# Thread: Converting instantaneous Reliability at time (t) to normalized failure rate (fpmh)

1. ## Converting instantaneous Reliability at time (t) to normalized failure rate (fpmh)

Given the reliability at 2100 hours =0.992, then lambda(2100 hours) = -Ln(0.992)=0.008. I need to convert the hazard rate (lambda) for 2100 hours to the normalized value in terms of failure rate per million hours (fpmh, 10^6 hours).
I am foggy on the process from this point; should I use the pdf function to convert such as:
F(t)=1-(1+0.008*10^6)^-1
Then take the derivative f(t)=0.008 (1+0.008*10^6)^-2
Then h(t): f(t)/1-F(t)

Can someone point me in the right direction?

2. ## Re: Converting instantaneous Reliability at time (t) to normalized failure rate (fpmh

Originally Posted by halfdome
Given the reliability at 2100 hours =0.992, then lambda(2100 hours) = -Ln(0.992)=0.008. I need to convert the hazard rate (lambda) for 2100 hours to the normalized value in terms of failure rate per million hours (fpmh, 10^6 hours).
I am foggy on the process from this point; should I use the pdf function to convert such as:
F(t)=1-(1+0.008*10^6)^-1
Then take the derivative f(t)=0.008 (1+0.008*10^6)^-2
Then h(t): f(t)/1-F(t)

Can someone point me in the right direction?
To begin, you're not going to find your answer by taking the derivative of a constant (i.e. the variable t does not appear on the right-hand side of F(t)), which is what you have presented above. I am assuming you have a constant failure rate and thus the density function is exponential, I suspect. In short, you need to get your notation correct so that you can get an appropriate response.

3. ## Re: Converting instantaneous Reliability at time (t) to normalized failure rate (fpmh

Thank you for your comment. The equations for F(t) and f(t) were taken from "Applied Reliability", Tobias and Trindade, pg. 35, Example 2.3 Failure Rate Calculations as method to determine the cummulative hazard rate function h(t). The 0.992 value for reliability is taken from an exponential graph of reliability vs. time resulting from product life testing.

4. ## Re: Converting instantaneous Reliability at time (t) to normalized failure rate (fpmh

For the notation issue, I think you can also refer to

http://en.wikipedia.org/wiki/Survival_analysis

which has some fundamental relationship between

Here you need to be more specific to say whether you are interested in the instantaneous hazard rate or the cumulative hazard. (supposed to be different)

The second thing is that we are not sure about the parametric form of any one of . If you can type the exact parametric formula for any one of them before doing any numerical substitution, that will be much better.

The most important thing is that we are not sure, say if you are concerning changing from 1 unit/scale to another unit/scale, or you are given some information and want to know how to make use of the information and the relationship I quoted above to find the desired (cumulative) hazard.

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