A short note on my definitions of hazard rate and failure rate. Not going to clear anything up, yet highlight we may not be talking about the same thing.

I too have found these terms used interchangeable in many papers and references.

(This note is in response to a question on a forum asking about the difference between these two terms. The question prompted some interesting discussion and no clear resolution as various authors and authoritative works do not seem to agree.

Therefore, I highly recommend you define these terms with those you converse.

While I do not have a definitive source for the difference, I have this working understanding The hazard rate is a function and is the function that describes the conditional probability of failure in the next instant give survival up to a point in time, t. h(t) = f(t) / R(t).

Thus hazard rate is a value from 0 to 1. Failure rate is broken down a couple of ways, instantaneous failure rate is the probability of failure at some specific point in time (or limit with continuos functions.

It is the chance of failure calculated by h(t) for a specific t. Failure rate can also be an average chance of failure over some period of time – not as precise yet very commonly used. I try to avoid this as it presumes a constant failure rate over the duration. And, some don’t even provide the duration and simply state a failure rate per hour, for example.

Well, over which group of hours ( like a year ) does this rate apply? Failure rate as the count of failures per unit time, and can be a value greater than one. For example, 2 failures per year, or a 200% annual failure rate.

Given the number of different ways to interpret the term failure rate, I suppose we should careful. My definitions may not clear up any confusion, it’s just the way I think about these terms. cheers, Fred http://creprep.wordpress.com/2011/09/20/the-four-functions/

## Author: Fred Schenkelberg

I am an experienced reliability engineering and management consultant with my firm FMS Reliability. My passion is working with teams to create cost-effective reliability programs that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs.
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Help. I am a student and trying to understand the following book problem.

h(t)= 0.0005(2 + 4t + 2^1.5)

a. what is the reliability at t=5000h

b. what is the mean time to failure for this system?

c. What is the expected number of failures in 1 year of operation.

I am going round and round and the text does not cover this very well Can you help?

Hi Joe,

Sure, you have a hazard function and need the reliability function to answer a. See https://accendoreliability.com/2011/09/20/the-four-functions/ to see the relationships between functions.

The MTBF is basically the time, say a year, divided by the number of failure over a year.

I’ll leave c. for you to sort out.

Cheers,

Fred