Reliability of Machine Components
Mean Time Between Failure - MTB and reliability of machine components and systems
Reliability characterizes components or system of components by the probability they will perform the desired functions for a given time.
In general -
- more components and/or more complicated systems reduces reliability
- simpler systems with few components increases reliability
Reliability equations:
Reliability
Reliability at a given time:
R = e-λt (1)
where
R = reliability. Values between 0 - 1 where value 1 indicates 100% live components and value 0 indicates 0% live components.
λ = proportional failure rate - a failure rate expressed as a proportion of initial number of live components - No
t = time
Unreliability
The connection between reliability and unreliability:
R + Q = 1 (2)
where
Q = unreliability. Values between 0 - 1 where value 1 indicates 0% live components and value 0 indicates 100% live components.
(1) and (2) can be used to express unreliability
Q = 1 - e-λt (3)
Number of Live Components
The number of live surviving components in a system at a given time:
Ns = No e-λt (4)
where
Ns = number of live surviving components at time t
No = initial number of live surviving components at time zero
Number of Failure Components
The number of failure dead components in a system at a given time:
Ns = No (1 - e-λt) (5)
where
Ns = number of live surviving components at time t
No = initial number of live surviving components at time zero
Mean Time Between Failures - MTBF
Mean time between failures - MTBF:
m = 1 / λ (6)
where
m = MTBF - Mean Time Between Failure
- MTTF - Mean Time To Failure is also used and equal to MTBF
Mean Time Between Failure (MTBF) can be determined by rating Total Surviving Hours against Number of Failures as
m = ts / nf (7)
where
ts = total surviving hours
nf = number of failures
Combining (5) with the formulas for reliability and more
R = e-t/m (1b)
Q = 1 - e-t/m (3b)
Ns = No e-t/m (4b)
Ns = No (1 - e-t/m) (5b)
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