Failure Rate - Failure Rate in The Discrete Sense

Failure Rate in The Discrete Sense

The failure rate can be defined as the following:

The total number of failures within an item population, divided by the total time expended by that population, during a particular measurement interval under stated conditions. (MacDiarmid, et al.)

Although the failure rate, is often thought of as the probability that a failure occurs in a specified interval given no failure before time, it is not actually a probability because it can exceed 1. Erroneous expression of the failure rate in % could result in incorrect perception of the measure, especially if it would be measured from repairable systems and multiple systems with non-constant failure rates or different operation times. It can be defined with the aid of the reliability function, also called the survival function, the probability of no failure before time .

, where is the time to (first) failure distribution (i.e. the failure density function) and .
\lambda(t) = \frac{R(t_1)-R(t_2)}{(t_2-t_1) \cdot R(t_1)} = \frac{R(t)-R(t+\triangle t)}{\triangle t \cdot R(t)} \!

over a time interval from (or ) to and is defined as . Note that this is a conditional probability, hence the in the denominator.

The function is a CONDITIONAL probability of the failure DENSITY function. The condition is that the failure has not occurred at time .

Hazard rate and ROCOF (rate of occurrence of failures) is often incorrectly seen as the same and equal to the failure rate. And literature is even contaminated with inconsistent definitions. The hazard rate is in contrast to the ROCOF the same a failure rate. ROCOF is used for repairable systems only. In practice not many serious errors are made due to this confusion (although this statement is hard to validate...).

Read more about this topic:  Failure Rate

Famous quotes containing the words failure, rate, discrete and/or sense:

    “Evil is simply
    a grammatical error:
    a failure to leap
    the precipice
    between “he”
    and “I.””
    —Linda Pastan (b. 1932)

    “I don’t know but a book in a man’s brain is better off than a book bound in calf—at any rate it is safer from criticism. And taking a book off the brain, is akin to the ticklish & dangerous business of taking an old painting off a panel—you have to scrape off the whole brain in order to get at it with due safety—& even then, the painting may not be worth the trouble.”
    —Herman Melville (1819–1891)

    “The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.”
    —W.V. Quine (b. 1908)

    “Profundity easily turns into dullness and astuteness deteriorates into wit. Be guided by natural common sense and it will accommodate great and small.”
    —Franz Grillparzer (1791–1872)