Page 242 - Design of Simple and Robust Process Plants

228 Chapter 6 Process Design Based on Reliability
The failure rate occurrence becomes equal to the failure rate when we ignore the
repair time as being small compared to the mean time between failures, then x = k
R t
Now, the number of failures becomes; N(0,t) = x t†dt = k t (6)
0
6.2.2
Reliability Data and Distribution

Reliability data bases are available in the public domain for all kinds of components
(CCPS, 1989; Oreda,1992). These databases embody not only the raw data but also
the distribution functions with its parameters. Many larger companies have devel-
oped their own databases, but these are sometimes available for public data banks.
The importance of a company's own database is that these can be made much more
specific, especially with regard to the environment and the type of component. This
can be helpful for the maintenance department, and also for the reliability engineer
who will receive more specific information for new designs. The drawback is that
the databank must be maintained for quite some time before sufficient data are
available to obtain statistically relevant information.

Probability distributions We will now discuss some statistics relating to observati-
ons on failing components (events) as being the subject of reliability engineering.

The probability (P) of an event is defined by Leitch as: ª¼ the proportion of time that
we observe that event in a large number of trials, or the proportion of time we would
expect to observe, were we able to observe a large number of trialsº.

Probability is also defined as: ª¼ the likelihood of occurrence of an event (failure) or
a sequence of events (failures) under stated conditions during a periodº.
Probability can be expressed as a percentage of failures, or successes, of the total
number of trials; thus, the value will lie between 0 and 1.
There are, statistically, two important aspects relating to component or system
failures:

1. The average or mean value (with its standard deviation).
2. The mode of distribution.
The average value (l) for a discrete distribution is defined as:
P n
l = x i
n
iˆ1
where n is the number of items, and x is random variable.
The average or mean value for a continuous function is:
‡1
l = R x f(x) dx
1