Байланысты: Мехатроника 1 том Баймухамедов М.Ф., Джаманбалин Қ.Қ.,Ақгул м.К.
5.3 Reliability The main indicator of failure-free operation is the probability of failure-free
operation – the probability that failure will not occur within a given time or
specified operating time. The probability of failure-free operation is estimated
by the relative number of workable elements:
where
N is the total number of tested (operated) samples;
N p – number of
operable samples after testing (operation);
n is the number of failed samples
after the tests;
Q (t) is the failure probability, estimated by the relative number of
failures:
243 Since failure-free work and failure are mutually opposite events, then:
P(t) +
Q(t) = 1
at
t = 0 and
n = 0 we obtain
Q(t) = 0 и
P(t) = 1.
at
t = 0 and
n =
N ,
Q(t) = 1 and
P(t) = 0.
The distribution of failures in time is characterized by the function of
the distribution density
f (t) of the operating time to failure. In the statistical
interpretation:
in a probabilistic treatment:
where Δ
n is the increment in the number of failed objects and, accordingly, the
probability of failures in time
Δt .
The probability of failures and failure-free operation in the distributional
density function is expressed by the dependences
:
at
The failure rate
λ(t) refers to the number of workable objects
N(p) .
In the statistical interpretation:
in a probabilistic treatment:
The probability of failure-free operation, depending on the failure rate, can
be written as:
244 This is one of the basic relationships of reliability theory.