Probabilty of reliability and the failure rate

[scotchpie]

I am currently studying for a business qualification I am stumbling over a question.

It concerns calculating failure rate. The equation I know for this involves knowing the number of failures over a given time.

However the question is: "A device has a reliability of 0.8 over 2000 hours, calculate the failure rate."

How can I firstly work out the number of failures from this? It doesn't give any other information, ie total sample size etc. just the reliability over 2000 hours.

It's a bit of a killer as the next questions refer to MTBF (mean time between failures) and MTTF (mean time to failure) but I need to know the failure rate first before I can tackle these questions which I am confident in answering once the failure rate has been determined.

Thanks
Andrew

 

[uart]

You are probably meant to assume an exponential probabilty density model. The data "A device has a reliability of 0.8 over 2000 hours" will let you calculate the single constant in the model and everything else should follow from that.

That is, 0.8 = exp(-2000 k). Solve this for "k".

 

[tacman]

Hi Andrew,

Calculating the failure rate can be a bit tricky without the total sample size or the number of failures. However, we can use the given information of reliability and time to calculate the failure rate.

First, let's define reliability and failure rate. Reliability is the probability that a device will function properly for a given period of time, while failure rate is the number of failures that occur in a given period of time.

In this case, we know that the device has a reliability of 0.8 over 2000 hours. This means that there is a 0.8 probability that the device will function properly for 2000 hours.

To calculate the failure rate, we can use the formula: Failure rate = (1 - Reliability) / Time. This formula assumes that the device follows an exponential distribution, which is commonly used for reliability analysis.

So, in this case, the failure rate would be: (1 - 0.8) / 2000 = 0.0001 or 0.01%. This means that there is a 0.01% chance of the device failing in a given hour.

I hope this helps you in tackling the other questions related to MTBF and MTTF. Remember, MTBF is the average time between failures, and MTTF is the average time to failure. Both of these metrics can be calculated using the failure rate.

Best of luck in your studies!