percent.Therefore DC = 3.

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NOLTR 71-31

(2) Substituting values in the formaula:

5--6x1 x 3011 x 3 - 3 10

(3) Conclusion. The cost of the decal warning signsis just i f ied.

(4) In this case a review is indicated since th eDegree of Correction of this corrective action is consideredonly 50 percent to 75 percent. Prior to instal lat ion of th ewarning signs, the Risk Score was 5 x 6 x 1, or 30. Withthe signs, plus administrative action, the Exposure is con-sidered to be reduced considerably, so that the Risk Score Rwill equal 5 x 2 x 1 = 10. This is a relat ively low r isk, notof any emergency nature, but also not to be conpletely ignored.Longer range solutions should be considered such as insuringthat only sparkproof refr igerators wil l be purchased in th efuture, and that when maintenance or repairs are done on anyof the refr igerators , they be al tered and made sparkproof.

2 Example No. 6: The hazard of the blind corner in th eshop building hallway. The proposed corrective action is toinstal l a mirror so that persons approaching the blind inter-section can easily see t ra ff ic approaching from the otherdirection. Estimated cost is $85.00.


(a) C, E. and P, as discussed in Exarile No. 6oZ Chaptcr 2 were evaluated a t 1, 10 and 6, respectively.

(b) Cost Factor. Estimated cost is $85.00CF= 1.

(c) Degree of Correction is considered 25 percentto 50 percent . DC = 4.

(2) Using the formula:

1 1 x 6 60 15Jx4 = 4

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NOLTR 71-31

(3) Conclusion. The cost to al leviate the haz-ardous blind intersection by instal l ing a mirror is just i f ied.

(4) Review. It is considered that this correctiveaction will reduce Exposure and Probability to six and threerespectively, -making the Risk Score 18. For this now re la-t ively low priori ty hazard, providing a warning sign and/ormarking of t ra ff ic lanes could be considered, for added safety.

RECOITIERDED PROCEDURE FOR USING THE J' FOR1MUlA. Aconvenient J Formula Worksheet (Appendix A) and a RatingSurmiarv Sheet (Appendix B) are furnished for conveniencein undertaking a hazard analysis to determine the Just i f icat ionRating. Once a hazard has been recognized, the followingprocedure is reconemended:

a. State the problem brief ly.

b. Decide on the most l ikely consequences of an accidentdue to the hazard.

c. Review al l factors carefully, on the scene. Listth:e actual step-by-step sequence of events that is -most l ikelyto resul t in t he consequences chosen. You must be specif ic .

d. Decide on the most appropriate corrective actionand obtain or make a rough estimate of i ts cost.

e. Consider carefully the effect of the proposed cor-rective action on the hazard, and estimate roughly the degreeto which the dangerous si tuat ion wil l be alleviated.

f. If alternative corrective measures are possible.repeat steps (d) and (e) for them.

g. Select the hazard-event (the first undesirableoccurrence that could s tar t the accident sequence.

h. Consider the e:.:isting si tuat ion carefully to determninet-he frequency of the occurrence of the hazard-event, by on th escene observation and then decide on the Exposure Rating. If

in doubt betwen two ratings, interpolate.i. For the Probability Rating, consider the l ikelihood

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NOLTR 71-31

of the occurrence of each event of the accident sequence,including the resulting injury and/or damage, and form anopinion based on the descriptive words. For example, iftwo unusual coincidences are required, th i s could beconsidered remotely possible ; two 'remotely possibleoccurrences could be conceivably possible ; etc. If indoubt between two ratings, interpolate. Endeavor to beconsistent. Consider the occurrence of only the sameconsequences which were decided on in step (b) above. Forexample if you decided on consequences of a fatal i ty, thenin th i s step you may only consider the probabi l i ty of afatal i ty. If you also wish to consider lesser injur ies ,a separate and additional conputation must be made, sinceboth

the Consequences and Probability evaluations would bedifferent . Scores should be added.

j. You have now obtained ratings for al l the elementsof the J formula. Substitute in the formula and computethe Just i f icat ion Score.

k. If al ternat ive corrective measures are being con-sidered to al leviate the hazard, compute their Just i f icat ionScores also.

1. If there are al ternat ive corrective measures whichhave acceptable Just i f icat ion Scores, the most desirable

from the Safety standpoint is the one which would make th egreatest reduction in the Risk Score. Therefore, for eachal ternat ive, assume that the corrective measures are ineffect and recompute the Risk Score. Of course this select ionmay also be affected by external (nonsafety) considerationssuch as the size of investment required, the relat ive effectson morale, esthet ics , efficiency, convenience, ease ofimplementation, etc.

EXCEPTION TO RELIANCE ON THE J FORM•LA. A highlyhazardous si tuat ion may exist for which no corrective actionwhich wil l give an acceptable Just i f icat ion Score can bedevised. Obviously in such a case, whatever corrective

action is necessary to reduce the Risk Score should be takenregardless of the Just i f icat ion Score.

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NOZaTR 71-31

Appendix A

J FORMULA WORKSHEETPROBLEM:

Sequence of events or factors necessary for accident:

1.

2.

3.

4.

5.

6.

7.

Formula Factors: Rating

C Consequence:

E Exposure:

P Probability:

CF Cos t F a c t o r :

DC Degree o f C o r r e c t i o n :

J Jus t i f i ca t ion : J = C x E x P x x

CF xDC xThe estimated cost of corrective action i s / i s not just i f ied.

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LOLTR 71-31

Appendix B

RATING SUMM RY SHEET FOR J FORMULA

Factor ~Classification Rtn

.. Consequences. a. Catastrophe, numerous fa ta l i t ies ; damage over$1,000,000; major disruption of act ivi t ies . . . 100

b. Multiple fa ta l i t ies ; damage $500,000 toMost probable $1,000,000 ................................... 50result of the c. Fatality, damage $100,000 to $500,000 ........ 25potential d. Extremely serious injury (amputation, permanentaccident. disability); damage $1000 to $100,000 ........ 15

e. Disabling injury; damage up to $1000 ......... 5f. Minor cuts, bruises, bumps; minor damage ..... 1

2. Exposure. Hazard-event occurs:a. Continuously, (or many times daily) .......... 10b. Frequently (approximately once daily) ........ 6

The frequency c. Occasionally (from one per week to once perof occurrence month) ....................................... 3of the hazard d. Unusually (from once per month to once perevent. year) ........................................ 2

e. Rarely (it has been known to occur) .......... 1f. Remotely possible (not known to have occurred) 0.5

3. Probability. Complete accident sequence:a. Is the most l ikely and expected resul t if th e

hazard-event takes place ..................... 10

Likelihood that b. Is quite possible, not unusual, has an evenaccident sequence 50/50 chance ................................. 6

will follow to c. Would be an unusual sequence or coincidence.. 3

completion. d. Would be a remotely possible coincidence ..... 1e. Has never happened after many years of exposure,but is conceivably possible .................. 0.5

f. Practically impossible sequence (has neverhappened) .................................... 0.1

4. Cost Factor a. Over $50,000 ................................ 10b. $25,000 to $50,000 .......................... 6

Estimated dollar c. $10,000 to $25,000 .......................... 4cost of proposed d. $1,000 to $10,000 ........................... 3corrective e. $100 to $1,000 .............................. 2action. f. $25.00 to $100 .............................. 1

g. Under $25.00.................................0.5

5. Decree ofCorrection. a. Hazard positively eliminated, 100 ......... 1

b. Hazard reduced a t least 75% ................ 2Degree to which c. Hazard reduced by 50 to 75% ............... 3hazard will be d. Hazard reduced by 25% to 50 ............... 4reduced. e. Slight effect on hazard (less than 25%) ..... 6

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UNCLASS IFIEDSecuritv Classification

DOCUMENT CONTROL DATA - R & D Securi ty c l a s s i f i c a t i on of t i t le , body of abstract a n d i n d e x i n g annotat ion must be entered when tite overall report s cl ssi i ted

1. ORIGINATING A C T I V I T Y C o r p o r a t e author 2&.2.R E P O RT S E C U R I T Y C L A S S I F I C AT I O N

Naval Ordnance Laboratory |UNCLASSIFIEDWhite Oak, Silver Spring, Maryland 20910 • b ROUP

3. R E P O RT T I T L E

MATHEMATICAL EVALUATIONS FOR CONTROLLING HAZARDS

4. D E S C R I P T I V E N O T E S Ty p e of repet as td inclusive dates

S AUTHOR(SI F i r s t name, middle i n i t i a l , last n a m e )

William T. Fine

6 R E P O R T D T E 7a T O TA L NO. OF PA G E S 17b. NO. OF R E F S

8 March 1971 45 0as. C O N T R A C T OR G R A N T NO. as O R I G I N ATO R ' S R E P O RT NUMBERIS)

b. PROJECT NO. NOLTR 71-31

C Sb. O T H E R R E P O RT NO S) A n y other nulnbers that m a y b e aassgnedthie report

d.

10. D I S T R I B U T I O N S TAT E M E N T

This document has been approved for public realease and sale,its dis t r ibut ion is unlimited.

It S U P P L E M E N TA R Y N O T E S 12 S P O N S O R I N G M I L I TA RY A C T I V I T Y

13. A B S T R A C T

To fac i l i t a t e expedit ious control of hazards fo raccident prevention purposes, two grea t needs have beenrecognized. These are for t1 a method to determine th ere la t ive seriousness of all hazards for guidance in assign-ing pr io r i t i e s for preventive effor t ; and (2) a method togive a def in i te determination as to whether the est imatedcost of the contemplated corrective action to eliminate ahazard is jus t i f ied .

To supply these needs, a formula has been devised which weighsthe cont ro l l ing factors and ca lcu la tes the r i sk of a hazardouss i tua t ion , giving a numerical evaluation to the urgency fo rremedial at tent ion to the hazard. Calculated Risk Scores arethen used to es tabl i sh pr io r i t i e s for corrective effor t . Anaddit ional formula weighs the estimated cos t and effectivenessof any contemplated corrective action against the Risk Scoreand gives a determination as to whether the cos t is j u s t i f i ed .

DD '° V.a1473 (PAGE I) U1CIASSIFIEDS/N 0101.807 .6801 Security Classification


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UNCLASSIFIEDSecurity Classification

K L N K A L I N K S L I N K CKKRYWOROI

r O L L WIT R O L E WT R O L E WT

J Formula

Risk Score Formula

Accident sequence

Calculated risk

Hazard-event

Consequences

Exposure

Probabi l i ty

Cost Factor

Degree of Correction

Jus t i f i ca t ion

Risk Score

DD. 2 ..1473 BACK) UNCLASSIFIEDPAGE 2) Security Classification

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