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Try a full lesson: Incidence and DART rates

This is a complete lesson from the course (module 1 of 9, Topic ASP.1), followed by 10 practice questions with full explanations. Nothing to sign up for.

What this lesson covers

Injury rates are the most common calculation in safety work and a reliable topic in the Mathematical Calculations domain, which is 10% of the ASP blueprint. This lesson gives you one method for every rate question: pick the right numerator, use hours worked, multiply by the base, divide by hours. Then it shows how to read the result.

Why rates, not counts

A plant with 2,000 workers will have more injuries than a shop with 20, even if the shop is far more dangerous per person. A rate puts both on the same footing by dividing by exposure (hours worked) and scaling to a standard base.

The common US base is 200,000 hours: 100 full-time workers x 40 hours a week x 50 weeks. A rate of 3.0 means about 3 cases for every 100 full-time workers in a year.

Step 1: pick the numerator

RateCount in the numerator
Total recordable incidence rate (TRIR)Every recordable case
DART rateCases with days away from work, restricted work or job transfer
Days-away case rateCases with days away only
Severity rateDays lost or charged, not cases

Three rules settle most questions:

  1. DART counts cases. A worker who has 3 days away and then 10 days of restricted work is one DART case.
  2. Severity counts days. The same worker adds days to a severity rate (which days, away only or away plus restricted, depends on the definition in the question).
  3. The DART rate can never be higher than the TRIR, because every DART case is also a recordable case.

Step 2: use hours worked

Use hours actually worked, including overtime. Leave out vacation, holidays and sick leave, which are paid but not worked. If a question gives headcount, it must also give hours per week and weeks; multiply them out:

150 workers x 40 hours x 50 weeks = 300,000 hours

Step 3: calculate

rate = numerator x 200,000 / hours worked

Worked example

A distribution center worked 412,000 hours last year and had:

  • 5 cases with days away
  • 2 cases with restricted work only
  • 1 case with a job transfer
  • 9 other recordable cases (medical treatment only)

Total recordable cases = 5 + 2 + 1 + 9 = 17.

The working (3 steps)
  • TRIR = 17 x 200,000 / 412,000 = 3,400,000 / 412,000 = 8.3
  • DART = (5 + 2 + 1) x 200,000 / 412,000 = 1,600,000 / 412,000 = 3.9
  • Days-away case rate = 5 x 200,000 / 412,000 = 2.4

If the 5 days-away cases lost 64 days in total, the days-away severity rate = 64 x 200,000 / 412,000 = 31.1 days per 200,000 hours.

Check the size. 412,000 hours is about two 200,000-hour units, so each rate should be about half its count: 17 to 8.3, 8 to 3.9, 5 to 2.4. If your answer is twice the count, you multiplied where you should have divided.

Step 4: read the result

  • Comparing sites: compare rates, never raw counts. A site with 8 cases in 400,000 hours (4.0) is safer per hour than a site with 5 cases in 200,000 hours (5.0).
  • DART versus severity: if the DART rate falls but the severity rate rises, there are fewer serious cases but each one costs more days. Look for a change in the type of injury.
  • Percent change: (old - new) / old. A TRIR moving from 4.0 to 3.0 is a 25% drop, not 33%.
  • Small numbers swing: a 50-person shop works about 100,000 hours a year, so one case moves its rate by 2.0. Look at several years before drawing conclusions.
  • Rates are lagging indicators. They tell you what already happened. Pair them with leading indicators such as inspections completed and corrective actions closed.

Working backward

Sometimes you know the target rate and need the case count. Rearrange:

cases = rate x hours / 200,000

A site that works 500,000 hours and wants to stay at or below a TRIR of 3.2 can have at most 3.2 x 500,000 / 200,000 = 8 recordable cases.

The slips that make the wrong options

SlipWhat it produces
Multiplying by hours / 200,000A number larger than the count when hours exceed 200,000
Using 100,000 or 1,000,000 as the base when the stem says 200,000Half the right answer, or five times it
Putting every recordable case in the DART numeratorThe TRIR, not the DART rate
Counting a days-away and restricted case twiceA DART rate that is too high
Using days in the DART rate or cases in a severity rateThe wrong kind of rate
Using paid hours or 52 weeks when the stem says 50A slightly-off rate that sits close to the key
Dividing the change by the new valueAn inflated percent change

Check yourself

Try the ten questions in the free practice set for this lesson. Each one uses the four steps above, and every input you need is in the question.

Not affiliated with or endorsed by BCSP. ASP and BCSP are BCSP's marks and are used here only to name the exam.

Practice set

Print these questions for a class (PDF) Answer key on page 2. Free, no signup.

Pick an answer, then check it. Every wrong option is explained too.

1. Mathematical Calculations

A plant had 6 recordable cases in a year in which its employees worked 240,000 hours. Using 200,000 hours as the base, what is the total recordable incidence rate, to the nearest 0.1?

2. Mathematical Calculations

A site has 150 full-time employees who each worked 40 hours a week for 50 weeks, with no overtime. It recorded 9 recordable cases. Using 200,000 hours as the base, what is the total recordable incidence rate, to the nearest 0.1?

3. Mathematical Calculations

A facility worked 280,000 hours and had 10 recordable cases: 4 with days away, 2 with restricted work only, 1 with a job transfer and 3 with medical treatment only. Using 200,000 hours as the base, what is the DART rate, to the nearest 0.1?

4. Mathematical Calculations

A plant worked 320,000 hours. Six cases involved days away from work, totaling 96 days away. Using 200,000 hours as the base, what is the days-away severity rate (days per 200,000 hours)?

5. Mathematical Calculations

Why do US injury rates commonly use 200,000 hours as their base?

6. Mathematical Calculations

Site A had 9 recordable cases in 600,000 hours. Site B had 6 recordable cases in 300,000 hours. Using 200,000 hours as the base, which site has the higher total recordable rate?

7. Mathematical Calculations

A site expects to work 750,000 hours next year and wants its total recordable rate to stay at or below 2.4 (base 200,000 hours). What is the most recordable cases it can have?

8. Mathematical Calculations

One injured worker had 2 days away from work and then 15 days of restricted work for the same injury. How many cases does this add to the DART numerator?

9. Mathematical Calculations

Year over year, a site's DART rate fell from 3.0 to 2.2 while its days-away severity rate rose from 40 to 65. What is the most likely reading?

10. Mathematical Calculations

A site's total recordable rate fell from 5.0 last year to 4.0 this year. What is the percent change?

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