Мехатроника 1 Бөлім mechatronics



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Мехатроника 1 том Баймухамедов М.Ф., Джаманбалин Қ.Қ.,Ақгул м.К.

5.2 Features of reliability
The main characteristics of reliability are: reliability, durability, maintaina-
bility and maintainability [22].
Infallibility is the property of the product to remain permanently operable 
for a given time or operating time. This property is especially important for 
PR, the failure of which is associated with the danger to human life, with 
interruptions in work and the stopping of automated production or with the 
marriage of an expensive product.
Indicators of infallibility operation. The probability of failure-free operation 
P(t
o
) is the probability that a failure will not occur within a given operating 
time:
P(t
o
) = 1 – F(t
0
)
where F(t
0
) is the distribution function of the time between failures.
The average operating time to failure is the mathematical expectation of the 
operating time to failure of the non-renewable product. By working time we 
understand the duration or volume of the work done by the object.
Mean time between failures is the ratio of the operating time of the object to 
be restored to the mathematical expectation of the number of its failures during 
this operating time.


241
The failure rate 
λ(t)
is the conditional probability density for the failure of 
an unrestored object for the time under consideration, provided that there was 
no failure until this time.
It is defined as the ratio of the average number of objects that failed in a 
unit of time (or the operating time in other units) to the number of objects that 
remain workable:
Approximately:
where 
n
is the number of products that failed during the test during the time 
interval Δt; 
N
is the total number of products tested.
For most objects, the dependence 
λ(t)
can be represented by a curve (figure 
5.1) having three sections
Figure 5.1
The first segment 0 ≤ t ≤ t
1
is called the run-in period or the period of 
early failures. The appearance of failures during this period is usually caused 
by structural or production defects. The second section t

< t < t
2
of constant 
intensity characterizes the normal operation on this section 
P(t)
= e
-
λt
. The third 
section t > t
2
is called the period of wear failures.
Parameter flow of failures is an indicator of reliability of restored products 
equal to the ratio of the average number of failures of restored object for 
arbitrarily small time to value the achievements (corresponds to the failure rate 
for parameters products, but includes repeated failures).
Durability is a property products keep working to limit state, with the 
necessary breaks for maintenance and repair.
Performance durability. Technical resource (resource) – life object from 
the beginning of its operation or renewal of operation after repair before 


242
 
 

a limiting condition. The resource is expressed in units of time (hours) path 
length (kilometers) units of output. For non-repairable products, the concept of 
technical resource and time to failure are the same.
Service life – calendar life up to limiting state. Express usually in the years. 
For details of mechatronic modules as a criterion for durability of use technical 
resource. Durability is divided into gamma-percent average to the current (or 
major) repair, complete, average to disposal. They characterize the longevity 
of the products for a given probability of preservation of health. For example, 
gamma-percent life tγ is the time at which the object will not reach limit state 
with given probability at expressed in percentage. 
For products of serial and mass production the most often used 90% of 
the resource. If the refusal is dangerous to human life, the resource closer to 
100%. Maintainability – adaptability of the product to the prevention, detec-
tion and elimination of failures and malfunctions by carrying out maintenance 
and repairs. Persistence is a property of the product to preserve the value of 
indicators of reliability, durability and maintainability during and after an 
established period of storage and transportation.
Indicators of maintainability and persistence. The average time to recover a 
healthy state, the shelf life is average and percent. 
Comprehensive reliability. Coefficient of technical use – the ratio of 
expected uptime for a certain period of operation to the sum of mathematical 
expectations of uptime and downtime for all repairs and maintenance.
Availability – the probability that the object will be in working state at any 
time, except for periods in which operation is not provided. It is defined as the 
ratio of expected time spent in a healthy state to mathematical expectation of 
amount of this time and unscheduled repairs.


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