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Likelihood Evaluation

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Figure 15-1 Failure rate vs time

15.4 Reliability and Failure Probability

Generally, data is collected on the failure rate of a hardware component. With sufficient data, the reliability may be
expressed by a Poisson distribution based on a constant failure rate. As time increases, reliability decreases. The failure
probability is 1 minus reliability and increases with time.

Equipment failures in a process occur as a result of complex interactions of the individual components. The Probability
that a particular hardware component will not fail during the time interval, t, for a constant failure rate, , is estimated using
Equation 15-1[18, pp. 550-558]:

R(t) = e - t Equation 15-1

where R is reliability over the time interval

The Failure Probability over this time interval, P(t), assuming zero time for repair, 1 – Reliability or Equation 15-2:

P(t) = 1 – R(t) = 1 – e - t Equation 15-2

The Mean Time Between Failure (MTBF) for constant failure rate is estimated by Equation 15-3:

MTBF = 1 /  Equation 15-3

The Mean Time to Repair (MTTR) is the mean time to restore a failed component or system to operation.:

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