Question

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10. Airbags are concealed in the center of the steering wheel and in dashboards. When the front end of the vehicle strikes another object, the airbag inflates. The airbag will fully inflate upon impact in one-tenth of a second, providing a barrier to protect the driver. More advanced airbag systems have smart sensors that sense key elements related to the accident and determine the amount of force the detonator needs to emit, The dia- gram below shows the key elements that must operate in order for the airbag to inflate. Calculate the reliabilit of the system. Crash sensorsSmart sensors 0.97 0.95 Diffuser Airbag Detonator Azide 0.98 0.99 0.97 0.99 0.97 0.95

Answer 1

See there are two crash sensors and smart sensors working in parallel. This means for each of the pair the reliability is 0.97*0.95 = 0.9215

That means the chance of one failing is 1 - 0.9215 = 0.0785

The chances of both failing is 0.0785*0.0785 = 0.0061

The chances of both not failing is 1 – 0.0061 = 0.9938

Hence the parallel section of crash and smart sensor’s reliability is 0.9938

Now the rest of the process is in series. Hence we need to multiply all of them

0.9938*0.99*0.98*0.99*0.97 = 0.9259

That is the reliability of the entire system = 0.9259