I am too new for words

#1
Ok, I am quite new to statistical analysis and will be training myself. I am working in Quality Assurance at a nuclear site.
Here is the premise:
Many models of issue deficiencies us a "Bird's Triangle" model. Industrial Safety for example. In each tier of blocks the numbers change to indicate the number of incidences that rise to a level of severity. If the top block in a triangle is a fatality on the job, the next tier down will be, say 6 instances where the worker is transported to medical attention with a lost-time injury. The tier below that might be 30 occurrences of first aid given on site, and below that a tier of near-misses numbering maybe 300.

What I am not sure of is the statistical validity of using the model as a predictor of future occurrence. I wonder if the "Gambler's Fallacy" is true here. To explain:

If I am near the top of the safety model I described, that I have 6 recorded injuries in a year or so then the "appearance" is that we are doomed to have a fatality in the near future. I know that that is not true. The Gambler fallacy notes that flipping a coin 6 times for heads does not make it more likely that the 7th will be tails, it is still 50/50.
So statistically the ratio of next-to -top tier and top tier is more of a statistical "warning"? That given a very large dataset the ratio will hold true? How can I demonstrate the reality and both caution against complacency and not calling the sky to fall?
 

Miner

TS Contributor
#2
Note the linked article: http://crsp-safety101.blogspot.com/2012/07/the-safety-triangle-explained.html


In short, these ratios have a lot of variation. The linked article references three separate studies that each resulted in different ratios. Note that these are overall incident rates in a large population, and an individual facility may not experience the same ratios. There is also an underlying assumption that "At-Risk Behavior" drives "Near Misses", which in turn drives "Recordable Injuries" and so forth. So there is no assumption of independence as per the coin flipping scenario.


Other things to consider is that the level of safety has changed tremendously over the 80 years since the initial study. In the 1930s, guarding was virtually nonexistent, and agencies such as OSHA (USA) did not exist. Today, we have governmental agencies, safety products such as light curtains and SIL rated safety products. There is also a much greater variation in safety levels from facility to facility than there would have been 80 years ago.