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Reliability of Machine Components

Mean Time Between Failure - MTB and reliability of machine components and systems

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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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