note3 - measures(1)

7/28/2019 Note3 - Measures(1)

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Fundamental Safety Engineering and Risk Management Concepts, 2012/2013by N. C. Renton, and M. J. Baker and H. Tan

SAFETY AND RISK MEASURES

1. Introduction

In the last lecture, a simple definition of the word risk was presented:

fRisk = [ ]P E C (1)

While the above definition has achieved widespread acceptance, there are also a number of current risk

measures that, while they dont fit the above definition, still give an indication of the size of the risk

associated with a particular hazard. One of the features of the measures considered is their ability toallow comparisons between installations, companies, job-functions, and industries.

The most common measures can be split into two broad types:

Individual risk measures. Societal risk measures.

Both will be discussed in the course of this lecture.

2. The Fatal Accident Rate (FAR)

The fatal accident rate (FAR) is a measure of the risk present from hazards that have experienced actual

failure events that resulted in at least one fatality. The FAR is usually quoted as the number of fatalitiesthat occur in a defined group of people per 108 hours of exposure to the activity (108 hours of exposure

corresponds to roughly the total number of hours worked by 1000 people during their working lives).

Some definitions are required to calculate a numerical value of the FAR. Define the population of

workers in yeari as wi, and the number of fatalities in yeari across population wi asN(wi). If there areroughly 240 working days per annum and a shift lasts 8hrs per day, then the FAR can be quoted as

follows:

8

1

1

10FAR =

240 8

m

im

i

i

i

N w

w

,

(2)

where m is the total number of years for statistics. The form of the above equation means it is possible

to compare the FAR for individual years, or sum the results from a number of years to gain the FAR fora longer time period - both approaches are valid.


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Example: A company employs 610 individuals in year 1, 500 in year 2, and 690 in year 3. Over the

course of the three year period, the company experienced 2 fatalities. What is the FAR for the threeyear period?

Solution: The FAR can be calculated from Equation (2) as:

8

8

10 2FAR

240 8 610 500 690

57.87 fatalities per 110 exposure hours

(3)

Calculating the fatal accident rate requires data on historical events. This makes the measure subject to

statistical uncertainty for two reasons:

inhomogeneity of the data - e.g. collected across groups exposed to different tasks. Limited sample set - the event happens so infrequently there are only a few recorded instances.

Care should therefore be taken in creating an estimate of the fatal accident rate or in using other

published values.

It is also worth noting that the FAR does not reflect the risk associated with hazards that have not been

released by a failure event, and so only gives a partial insight into the risk present. In particular, it is apoor measure of major accident hazards and other infrequent events.

3. Serious Injury Rate (SIR)

The serious injury rate (SIR) is a measure of the risk present from hazards that have experienced actual

failure events and the undesired human consequences in the form of serious injuries. The SIR is alsoquoted as a function of 110

8exposure hours, and is calculated in a very similar manner to the FAR:

8

1

1

10SIR =

240 8

m

im

i

i

i

S w

w

(4)

where m is the total number of years for statistics, S(wi) is the number of serious injuries in yeariacross the population wi. Again, the SIR does not reflect the risk associated with hazards that have not

been released by a failure event giving, like the FAR, only a partial insight into the level of risk present.

4. Individual Risk (IR)

The Individual Risk is the probability of death in a calendar year for an individual member of aspecified group. Like both FAR and SIR, the measure can be calculated for periods of time, or on a per

annum basis:


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1

1

1IR =

m

im

i

i

i

N w

w

,

(5)

where m is the total number of years for statistics,N(wi) is the number of deaths in yeari across thepopulation wi.

Example: A service company employs 2000 individuals in year 2004; 1850 in 2005; and, 2110 in

2006. During that period the company experiences 1 fatality in 2004, none in 2005, and 1 in 2006.

Calculate the IR for the period.

Solution: Using Equation (5), the IR for the period 2004-06 is (1+0+1)/(2000+1850+2110)=0.000336

5. Annual Fatality Rate (AFR)

The AFR is often defined as the best estimate (expected value) of the predicted number of fatalities per

year for the plant, or activity. Note that this expected number is not required to be an integer, and can

be considerably less than unity. It is a simpler measure than the FAR, as it does not reflect the numberof people exposed per annum:

1

1AFR =

m

i

i

N wm

(6)

where m is the total number of years for statistics.

Example: A company experiences 1 fatality in 2004, no fatalities in 2005, 2006 or 2007. The AFR is

(1+0+0+0)/4 = 0.25 fatalities per annum.

6. Potential Loss of Life (PLL)

The potential loss of life is gained from the AFR and a time period of interest. It is the expectednumber of fatalities within an operational time period of interest, To, in the future:

PLL =AFRo

T (7)

7. Societal Risk and F -N Curves

It is well understood that some accidents can be more severe than others. The Buncefield explosion in

2005 was many times the magnitude of the explosion at Flixborough in 1974; however there were no

fatalities in the first event and the second killed 28 people and injured 36. The distribution of fatalities


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per accident in a particular industry or activity is of interest and gives an insight into the societal risk.

The term Societal Risk is used in a number of different ways, but here it will be used to describe thefrequencies of multiple-fatality accidents. One way of representing the frequency of N-or-morefatalities is through the use of anF-Ncurve [1, 2].

Two concepts are involved in anF-Ncurve. The F is the annual frequency with which a particular

type of fatal event occurs. The N is the number of fatalities caused by a particular failure event. TheF-N curve plots annual event frequency againstNor more fatalities in the event. An exampleillustrates the ideas.

Example: The following data set of fatal accident events across a national industry is available for thetime period 2004-2007:

2004: 4 events with 1, 1, 3, 2 fatalities respectively ( 1 in the first event, 1 in the second event, 3in the third event, and 2 in the fourth event).

2005: 3 events with 6, 2, 1 fatalities. 2006: 5 events with 1, 1, 1, 2, 1 fatalities. 2007: 2 events with 1, 1 fatalities.

Looking at 2004, it is possible to calculate the number of events with N-or-more fatalities as; 4 eventswith 1 or more fatalities; 2 events with 2 or more fatalities; 1 event with 3 or more fatalities. This

calculation is repeated for all years.

The annual frequency for each type of event is then calculated by averaging the number of events with

N-or-more fatalities across the number of years in the data set. Taking 1-or-more as an example: in

2004 there are 4 events with 1 or more; 3 in 2005; 5 in 2006; 2 in 2007; hence (4+3+5+2)/4 = 3.5.Hence; for 1 or more fatalitiesF= 3.5. The full results for the example are shown in Table (1). The

final step is to plotFagainstNor more fatalities to give theF-Ncurve, shown in Figure 1.

Year Type of fatal event

1 or more 2 or more 3 or more 4 or more 5 or more 6 or more 7 or more

2004

2005

20062007

4

3

52

2

2

10

1

1

00

0

1

00

0

1

00

0

1

00

0

0

00

Average

rate 3.5 1.25 0.5 0.25 0.25 0.25 0

Table 1: Calculation of ExampleF-NData


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Figure 1, ExampleF-NCurve

F-Ncurves are a much broader measure than those looked at in the lecture so far. Plotting anF-Ncurve

requires a large data set of failure events that have resulted in a fatality or fatalities. They are used toindicate the effect of a particular hazard on society, and give an insight into the performance of the

control measures used.

Similar curves to the one shown in Fig.(1) have been developed for whole industries and activities,

examples are contained in Evans[5] (See Figure 1, page 10 of [5] as an example of cross industry

comparisson and Figure 2 on page 18 of [5] as an example of use in within industry comparison). On apractical note, it is typical for the data to be plotted on double logarithmic scale due to the large data

sets involved.

The curves are a useful way of comparing industries, however, they have also been used in the past to

judge whether or not risk is being reduced to a level that is as low reasonably practicable (This is the

legal requirement in the U.K. as stipulated in the Health and Safety at Work Act 1974.) through the useof so-called criterion lines (For example, see Figure D1, page 58 of [6]). This use ofF-Ncurves has

been challenged by some authors [3, 4] as it does not conform with decision theory, which has

demonstrated that it is the expectation (or average) fatalities per accident that should be used to

determine the optimum investment in control measures [7].

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6 7

AccidentsperyearwithN-or-MoreFatalities

(yr-

1)

Number of Fatalities,N


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