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# Failure rate vs. failure probability

Good Morning,

I've seen 1-R as the definition of failure probability, and elsewhere as the failure rate limit.

Is it a hasty generalization to conclude that  the failure probability is the maximum failure rate?

Thank you

aasikolo
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aasikolo
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2 Solutions

Commented:
Not enough information.

What are the units of Failure Rate?  And what is the time window?

42% of businesses fail within the first year.

50% of marriages fail.

The probability of a 5 year old car failing a safety inspection is 20%.
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Commented:
If the failure rate for new businesses is 10% per year ...
Then the probability of a new business failing in the first year is also  0.1  or  10%

I don't see how  (1 -R)  would be relevant, except that it is the success rate or probability.
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Commented:
"Is it a hasty generalization to conclude that  the failure probability is the maximum failure rate?"
yes
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what do you mean by maximum failure rate?
A failure rate is a failure rate, it has no maximum. If it is calculated differently or with a different group of items it can change but by itself it has no maximum.
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Author Commented:
From the Weibull.com website:

...the failure rate is defined as the rate of change of the cumulative failure probability divided by the probability that the unit will not already be failed at time t.

Also, please see the attached excerpt on the Bayes Success-Run Theorem from a chapter from the Reliability Handbook.

Hence the question.
Reliability-Handbook-Bayes.pdf
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Commented:
"...the failure rate is defined as the rate of change of the cumulative failure probability divided by the probability that the unit will not already be failed at time t."

Given this definition I can say that there are others which can analyse the situation better than I can BUT
it is hard to see that the failure rate is other than a constant function of time (hence does not have a maximum) which starts at 1 and goes to 0/0 at large t.
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Retired considering supplemental income.Commented:
To me "probability" means when the outcomes are of a well defined random event or experment like a coin toss or dice throw.

But, I think of "probability rates" as the result of data collection that is not random but is altered by unknown factors and is a measurement of observed frequency.  To my mind this belongs to the area of Statistics.
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Author Commented:
As you both recall, there are three periods of a product's life cycle: infant mortality, where the failure rate begins high and drops to the constant rate of the next period, the useful life, where it remains constant until the third period where the product begins to reach the end of its useful life and the failure rate increases. Plotting this rate is known as the bathtub curve, or the Weibull distribution(s), from before.

Referring to the initial question, understanding that R and 1-R comprise the area under the failure rate curve, the failure and reliability probabilities are complimentary, as opposed to the confidence level and failure rate are complimentary.  Where the failure rate and failure probability are numerically equal carries no significance for the question posed.

I believe what we have here is a transcription error between R and RLT from the reliability article on my part.  That is the problem with doing this stuff under the gun; sometimes when you are terrorized you cannot think.

dshindy's "1 to 0/0" and aburr's "observed frequency" (vs probability are estimates) were both good hints.  Are you two agreeable to splitting the points down the middle?
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Commented:
"Are you two agreeable to splitting the points down the middle? "
yes
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Author Commented:
Thank you
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Retired considering supplemental income.Commented:
Yes, thanks for the points.  I was just commenting.  aburr should have gotten the bulk of the points since he answered first.
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