Page 241 - Design of Simple and Robust Process Plants

6.2 Basic Theory of Reliability 227

Turn around
Time between
Planned process stops
failures
Unplanned stops
Mission time

0
t() Time
Fig. 6.5. Time line for a process plant.

With the constant failure rate, the relationship can be rewritten as:
t
h i
R(t) = exp
MTBF
Unavailability U(t) is defined as:
U(t) = 1 ± A(t) (4)
The unavailability due to failures (excluding regeneration stops) is expressed on a
Markov technique.
1
When we write the mean time to repair MTTR as; h ˆ
l
k
U(t) = (5)
k‡l1 e k‡l†t
derived by Markov analysis (Red book, 1997).
k
The limiting value average unavailability becomes: U=
k‡l
The formulae can be simplified:
3 k
If l>>k and t then U(t) =
l l
Or h << MTTF and t 3 then U(t) = kh

As A(t) = 1 ± U(t), the availability is now known.
R t
The number of failures is N(0,t) = x t†dt
0
where x is the failure occurrence rate, which is the probability that a component
fails during the next time interval, given that no failure will occur at time zero.