Using the Bell Formula to Help Determine Costs or Savings

It is never permissible to let the results of a cost-benefit analysis dictate whether a health or safety precaution is worth implementing, because one cannot place a value on human life.  It may be appropriate, nonetheless, to consider the costs and benefits of implementing a comprehensive safety and health program.  An employer who is interested in gauging whether the start-up and maintenance costs of such a program would result in long-term savings may wish to apply the methodology that follows.

In his article, "Gauging Safety Outlays and Objectives," in Occupational Hazards, June 1987, David R. Bell describes a method you can use to determine the costs to your worksite when injuries occur, and the costs that are saved when injuries are prevented.  You can compare your worksite's experience to your industry's average for lost workday case rates.  To do this, you use information published annually by the Bureau of Labor Statistics (BLS), other information easily available at your worksite, and Bell's formula for the calculation of "lost workday cases avoided."

To begin, find the latest published lost workday case rate for your industry by checking the BLS Occupational Incidence Rates tables. (The BLS statistics are published annually -- usually 1.5 years after the year for which they were collected).  Locate the table entitled "Reported occupational injury rates by industry."  Make sure that you do not use the table that includes illnesses; the Bell formula doesn't include illnesses.  When you have found the correct table, look for the NAIC (North American Industry Classification Systeme) that best describes your industry.  From the table’s column headed "Lost Workday Cases," take the number reported for the most recent year.  That number represents the average lost workday cases per 100 workers.  It is lost workday case rate (LWCR) for your industry.

Next, calculate the employment at your site in terms equivalent to the data used by BLS.  The BLS number represents the equivalent of one worker’s full work year, whether it was actually worked through regular shifts, part-time work, or overtime work.  To figure your equivalent employment, divide the number of total hours worker by 2,000.  (The number 2,000 represents the average number of hours a full-time worker is generally expected to work each year in the United States.)

With this information, you can use the Bell formula to calculate how many injuries with lost workdays your site would have had if it had been exactly average for your industry.  You can compare this predicted case number (what Bell calls "expected cases") to the actual number of lost workday cases you had at your site.  If you had fewer cases than predicted, the difference between the number of predicted cases and the actual number of cases you experienced at your site is called "injuries avoided."  If you had more cases than predicted, the difference is called "excessive" cases.

Bell suggests that you also calculate the average cost of lost workday cases at your site.  Bear in mind both the direct and indirect costs; When you have found the average cost, you can use the Bell formula to figure how much you saved your company by "avoiding lost workday cases," or how much it cost your company to exceed the average.  You can also calculate the potential savings from sufficiently improving your safety and health management enough to avoid more injuries.

This is Bell’s formula:

[(Average Lost Workday Case Rate) x (Equivalent Site Employment)]/(100)= Predicted Lost Workday Cases

To illustrate further how this formula can work for you, consider a glass container plant that employed 200 workers in 1992.  To apply the Bell formula to this site's safety and health statistics, begin by looking up the SIC code for glass container plants in Table 3 of the BLS bulletin.  The SIC code is 3221.  The table shows that for that SIC code in 1991 (the most recent figures available), the lost workday cases averaged 8.0 per 100 workers in that industry.

Next, calculate the equivalent employment for this site.  You know from site records that in 1992 workers logged 456,432 hours of work at this site.  Using 2,000 as the average number of hours a full-time worker in the United States is expected to work each year, you divide 456,432 by 2,000 to find the full-time equivalent employment at this site.  The result of that division is 228.2.  Applying the Bell formula, you multiply the lost workday case rate (8.0) by the site's full-time equivalent employment (228.2).  The result of that multiplication is 1,825.6.  Finally, divide 1,825.6 by 100 to find the predicted lost workday cases if this site's experience mirrors its industry's average.  You can expect to find 18.3 (rounded down to 18) lost workday cases at this facility.

Rendering the Bell Formula mathematically, you get the following equation (with the answer rounded to the nearest whole number):

[(8.0) x (228.2)]100 = 18

This plant, with its very good safety and health program, had only six lost workday cases.  This was 12 (18 - 6 = 12) fewer than would have been expected had it been average for its industry.  The employer estimates that lost workday cases incur direct costs averaging $16,800.  By avoiding 12 of the predicted lost workday cases for its industry, this site saves $201,600 in direct costs each year.  Conversely, if this site had experienced 25 lost workday cases, subtracting predicted cases from actual lost workday cases (25 - 18) would show that this site had seven lost workday cases above its industry's predicted average.  These seven lost workday cases would have cost $117,600 more than predicted direct costs had the site been average.

The direct costs of occupational injuries and illnesses may be only the tip of the iceberg.  Indirect costs, less easily calculated, can place an even greater burden on the employer.

Although economic incentives are secondary to human health and safety as motives for safety and health protection, the potential economic benefit of effective safety and health management is considerable and clearly worth considering.

OSHA has encountered a number of people who, correctly or not, believe their operation is significantly different from others in their SIC and reject the use of the formula.  If you prefer to use your own past history or other hypothesis to calculate probable case rates, that certainly is not discouraged.  It is very important, however, to use some reasonable method to project a quantitative case rate as a standard of measure.

Think about the VPP sites and their rates, which are 60 to 80 percent below their industry averages.  How much would you save at your worksite if you could be that much below, or even 50 percent below, your industry average?  These figures can help you make a good economic case for improving the management of your safety and health effort even if some spending is required.

Source: Missouri Department of Labor and Industrial Relations

Certisafety Section Home Page