Kristiansen Svein. Maritime Transportation: Safety Management and Risk Analysis

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The first step is to order the observation by increasing loss magnitude given by the

fatality number. As we only have single observations for each year, the probability

distribution is approximated by ordering the observations with the same value f(x) ¼0.11.

This figure is obtained by dividing 1 by (N þ1) ¼9 where N is the number of observations.

In this case also it was decided to apply the log-normal distribution, and the model was

fitted to the data with Excel’s Solver as described in an earlier section (see Table 4.9).

The result is plotted in Figure 4.12. It can be seen that the model estimates the fatality

number pretty well with the exception of the largest one. It is clear that even this model

underestimates the probability of this event. This is, however, not unexpected bearing in

mind that the available data cover a fairly short period.

The fact that the Alexander L. Kielland number (123 fatalities) lies below the model

curve may give same weight to the suspicion that the safety control deteriorated somewhat

during the 1970s.

116 CH APTER 4 STATISTICAL RISK MO N IT O RI N G

REFERENCES AND SUGGESTED READI NGS

Beyer, W. H., 1968, Handbook of Tables for Probability and Statistics. The Chemical Rubber Co.,

Cleveland, Ohio.

Brilon, W., 1973, Konﬁdenzintervalle von Unfallzahlen. Accident Analysis and Prevention, Vol. 5,

321–341. Pergamon Press, Oxford, UK.

Evans, M. et al., 2000, Statistical Distributions. Wiley-Interscience, New York.

Juran, J. M. and Gryna, F. M., 1988, Juran’s Quality Control Handbook, chapter 23: Basic statistical

methods. McGraw-Hill, New York.

Lillestøl, J., 1997, Probability and Statistics [In Norwegian: Sannsynlighetsregning og statistikk Med

anvendelser]. Cappelen Akademisk Forlag, Oslo.

Vose, D., 2000, Risk Analysis: A Quantitative Guide. John Wiley, Chichester.

117

DECISIONS IN OPER ATION

Experience is a good teacher, but can sometimes be very expensive.

(Norwegian proverb)

5.1 IN TRODU CT ION

As a part of the management and operation of the company, certain preventive and

consequence-reducing measures are proposed for implementation. In this chapter we

will outline how such measures or controls can be assessed with due consideration of

uncertainty factors. As already discussed, accident data are subject to different forms

of uncertainty: measurement problems, limited data, external effects, and unknown

mechanisms in processes and accident development.

Many of the examples given are related to occupational safety and manpower training.

5. 2 WORK ACCIDENT MEASUREMENT

5.2.1 Acci den t Frequency Rate

The frequency of work accidents is given in terms of AFR, whi ch is a measure related to a

standardized exposure (S):

AFR ¼

EMP  AH

where:

DI ¼ number of injuries or work accidents per yea r

EMP ¼ number of employees

AH ¼ average annual hours work per employee

¼ 40  50 ¼2000 (hours/year)

S ¼ 200,000 worker-hours/year

This means that the accident frequency is scaled relative to 200,000 worker-hours per

year. It is therefore necessary to include the actual worker-hours which are expressed by

119

the term (EMP AH). The scaling factor is based on a standardized company with the

following operation:

S ¼ 100 employees  40 hours=week  50 weeks=year

¼ 200,000 worker-hours

It should be mentioned that other scaling factors are also used, such as 100,000 and

1 million work-hours. It should also be kept in mind that the term lost time incidence

(LTI) rate is used instead of AFR.

Figure 5.1 shows how the LTI rate dropped in Texaco during an improvement

programme on work safety (Wills et al., 1996). The LTI parameter can also be applied

to measure the effect of specific safety measures. Schlumberger Anadrill (Aitken, 1996)

correlated the accident frequency against the number of risk reports handed in per

employee as shown in Figure 5.2. Better incidence reporting seems to contribu te to

fewer accidents.

Exam p le

A company has reported the following accident figures for two departments:

Department A B

EMP ¼employees 6 30

DI ¼number of injuries/year 40 250

Figure 5.1. Lost time incidence rate (LTI) at Texaco Inc. during a three-year improvement plan: LTI per

100,000 work-hours. ( A dapted f rom Wil ls et al .,1996.)

120 CHAPTER 5 DECISIONS IN OPERATION

The following values for the accident frequency rate can be computed:

AFR

40  2000

200,000 ¼ 15

AFR

250  2000

200,000 ¼ 12

It can be concluded that department B has a lower injury frequency:

ð15  12Þ100=15 ¼ 20% lower

5.2.2 Acci dent Severi ty Rate

The accident severity rate (ASR) measures the consequence of a work injury in terms of

number of lost work-days on the same basis as for the frequency:

ASR ¼

LWD

EMP  AH

where LWD ¼accumulated lost work-days per year for 200,000 worker-hours.

Like the frequency rate, the severity rate may also be used to monitor the development

of the safety conditions in an operatio n. Aitken (1996) compared the number of lost

work-days against the number of days spent on safety training. As shown in Figure 5.3,

the lost work-days went down dramatically during a four-year period when the number of

days spent on training was increased significantly.

Figure 5.2. Lost time incidence rate versus number of risk reports per employee, Schlumberger Anadrill.

(Adapted from Aitken,1996.)

5.2 WORK ACCIDENT MEASUREMENT 121

Exam p le

A company with 25 employees has reported 105 lost work-days for the recent year. The

accident severity rate is:

ASR ¼

105

25  2000

200,000 ¼ 420

5.2.3 Frequency-Severity Indi cator

In risk analysis we are often confronted with the matter of selecting a single measure

in order to rank different alternatives from a safety point of view. For so-called

concept-related risk (the risk of ships), we often use the following measure:

R ¼ p  C

where p is the probability of an accident and C is the expected outcome. An alternative

measure for work-related accidents is the so-called frequency-severity indicator:

FSI ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

AFR  ASR

1000

This criterion has something in common with the one above apart from the square sign.

A rational argument for squaring the expression is the fact that our risk aversion is not

linear with the numerical severity of an accident. An accident taking 20 lives is not

necessarily twice as serious as one leading to 10 fatalities.

Figure 5.3. Lost work-days per employee versus number of days spent on safety training per employee,

Schlumberger Anadrill . (Adapted from Aitken,1996. )

122 CHAPTER 5 DECISIO NS IN OPERATIO N

Exam p le

A shipping manager has analysed the safety performance of the crew members he is

handling for two periods. The result was as follows:

Period 1991–95 1996–2000

AFR 13.5 10.2

ASR 205 220

The question is whether the risk level has gone down or not. The following computations

can be made:

199195: FSI ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

13:5  205

1000

¼ 1:66

19962000: FSI ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

10:2  220

1000

¼ 1:50

In other words, it can be concluded that the worker risk level ha s gone down during the

10-year period.

5. 3 S AFETY COMPETENCE : CORREL ATION ANAL YSIS

An important aspect of any safety programme is to continuously assess attitudes and

competence among the crew or employees. There are different sources that may be used

for such an assessment:

. Examination scores

. Inspection and evaluation of work behaviour

. Questionnaire study

. Assessm ent of personnel by their supervisors

In order to cross-check this kind of information, one may perform correlations on the

data from such studies. Let us take the following situation: a company has invested in

a safety awareness and training programme and has later done an evaluation of the

competence of the workforce. This leaves us with two sets of data:

1. Training program examination score (Score).

2. Safety rating by supervisor (Rating).

The assessment data on the competence for the crew of a vessel are shown in Table 5.1.

Both sets were based on a ranking scale from 1 (low) to 10 (high). It can be seen that

the mean Score is 7.5, which is somewhat higher than the mean Rating value of 7.1.

5.3 SAFETY COMPETENCE: CORRELA TION ANALYSIS 123

The standard deviation for the exam scores (1.8) is slightly smaller than for the ratings

(2.0). One possible interpretation of these observations might be that:

. The exam scores are overest imating the safety competence.

. The rating approach is better at differentiating the competence among the individual

crew members.

The results are also plotted in a scatter diagram as shown in Figure 5.4. Although we

can see a certain relation between score and rating, there is also considerable scatter of

the data.

A more precise measure of the relationship between the two assessment parameters is

the correlation coefficient:

 S

where:

ðX



XÞðY

 YÞ

ðX



XÞ

ðY



YÞ

Ta b l e 5 .1 . Assessment of safety programme

Crew member Rating (X) Score (Y)

145

298

379

498

534

678

788

857

9108

10 6 5

11 8 9

12 8 7

13 6 7

14 9 10

15 8 10

Mean 7.1 7.5

St. dev. 2.0 1.8

124 CHAPTER 5 DECISION S IN O PERATIO N

Numerical computations by means of Excel gives:

¼ 2:00; S

¼ 1:77; S

¼ 2:53

which gives:

¼ 0:717

The fact that the correlation coefficient may take values from 1toþ1 indicates that

we have a fairly good relationship between exam scores and supervisor ratings. The safety

management might therefore de cide to use the examination method only, as this is more

efficient and time-saving. However, some effort should be directed towards improvement

of the examination programme in order to improve the differentiation between the

candidates.

5.4 TESTING OF A DISTRIBUTIO N MODEL

The previous chapter spent considerable effort on the estimation of distribution models for

empirical safet y data. Here we shall look a little closer at how to test whether a potential

model is appropriate for the data set at hand.

Let us look at following case given by ReVelle and Stephenson (1995). A company

has kept records on the number of lost-time accidents (LTA) per week for a period of

Figur e 5.4. Scatter diagram: score versus rating.

5.4 TESTING O F A DISTRIBUTION MODEL 125