Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Reliability of Machine Components

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

Sponsored Links

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 at a given time:

R = e-λt                                (1)


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


The connection between reliability and unreliability:

R + Q = 1                              (2)


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)


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)


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)


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)


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)

Sponsored Links

Related Topics

Related Documents

Tag Search

  • en: reliability machine components mtbf mean time failure
Sponsored Links

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate this page to
About the Engineering ToolBox!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.


This page can be cited as

  • Engineering ToolBox, (2005). Reliability of Machine Components. [online] Available at: [Accessed Day Mo. Year].

Modify access date.

. .


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

11 29

Sponsored Links