# Difference between hazard and failure rate

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/ 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.

## 9 thoughts on “Difference between hazard and failure rate”

1. Joe says:

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?

1. Fred Schenkelberg says:

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

2. Maverick says:

Respected sir,
I am a student of industrial engineering. I am working on a problem of finding reliability function and hazard rate function of an assembly.
I am provided only with dates of failure of the assembly and not of individual parts.

can i do censoring of the failure data ?

1. Fred Schenkelberg says:

Hi Maverick – censoring is a feature of the data meaning that some of the assemblies haven’t failed yet. So, if you have 10 assemblies operating, and 4 have failed, and you have the time to failure data for those four, that is the failure data, the remaining 6 assemblies have not failed, and they provide the censored data.

Censored data is unrelated to whether you have component, assembly, or system level data.

hope that helps.

Cheers,

Fred

3. Marc says:

“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.”

I have a doubt on this. Taking the exponential random variable with parameter L, we get h(t)=L. But L can exceed 1. So how can this necessarily be a probability?

1. Fred Schenkelberg says:

Hi Marc, L is value that represents a rate, an instantaneous probability of failure – thus is between 0 and 1 – if you take the inverse 1/lambda = MTBF… MTBF is the inverse of a fraction -thus greater than one. Or, maybe I’m missing something here. cheers, Fred

1. Marc says:

Hmm, I think we must have differing definitions of the exponential distribution. The definition I’m acquainted with, the same as that on Wikipedia, requires that L (i.e., lambda) be positive but not necessarily less than 1. And using the formula f(t) / R(t) on this distribution, once derives a hazard function that is constantly L.
How do you define an exponential random variable?

4. S.K. says:

Haven’t you faced here the difference between probability density distribution (pdf) and cumulative density distribution (cdf) and failure rate function?
Reference: https://www.reliasoft.com/products/weibull-life-data-analysis-software/the-risks-of-using-failure-rate-to-calculate-reliability-metrics

1. Fred Schenkelberg says:

Thanks for the note S.K. I had not seen that article over at reliasoft. good stuff

cheers,

Fred