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
| Rate | Count in the numerator |
|---|---|
| Total recordable incidence rate (TRIR) | Every recordable case |
| DART rate | Cases with days away from work, restricted work or job transfer |
| Days-away case rate | Cases with days away only |
| Severity rate | Days lost or charged, not cases |
Three rules settle most questions:
- DART counts cases. A worker who has 3 days away and then 10 days of restricted work is one DART case.
- 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).
- 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
| Slip | What it produces |
|---|---|
| Multiplying by hours / 200,000 | A number larger than the count when hours exceed 200,000 |
| Using 100,000 or 1,000,000 as the base when the stem says 200,000 | Half the right answer, or five times it |
| Putting every recordable case in the DART numerator | The TRIR, not the DART rate |
| Counting a days-away and restricted case twice | A DART rate that is too high |
| Using days in the DART rate or cases in a severity rate | The wrong kind of rate |
| Using paid hours or 52 weeks when the stem says 50 | A slightly-off rate that sits close to the key |
| Dividing the change by the new value | An 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.