# Probabilty of reliability and the failure rate

1. Sep 8, 2006

### 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

2. Sep 8, 2006

### 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".