Deterministic or Probabilistic? Can you really ever leave your dog in the car?

Probabilistic Safety Assessment (PSA) is often described as a complement to Deterministic Safety Assessment (DSA), but what does that mean?

DSA comes first, in the design and licensing phase, as its main purpose is to show what will be needed from the safety systems for the most expected cases, so they can be built appropriately; it is the design basis analysis. These analyses are typically done conservatively, with large margins and assuming that part of the system won’t be available. After all, if your safety system isn’t able to ensure safety even when working as intended, then the probability of failure doesn’t matter.

DSA does this by defining specific scenarios that the safety systems are expected to be able to deal with and then tries to calculate how different physical parameters like pressure, temperature, water level, etc., will change over time, in order to show that the safety limits will not be exceeded.

Let’s think of an example: imagine going to buy some groceries on a hot summer day and leaving your dog in the car. (Disclaimer: I own neither a car nor a dog.)

In this scenario, a DSA might ask, “Does it get too hot?” and choose the air temperature in the car as the parameter to be analysed over time. The conservative assumptions could be that the AC doesn’t work, so you open the window a crack, that the car is parked in the sun (a very conservative assumption), and there is an unusually long queue at the register. The safety limit could be that the temperature can’t rise so much that the dog starts panting (e.g. defined as being above temperature X for amount of time Y).

The calculation would quickly show what most of us know already: don’t do this, because it gets too hot and the dog will die. In this case, the “safety system” has been proven inadequate, and you should go back and rethink some things.

In contrast, a PSA for the same scenario could ask “how likely is it that the dog dies” and analyse this by finding the sequences of events that would lead to the dog dying and assigning probabilities for the individual events to happen. These analyses are typically done more realistically than conservatively, so the events might include the probability that the AC isn’t working, that the day is hot but cloudy or there is shade, that you forget to wind down the window, or even that a passer-by notices and decides to save the dog by smashing the window.

Quantifying the probability of each sequence of events leading to the death of the dog in this specific case would give you the Conditional Dog Death Probability, CDDP – the probability the dog will die, assuming that it is summer and a hot day, but not assuming that you park in the sun or that the AC isn’t working.

In this case, there is a large overlap between the PSA and DSA in that they assume a very specific circumstance, but analyse it in complementary ways with different criteria for what is considered acceptable. But even here, the PSA can give further insights by showing the relative strengths and weaknesses of the different parts in the “safety system”, helping you decide which ones to improve first.

Additionally, in a typical PSA you would also include the frequency of grocery trips over the analysed time interval, e.g. N/year, in order to be able to calculate the Dog Death Frequency, DDF. The different sequences of events leading to the death of the dog would then be summed up, giving you a frequency showing you how many dogs you could expect to lose each year if you did this constantly with callous disregard to the dog's well-being (you psychopath).

The main difference in this example is that the PSA when calculating the CDDP takes into account that the AC works more often than not, that you don’t always park in the sun, that you might forget to roll down the window and that many passers-by would rather break your car window than let a dog suffer; and when calculating the DDF that not every day of the year is hot enough to cause harm (at least not here in Sweden).

In both cases, one outcome of the analysis might be that an administrative rule is introduced in order to manage the risk to the dog, by saying that you must never leave the dog in the car when the temperature is above a certain threshold.

But where the Deterministic analysis might (or might not) conclude that this is enough to eliminate the risk, the Probabilistic would often just add to the analysis the probability that you forget this rule or don’t notice how hot it is outside, and calculate a lower DDF – serving as a reminder that no risk can ever be fully eliminated, just mitigated and minimized to an acceptable level.

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