# How to obtain sensor failure probabilities?

I'm a computer science student doing research in wireless sensor networks (WSN) optimization. Based on past research works, sensors are capable of failing due to a number of factors such as harsh environmental conditions, communication errors, and malicious attacks. According to this source, it is possible to assign a failure probability to each sensor. The source states that initially, it can be set by the manufacturer; however, many factors such as weather, accidents, interferences can affect the sensor failure probability.

Given that the network topology is known (the location and therefore environment is known) and that I have access to some hazard maps, how do I assign failure probabilities to each sensor? For example, if sensors in flood-prone areas are more likely to fail, how do I set the exact values of the failure probabilities? Is it acceptable to just assign arbitrarily higher values to sensors in harsher environments? Is there a way quantify this from an engineering perspective?

Thanks and any insight would be extremely helpful.

• As a computer science student you should know that answering this question is NP-hard :-) Nov 12, 2016 at 15:21
• Seriously though, you need the manufacturer's data to answer this with high probability, if the manufacturer has not put the sensor through rigorous testing under adverse field conditions and collected the data for a long period of time , you are out of luck, you will have to do all the testing yourself to compute the failure probabilities :-( Nov 12, 2016 at 15:34

Probabilistic Risk Assessment (PRA) is a big deal in the Nuclear industry, basically it is a mathematical approach to quantify how safe/unsafe a power plant is. Without going too deep into PRA it is a method to combine risk factors from many different failure possibilities and their interactions with everything else; everything from major weather events like earthquakes and hurricanes/tsunamis to human error in the face of stressful environments to sensor and actuator failures.

PRA has to deal with two major problems, epistemic and stochastic uncertainties in failure events. For example, having a new sensor for which no one knows the failure probability (i.e. #failures/time) is a stochastic uncertainty, there is simply not enough data to provide a believable failure probability. The best way to overcome stochastic uncertainty is to get some data. Epistemic uncertainties are when the model used to predict failures is not accurate, like having inaccurate weather records to predict how often hurricanes will occur.

So to answer your question, if you know your system layout and you have failure probabilities you can use the methods in PRA to properly combine all the failure modes (like combine flooding probability with other ways the sensor could fail). In the cases where you don't have data you should either collect/find some or consult an expert who can give you an idea of how conservative to be. No matter what you choose to do, there will always be scrutiny on values you make a "guess" for.

Your question is very general and it is difficult to give specific answers, but I will try to offer some pointers. For example I cannot determine whether you are interested in time to failure, general system reliability or both. Also you indicated that the failure could be driven by a number of factors, such as weather, accidents or interferences.

Each of these potential causes of failure is different. For example, weather, as a natural hazard, may be considered as time dependent - being related to the risk of a storms over a period of time. The others could simply be due to random or unpredictable causes; therefore each of these factors may require a different probability density form.

In any case, the first step is to determine the form of mass or density function that will be used to model the failure of each sensor. For time to failure, a density function often used is the Hazard function or one of its derivatives. In simple terms the Hazard function is also called a bathtub function as the failure risks are typically much higher in early-life, decrease in mid-life and increase again at end-of-life. Human life can be modelled with this form of a risk profile.

The manufacturer may offer useful data as the Hazard function is commonly used in product reliability assessment. For example, the risk of failure of light bulbs is modelled well with a Hazard function. In your case, a paper illustrating the application of the Hazard function to natural hazards is found here.

Proper assessment of the risk of flooding due to weather requires consideration of the rainfall intensity associated with a, say, 100-year storm, for example, and the associated flooding levels from the characteristics of the watershed and it's unit hydrograph.

Consideration of the forms associated with accidents or interferences and how they may be combined is important. If the events are statistically independent then the overall result may be computed as a product of the probabilities. Otherwise dependency effects must be considered.

If you want to assess the reliability of the entire system - this is again another rather large subject. I have set out several alternative techniques in this thread.