ManufacturingSix Sigma

How to Create Meaningful Safety Graphs

By Ron Pereira Updated on December 2nd, 2008

Creating meaningful charts and graphs for safety related issues can be hard, not to mention confusing. It doesn’t have to be. In this article I will share a technique that may help bring some clarity to the situation.

The Wrong Approach

First, let’s assume a company tracks the number of accidents per month. For the sake of an example let’s use this totally fabricated data set:

  • Jan-07: 0
  • Feb-07: 1
  • Mar-07 : 0
  • Apr-07: 0
  • May-07: 0
  • Jun-07: 1
  • Jul-07: 1
  • Aug-07: 0
  • Sep-07: 0
  • Oct-07: 0
  • Nov-07: 0
  • Dec-07: 1
  • Jan-08: 0
  • Feb-08: 0
  • Mar-08 : 0
  • May-08: 1
  • Jun-08: 0
  • Jul-08: 0
  • Aug-08: 0
  • Sep-08: 1
  • Oct-08: 0
  • Nov-08: 0
  • Dec-08: 1

With this data, some may attempt to create a c chart. When they do they get something that looks sort of like this.

c chart of Safety Rate

The upper control limit is 1.959 and the measure of central tendency is 0.304. Friends, this graph is pretty much useless. There is really no way of determining if things are getting better, worse, or staying the same.

A Better Approach

A better approach would be to somehow convert this data into a yearly rate. There are a number of formulas you can use to do this… but one I quite like is to simply count the days between accidents and multiply is by 365.

For example, the first accident (in our made up data set) happened on February 8, 2007 and the second accident occurred on June 16, 2007. This means there were 128 days between accidents.

So, our annual accident rate could be calculated as follows: (1 accident/128 days) * (365 days/year) = 2.85 accidents per year.

When we work the math for the rest of the data we see something like this.

  • 8-Feb-07, first accident
  • 16-Jun-07, 128 days between accidents, rate = 2.85
  • 10-Jul-07, 24 days between accidents, rate = 15.21
  • 17-Dec-07, 160 days between accidents, rate = 2.28
  • 1-May-08, 136 days between accidents, rate = 2.68
  • 6-Sep-08, 128 days between accidents, rate = 2.85
  • 11-Dec-08, 96 days between accidents, rate = 3.80

Now, by using the rate data we can create an Individuals and Moving Range Chart (I-MR) that looks something like this.

I-MR Safety Graph

This graph is far more powerful than the c chart. From this I-MR chart we can see that we had a blip early on but have since leveled off.

In other words things are pretty much staying the same. And since we’re talking about the safety of our workers the fact things are moving sideways – averaging around 5 accidents per year – is probably cause for strong action in most companies.

Not the Only Way

As I mentioned, this is not the only way to calculate an annual accident rate. With this said, I would be very interested to hear how your company goes about this.

  1. tom

    December 2, 2008 - 6:05 pm

    I’m new to this forum and found this quite interesting. My one question is why do you have a mean of the moving average?
    This seems very misleading and perhaps unhelpful.
    The moving average is already averaging data for you why would you average it again?

  2. Jason

    December 2, 2008 - 6:26 pm

    I see this a lot in executive presentations. I don’t know how it’s a useful measurement tool when it’s something like 1 in the entire division over the course of a year.

    Something like accidents/hours worked would be a better measurement and allow for “normalizing” if hours significantly increased – say through an acquisition or some such.

  3. Ron Pereira

    December 2, 2008 - 8:46 pm

    Hi Tom, welcome to LSS Academy! If understand your question… I think you are referring to the moving range (i.e. the bottom part of the graph). If so, this is not an average of an average. Instead it is simply graphing the difference between the data points. So, for example, if you look at the first two data points we calculate and graph a moving range of 12.26 (15.21 – 2.85). This is actually extremely useful information as sometimes this “range” can move out of control. Does this make sense?

    Hi Jason, you bring up some valid points, especially the hours worked aspect. With this said, an accident is an accident and just because more “hours” were worked doesn’t mean we should accept more accidents or try to “normalize” them away. Finally, I think my approach is probably best suited as a plant level metric and not necessarily a “division” level metric for the very reasons you noted. Great comment, as usual.

  4. Adam Mooty

    December 2, 2008 - 9:07 pm

    normalizing is done by people attempting to twist data to suit their needs. so while it would seem to make sense to allow for more accidents if more hours are worked i think this is what you would call a slippery slope. with this said, my company does take hours into account but i think simply counting lost time events as shown above is probably best. our goal, no matter how big or small the company or how many hours worked, should be always be 0 accidents.

  5. Ron Pereira

    December 2, 2008 - 9:18 pm

    Hi Adam, thanks for the comment.

    I am not sure I completely agree on the first point about people trying to normalize are attempting to twist data. Truth be told, I am not a big fan of normalizing data but will admit there are some situations where it is valid and makes sense.

    With this said, I do agree that 0 accidents should always be our goal no matter the size or complexity of the business.

  6. David King

    December 3, 2008 - 2:11 pm


    What type of approach would you take to display your safety information when you have multiple accidents in one day and you are also keeping track of multiple safety categories, i.e. near misses, first aids, recordable injuries, lost time injuries, cumulative total recordable injuries (recordable + lost time) and hours worked for the month?

    Here is a examlple of how we publish our safety data:

    Month First Aids Rec. InjuryLost Time Total Rec Cum. TRI Hrs Worked
    1/5/08 12 2 0 2 5.15 388326
    2/5/08 14 0 0 0 2.69 353885
    3/5/08 14 1 1 2 3.48 408362
    4/5/08 8 0 1 1 3.22 400591
    5/5/08 10 3 0 3 4.09 405722
    6/5/08 19 1 1 2 4.15 453344
    7/5/08 9 0 1 1 3.9 409834

  7. Ron Pereira

    December 3, 2008 - 3:52 pm

    Hi David, well you could take a similar approach for the different categories and as far as having more than 1 accident in a day you would simply divide 2/(days since last incident) * 365. Again, you could work the hours into the formula as well if this makes sense.

    In the end, I prefer to keep things real simple. Also, I think we all need to be careful with tracking too many things since this often leads to analysis paralysis. In other words, we spend more time making graphs than focusing on how to make the work place safer and more effective.

    Thanks for the comment!

  8. Eric H

    December 6, 2008 - 10:36 pm

    Random thoughts:

    1) I agree that some kind of accident ratio is in order. Per mile driven? Per trip taken? Seems like there is a SS measure of “opportunities for error” measure there. 0 sounds like a great goal, but there is some context. If that’s your goal and you’re a roofing contractor, you are always staring at evidence of your failure even though you might be smashing the industry average. If you operate an insurance claims office and you’re seeing 5 accidents per year among your adjusters, you really are failing.

    2) Safety theory (whatever that may be) suggests that for every bad accident, there are X minor ones and Y near hits. I have seen encouragement to keep track of all of the misses as well as the hits. Maybe overkill? Still, whenever you’re measuring teeny little numbers, you aren’t measuring anything useful. I have a sore spot on this because my mgt sometimes looks past my months on end with no injuries, then we have a spate of unrelated things, and they say, “3 last year, 6 this year – your injury rates have doubled!” Yes, random variation looks bad when you put it like that.

  9. Sharon

    June 3, 2011 - 4:57 pm

    I am new to this site and am honestly attempting to understand statistics. I am in healthcare and most of the data I look at is centered around compliance and patient safety…i.e. number of History and Physicals not completed by surgeon prior to patient having surgery…or number of times medication reconciliation was not done upon discharge of the patient, number of central line infections for each unit with a census that varies. My world is so different than manufacturing and I am wanting to learn what type of control chart to use for healthcare data that does not fit into the typical box of examples given.

    What type of graphs would I use for the above scenarios? Thank you. Sharon

    • Ron Pereira

      June 9, 2011 - 4:15 pm

      Sharon, the Individuals Chart will work for about any process out there. Be sure to read Wheeler’s book called “Understanding Variation.” It’s excellent.

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