Department of Safety Engineering, Seoul National University of Technology, 172 Gongleung-Dong, Nowon-Gu, Seoul, 139-703 Korea

1. Introduction

Safety management expenditure has been invested very differently in different fields of business despite the fact that in Korea there of Government guidance to suggest how to determine “Standard Safety Management Cost” for different classes of construction work [1]. While these classes are useful for planning more safety control measures, it is considered by the government that for giving greater flexibility, and having contractors self safety management conditions, different degrees of safety management expenditure might be available. For example it is considered by the Government that concentrated safety investment should be given in the following critical work areas; (ⅰ)foundations; (ⅱ) grading and backfilling; (ⅲ) reinforced concrete construction; (ⅳ) steel construction; and (ⅴ) water proofing. The expenditure on safety management for each of these areas might depend on the work process rate and other factors depending on the likelihood of accident occurrence.

In order to determine the most appropriate level of safety management investment a new practically oriented method of estimating direct costs, general insurance costs and compensation, and various indirect costs such as due to work stoppages, time taken to reach compromises, legal costs, cleaning of debris after an accident, and the costs associated with demoralization of the work force should be considered. An area of particular difficulty is the estimation of the indirect costs associate with the particular structural accident. Unfortunately it is difficult to determine these costs as usually no records are kept.

The level of safety management investment for each type of work must be subject to review and clarification to ascertain its cost effectiveness. Accordingly, it is appropriate that a detailed model be established for the optimum level of safety management investment. Such a model is possibly best set within the overall financial objectives of a particular enterprise. It need not relate, necessarily, to underlying engineering notions of structural safety. The present study focuses on the experiences of the SI Construction Company over a period of three years [2].

From the analysis of the data available, it is possible to deduce a criterion for the optimal expenditure on safety management. The whole treatment takes account of events and accidents only during construction. The results are compared with other empirical and numerical values.

2. Model for estimating safety control costs

2.1 Theory of safety control costs

Fig. 1 depicts a well-known relation between safety performance and total costs [3]. The higher the design, implementation and construction safety levels to be achieved, the lower will be the overall expected costs, because of the smaller probability of accident. However, to achieve these higher levels of safety will require extra costs, costs which normally have to be borne by the contractor. Hence, it pays the contractor to ascertain the minimal overall expected total costs [4].

Some limits can be set to the curves in Fig. 1. Thus, it is clear that under a perfect state of safety, there will be no accidents and hence no costs associated with them. Conversely, to achieve a perfect state of safety implies that the costs are infinite. An achievable state of safety will lie somewhere between these two extremes (5). By adding the expected accident or damage costs and countermeasure control costs, the total expected costs curve for the structure could be obtained.

Fig. 1 Cost of safety

Evidently this curve has a minimum point T(n) for the total cost where the derivative of the total expected cost is zero. The total expected cost can be divided into two categories: (ⅰ) direct; and (ⅱ) indirect. The direct costs will include property damage, costs of injury and the costs involved in taking care of the dead.

The indirect costs are more difficult to determine. They relate primarily to loss of individual productivity, the loss of system productivity, and the unpredictable costs of insurance and litigation. It is often the case in practice that the indirect costs exceed the direct costs.

 Direct countermeasure costs will include design changes principally for safety, provision of safety personnel, installation and management of safety systems, safety education, and training programs. The indirect countermeasure costs also may be restrictions on system operation.

2.2 Modeling for reasonable safety control cost

The minimum total expected costs of damage and accident prevention will be considered the criterion for setting optimal safety levels.

Fig. 2 depicts the annual total expected cost T(n). This is the total costs in year n as a function of year n:

T(n) = H(n) + G(n)                 (1)

Where H(n), is the annual cost of accidents, and G(n) is the annual countermeasure (or control) cost. R* depicts the minimum cost point.

Fig. 2 Total expected cost curve

G(n) in Fig. 2 can be represented as a function of the total contract amount and the investment cost as follows:

G(n) = P(n)[1 + R(n)]                        (2)

Where G(n) is the countermeasure costs invested for industrial accident prevention in year n, R(n) the (countermeasure costs/total contract amount) of S construction company in year n, P(n) the total contract amount of S construction of R(n). Also let P(n) be taken as a constant amount in each year n.

The function H(n) can be obtained from statistical data for the accident rate, the direct costs of damage and loss per worker, and the number of workers per accident, as follows:

H(n) = DC + IC                               (3)

Where DC is the expected direct cost, IC the expected indirect cost. The direct cost can be given as:

DC = N(a) ´ dc                               (4)

Where N(a) is the total number of workers involved in accidents in year n, dc the direct cost of damage and loss pre worker and a the accident rate.

The total number of workers involved in accidents can be represented as a function of the accident rate as follows;

N(a) = a ´ regular time workers              (5)

Where a = (the number of  “accident” workers/number of workers) ´ 100 and where the number of regular time workers can be obtained from the total costs of the project, being the proportion of labor for the project divided by the unit labor wage rates and the number of working days.

Since the accident rate decreases as the investment rate increases it is possible to develop a correlation between them. This can be done by regressing the accident rate a on the investment rate R as follows:

a = f(R)                                           (6)

For simplicity the indirect costs can be assumed to be b ´ the direct costs of damage and loss. This allows the maximum loss cost H(n) to be represented as:

H(n) = (1 + b) ´{N(a) ´ dc}                       (7)

It has been suggested that the indirect losses might be up to four times the direct costs(6) but in practice it seems extremely difficult to estimate this ratio.

Once the above expressions have been obtained it is possible to select R* as the reasonable investment and safety control rate.

Table 1. Collection of direct of loss(1 US$ = ￦800 won, unit ￦ 1000won)


 

3. Case study for analyzing effect of safety management

3.1 Direct and indirect costs of damage and loss

 In order to illustrate the above concept a pilot study was conducted for the SI Construction Company. Three years of statistical data were used. For these years the direct costs of loss and damage for the company amounted to total 717,560,720(US$896,950). The indirect costs amounted to
,097,314,000 won (US$ 11,371,642). Thus, the ratio of direct to indirect costs is 1:1.5.

The statistical data for the Company indicated that the direct costs constitute mainly the industrial accident insurance costs. In addition, it is clear that the indirect costs are considerably less than has been suggested in the literature.

It is likely that the difference may depend on the Company operating practices, including their safety management processes, but also on costs related to death and injury applicable to a particular country (Tables 1 and 2).

3.2 Reasonability review of current safety control cost

The data for the SI Construction Company shows that for the eleven years between 1985 and 1995 the accident rate has decreased steadily and was inversely proportional to the amount invested in safety control (see Fig. 3 and Table 3) (7). It should be noted that the 1988 Government decreed “Safety Control Cost Recommendations” (1) were easily met in most subsequent years. It is also clear that there is an apparent limit to the reduction in accident rates that can be achieved.

Table 2. Collection of indirect cost of loss(1 US$ = ￦800 won, unit ￦ 1000won)


 

3.3 Comparison with national figures

The above results may be used with to estimate the effect of safety management for the particular case of the SI construction company, used here as a bench mark.

The following were used in the analysis:

● Total Contract Amount – this is the domestic Government contract amount for all construction, increased by 5% per annum to allow for inflation during the year.

● Number of Accident Workers – obtained from data collected by the Korean Department of Labor[1].

These include deaths.

● Direct Cost of Loss – as for the SI Construction Company, the direct costs were taken as the industrial accident insurance costs for each year increased by 5% per annum to allow for inflation during the year.

Fig. 3 Interrelation curve concerning Table 3

● Indirect costs – based on data obtained for the SI Construction Company, this was taken as 50% greater than the direct costs (see above).

● Amount of Loss Per Accident Worker – this was taken as the total amount of loss divided by the number of accident workers. The definition of “Accident workers” is given above.

● Number of Accident Workers – this was estimated as the target contract amount divided by the contract amount per accident worker.

● Estimated Loss – this was estimated from a number of accident workers multiplied by the loss amount per accident worker.

● Loss Prevention Efficiency Rate(%) – this was taken as the total loss amount divided by the total contract amount multiplied by 100.

Table 3. Interrelationship between safety control costs and accidents, 1985-1995

Fig. 4 Target accident rate

Fig. 4 shows the analysis and calculation procedure. Table 4 gives the historical calculations for 1993 – 1995 and the predicted results for 1996.

 It is seen that the predicted loss prevention efficiency rate is 1.72% on the total contract amount (or project cost) for 1996. This gives an indication of the savings predicted to be made due to losses associated with accidents.

Table 4. Yearly safety control effect and estimated effect for 1996(1 US$ = ￦800 won, unit: (hundred million ￦) (5%rising rate in prices and 5% wages increasing rate are applied for estimating the effect for the coming year, Item Ⅰ:Government statistics, Item Ⅱ: estimated, Item Ⅲ: accidents occurred actually, Item Ⅳ: effect obtained, Ⅳ = Ⅱ

Kind	Damage preventive effect from safety control (%)	Deduction rate of insurance (%)	Total rate (%)
Project cost Profit	1.73 17.3	0.32 3.20	2.05 20.5

Kind	Damage preventive effect from safety control (%)	Deduction rate of insurance (%)	Total rate (%)
Project cost Profit	1.73 17.3	0.32 3.20	2.05 20.5

Table 6 Effect in 1996 of no accidents rate of 0.2%

Kind	Damage preventive effect from safety control (%)	Deduction rate of insurance (%)	Total rate (%)
Project cost Profit	1.54 15.4	0.24 2.40	1.78 17.8

Table 7 Statistical analysis (regression analysis-exponential model: Y = exp (a+bX))

Dependent variable: a-ratio				Independent variable: R
Parameter	Estimate	Standard error		T value	Prob. level
Intercept Slope Analysis of variance Source	Sum of squares	Df	Mean square	8.05045 -6.60614 F-Ratio	.00002 .00010 Prob. Level
Model Error Total(Corr.)	6.840041 1.4106079 8.2506488	1 9 10	6.840041 .1567342	43.64102	.00010

Correlation coefficient = -0.910511

Stnd. Error of est. = 0.395897

R-squared = 82.90 percent

Table 8 ’93 year calculated result (1 US$ = 800 won, unit: a hundred millions won)

Investment rate	Accident rate	Direct cost	Indirect cost	Cost of damage	Cost of control	Total cost	Cost difference
0.0050 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110 0.0120 0.0130 0.0140 0.0150 0.0160 0.0170 0.0180 0.0190 0.0200	0.02564 0.02171 0.01839 0.01557 0.01319 0.01117 0.00946 0.00801 0.00679 0.00575 0.00487 0.00412 0.00349 0.00296 0.00251 0.00212	9.6681 8.1884 6.9351 5.8737 4.9747 4.2133 3.5684 3.0223 2.5597 2.1679 1.8361 1.5551 1.3171 1.1155 0.9448 0.8002	14.5022 12.2826 10.4027 8.8105 7.4620 6.3199 5.3526 4.5334 3.8395 3.2519 2.7542 2.3326 1.9756 1.6732 1.4171 1.2002	24.1703 20.4709 17.3378 14.6841 12.4367 10.5332 8.9210 7.5556 6.3992 5.4198 4.5903 3.8877 3.2927 2.7887 2.3619 2.004	6.4650 7.7580 9.0510 10.3440 11.6370 12.9300 14.2230 15.5160 16.8090 18.1020 19.3950 20.6880 21.9810 23.2740 24.5670 25.8600	30.6353 28.2289 26.3888 25.0281 24.0737 23.4632 23.1440 23.0716 23.2082 23.5218 23.9853 24.5757 25.2737 26.0627 26.9289 27.8604	2.4064 1.8402 1.3606 0.9545 0.6105 0.3192 0.0724 -0.1366 -0.3136 -0.4635 -0.5904 -0.6980 -7890 -0.8662 -0.9315

Table 9 ’94 year calculated (1 US$ = 800 won, unit: a hundred millions won)

Investment rate	Accident rate	Direct cost	Indirect cost	Cost of damage	Cost of control	Total cost	Cost difference
0.0050 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110 0.0120 0.0130 0.0140 0.0150 0.0160 0.0170 0.0180 0.0190 0.0200	0.02577 0.02183 0.01848 0.01566 0.01326 0.01123 0.00951 0.00806 0.00682 0.00578 0.00489 0.00414 0.00351 0.00297 0.00252 0.00213	10.0599 8.5202 7.2161 6.1117 5.1762 4.3840 3.7130 3.1447 2.6634 2.2558 1.9105 1.6181 1.3704 1.1607 0.9830 0.8326	15.0898 12.7802 10.8242 9.1675 7.7644 6.5760 5.5695 4.7171 3.9951 3.3836 2.8657 2.4271 2.0556 1.7410 1.4746 1.2489	25.1497 21.3004 18.0403 15.2791 12.9406 10.9600 9.2825 7.8618 6.6585 5.6394 4.7762 4.0452 3.4261 2.9017 2.4576 2.0814	6.2200 7.4640 8.7080 9.9520 11.1960 12.4400 13.6840 14.9280 16.1720 17.4160 18.6600 19.9040 21.1480 22.3920 23.6360 24.8800	31.3697 28.7644 26.7483 25.2311 24.1366 23.4000 22.9665 22.7898 22.8305 23.0554 23.4362 23.9492 24.5741 25.2937 26.0936 26.9614	- 2.6053 2.0161 1.5171 1.0945 0.7366 0.4335 0.1767 -0.0407 -0.2249 -0.3809 -0.5130 -0.6249 -0.7196 -0.7999 -0.8679

Table 9 ’95 year calculated (1 US$ = 800 won, unit: a hundred millions won)

Investment rate	Accident rate	Direct cost	Indirect cost	Cost of damage	Cost of control	Total cost	Cost difference
0.0050 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110 0.0120 0.0130 0.0140 0.0150 0.0160 0.0170 0.0180 0.0190 0.0200	0.02564 0.02171 0.01839 0.01557 0.01319 0.01117 0.00946 0.00801 0.00679 0.00575 0.00487 0.00412 0.00349 0.00296 0.00251 0.00212	18.0776 15.3108 12.9674 10.9827 9.3017 7.8780 6.6723 5.6511 4.7861 4.0536 3.4332 2.9077 2.4627 2.0857 1.7665 1.4961	27.1164 22.9661 19.4511 16.4740 13.9526 11.8171 10.0084 8.4766 7.1792 6.0804 5.1498 4.3616 3.6940 3.1286 2.6498 2.2442	45.1940 38.2769 32.484 27.4566 23.2543 19.6951 16.6807 14.1276 11.9653 10.1340 8.5829 7.2693 6.1567 5.2144 4.4163 3.7404	10.1650 12.1980 14.2310 16.2640 18.2970 20.3300 22.3630 24.3960 26.4290 28.4620 30.4950 32.5280 34.5610 36.5940 38.6270 40.6600	55.3590 50.4749 46.6494 43.7206 41.5513 40.0251 39.0437 38.5236 38.3943 38.5960 39.0779 39.7973 40.7177 41.8084 43.0433 44.4004	- 4.8842 3.8255 2.9288 2.1694 1.5262 0.9814 0.5201 0.1293 -0.2017 -0.4819 -0.7193 -0.9204 -1.0907 -1.2349 -1.3571

3.4 Insurance rate analysis

 A further effect of improving safety is the lowering of insurance premiums. This will now be analyzed for the situation pertaining in Korea. The Korean government has classified construction work into five (5) types of work(1). Of these, category A: General Construction will be considered. Three years of records were used for analysis of actual amounts of insurance premiums paid by companies. By government decree, premiums are discounted for a food record in industrial accident prevention. The maximum discount is 40% but typically, it is much less. The cost of labor as a proportion of total project cost is set by government (for insurance purposes). For the present analysis this is taken as 29%. Finally, the basic insurance rate as a proportion of the project labor cost is set by government from time to time. For the present it will be taken as 2.8%.

It follows that the maximum insurance cost exemption for a company receiving 40% discount is = labor cost rate ´ insurance rate ´ (maximum) discount rate = 29% ´ 2.8% ´ 40% = 0.32% of the total contract cost. This is the amount awarded as the maximum ‘bonus’ for a good safety record. For the case of the SI Construction Co. it is estimated that the maximum discount for 1966 for the whole year will be 30%, so that it follows directly that the maximum discount will be 0.24% of the total project cost.

 Thus the effect of the SI Construction company having a good record in industrial safety for the year 1995 has two effects: a saving in direct and indirect costs and a saving in insurance costs the following year. These effects are summarized in Table 5, assuming, as is typical for Korean construction companies, that the profit margin is around 10%.

 It is clear that the savings in this ideal case are potentially very considerable. This is increasingly being recognized but typically, they are not being achieved. One of the reasons for this is that the factors, which can bring about a lower accident rate are not sufficiently well understood. It is also one reason why increased safety management activities are becoming less effective. Since the effects sketched above are unlikely to be achieved in practice, consider now what would happen if the trend in Fig. 3 is continued into 1996. This would suggest that the accident rate could be reduced to 0.2%. In this case it may be shown that the expected cost reduction effect is equivalent to US$ 3.115 billon ´ 1.78% = US$ 5.54 million. Typically, for the SI Construction Company and its subcontractors, this will amount to US$ 0.8 Million and US$ 4.7 million, respectively. The estimated effects for the company for 1996 are summarized in Table 6. Although the savings are not as great as the previous (ideal) example with zero accident rate in 1995, the savings are still very considerable both for the main contractor and the subcontractors.

Table 11 Synthesis result (1 US$ = 800 won, unit: a hundred millions won)

The above has demonstrated the very considerable potential benefits resulting from reduction in accident rate. The question remains as to what might be and optimal safety control cost (or investment) R(n) (see Fig. 2).

Relationship (6) between accident rate (a) and annual safety investment R can be developed by assuming that it has the form a = exp(a +Br). Using the data in Table 3 for the SI Construction Company this curve can be fitted reasonably closely (R-squared = 82.90) with results shown in Table 7.

 Now using the direct and indirect costs shown in Tables 1 and 2, respectively, for the years 1993-1995 the effect of increasing annual investment in safety control (‘investment rate’) on total cost is shown in Tables 8-10. It is clear that in each case the optimal investment rate R* is around 1.2-1.3%. Table 11 shows the results and the relevant costs.

This theoretical result based on aggregate data is not inconsistent with the observations which can be made for the experience of the SI Construction Company as a hypothetical example. For example, Table 3 shows that the safety investment for 1991 and 1992 was around 0.9% for an accident rate of 1.4%. But the accident rate comes down to an average of 0.66% for the following 3 years when the investment rate is kept at around 1.3%. However, the data does suggest that the safety record does not depend only on financial investment, as indicated by the considerable variations in accident rates with little change in safety investment. Clearly, these matters require further study.

 The above suggests that an optimal level of safety investment is around 1.2-1.3% of the total project cost. This is supported to some extent by actual operational experience.

5. Discussion and conclusion

Using empirical data and modeling together with reference to practical observations suggests that an optimal level of safety control investment and hence safety management might be in the range of 1.2-1.3% of the total project cost. This rate is applicable to the construction industry generally and may vary somewhat depending on the work being performed. It is clear that more detailed modeling will be required for individual activities and for particularly difficult or dangerous construction activities.

 It was found that for the type of construction companies considered, when insurance effects are also taken into account, it might be more appropriate for individual companies with good safety records to spend rather more on safety management in order to maintain their record.  It is estimated that this should be around 1.7% of the total contract amount or 17.3% of profits for typical profit margins.

Further research is required to study the effect of work type on the above conclusion, on designing systems for better collection and estimation of direct and particularly indirect costs and on the influence of non-financial aspects of safety management.

References

[1] Ministry of Labor, Ministry of Labor, R.O.K. 1995. Standard criteria for estimating and using construction safety management cost, Ministry Guidance 95-6, Question and Answer Collections. p .142-72

[2] Korea Construction Association. Contract ability class of architectural and civil, a statistic status of construction companies, 1999.

[3] Melcher’s RE. Structural reliability analysis and prediction, 2^nd ed. Chi Chester, UK: Wiley, 1999

[4] Stranks JW. Dewis M. The cost of accidents, ROSPA health and safety practice, London; Pitman, 1986, p. 111-6

[5] Garibaldi JV. The significance of risk acceptability. In Safety Management, 4^th ed. Homewood,IL; Richard Irwin, 1984, p. 218-45.

[6] Roland HE, Moriarty B. System safety engineering and management, New York: Wiley, 1990. p. 319

[7] Korea Industrial Safety Press Co. Ltd. Status of accident occurrence and insurance compensation amount, analysis result for whole industry accident and loss, 165-59-75, 1993.