Page 262 - Design of Simple and Robust Process Plants

248 Chapter 6 Process Design Based on Reliability
6.7
Definitions

Availability A(t) is the fraction of time over a defined period (mission time) that a
component or system is fully operational.
Common cause failure is the failure of more than one component or system due to
the same cause.
Failure rate k(t) is the probability that a component or system, which survived up to
time t, will fail in the next time interval.
k(t) = f i and f i is n i
R i 1 N
where; n is the number of items failed in the ith interval
i
N the total number of failed items over the test period
R i 1 is the reliability at time t i±1
Failure occurrence rate x(t) is the probability that a component or system fails in
the next time interval not necessarily for the first time, with no failure at time zero.
Mean down-time (MDT) is the fraction of the mean time period observed that the
system cannot perform its function. MDT is the MTTR plus the mean time to take
the system out of operation for maintenance, plus the mean time to take the system
back in operation.
Mean time between failures (MTBF) is the mean value of time length between two
consecutive failures over a defined period (applicable for repairable items).
Mean time to failure (MTTF) is the mean time of a component or system failure
from t = 0 (applicable for nonrepairable items)
R 1
In formulae form; MTTF = t f(t)dt
0
Mean time to repair (MTTR) is the mean time taken to repair a component. This
starts at the moment a component is available for maintenance and continues until
the time it is made available for operation to return to service. The repair time
includes travel time, diagnosis, waiting time for repair items, and actual repair.
Mission time is the time between turnarounds, and should not be confused with the
time between planned shutdowns for regeneration or cleaning; for continuous
plants, this may be 4±5 years.
Probability (P) is the likelihood of occurrence of an event (failure) or a sequence of
events (failures) under stated conditions during a period. The probability is
expressed as between zero and unity.
Probability density distribution f(x)
The probability density function is f(x) = dF x†
dx
Probability distribution F(x) The probability distribution of a stochastic variable x
means the set of all values of x with the related probabilities
Probability of failure on demand (PFD(t)) The probability of failure on demand is
the likely hood a systems is down at time t and unable to operate if requested.