Note: The information below is provided as an overview of Availability, Reliability and Maintainability and .. More detailed
and reliable information is provided at the sites linked at the bottom of this page...
General An item or system is specified, procured, and designed to a functional requirement
and it is important that it satisfies this requirement. However it is also
desirable that the the item or system should be predictably available and this depends upon
the its reliability and availability. For some disposable products in our modern
society the availability requirement may be acceptably low. For a large range of
consumer products the availability, based on high reliability, is an important selling point.
For items and systems used in critical areas including military equipment, process plant ,
and the nuclear industry, the
availability, reliability and maintainability considerations are vital. AvailabilityThe ability of an item to be in a state to perform a required function under
given conditions at a given instant of time or during a given time interval,
assuming that the required external resources are provided.
Availability = Uptime / (Downtime + Uptime) The time units are generally hours and the time base is 1 year . There are 8760 hours in one year. Availability(Intrinsic) A _{i} = MTBF / (MTBF + MTTR) MTBF = Mean time between failures.. Availability (Operational) A _{o} = MTBM/(MTBM+MDT). MTBM = Mean time between maintenance.. ReliabilityThe ability of an item to perform a required function under given
conditions for a given time interval. The bathtub curve for mass produced mechanical items is controlled to minimise the initial early failure period by use of quality control to ensure uniformity of production of high reliability items. Before items are introduced onto the market they are rigorously tested to identify and correct design and manufacturing problems. A prime target of design, manufacturing and operation is to ensure that the useful life is extended by attention to the following factors.
For systems with items in series the overall reliability is the product of the reliabilities
of the individual components.. MaintainabilityThe ability of an item under given conditions of use, to be retained in,
or restored to, a state in which it can perform a required function, when maintenance is performed under given conditions and using stated procedures and resources.

Basic Notes on Factor of Safety The factor of safety also known as Safety Factor, is used to provide a design margin over the theoretical design capacity to allow for uncertainty in the design process. The uncertainty could be any one of a number of the components of the design process including calculations, material strengths, duty, manufacture quality. The value of the safety factor is related to the lack of confidence in the design process. The simplest interpretation of the Factor of Safety is FoS = Strength of Component / Load on component If a component needs to withstand a load of 100 Newtons and a FoS of 4 is selected then
it is designed with strength to support 400 Newtons...
Repeated Cyclic loads : A convenient method of ensuring safe confident design is to use design codes;
A good standard used by mechanical engineer is 
Note: The information below is provided as an overview of failure distributions.. More detailed
and reliable information is provided at the sites linked at the bottom of this page...
Introduction In determining the lifetime reliability of a population of components (bearings, seals, gears etc.)
sample information is obtained from testing programmes and operational feedback on the failure
history of components belonging to the population. From the information obtained
it is possible to produce a graph of the probability density function f(t).
This is a plot of the frequency at which components fail as a function of time divided by the whole
population. Associated with the pdf is the Cumulative Density Function F(t). This is simply
a plot of the cumulative fraction of the failure population against time. It is the integral
of the f(t) against time (t). This effectively means that at time 0 no failures have occurred. At infinity the whole population of components will have failed. Reliability The reliability may be expressed that.. for time = a ( e.g 10 years ) there is a 90% chance of the item surviving (not failing)... = 1 in 10 is likely to fail. Hazard Rate The hazard rate may be expressed as... the failure rate will be 2 x 10 ^{4} (failures /unit time) or 2 failures per 10 ^{4} time units Mean Life Function The mean life provides the average life to failure of components is also called the
Mean Life Between Failures (MLBF) and the Mean Time to Failures (MTTF) The MTTF /MTBF may be expressed as say 1,000 hours at which 50% of units have failed Failure Distributions The pdf curve can take many forms....Some of the different distributions are listed below Normal Distribution One curve representing purely random events
is the normal (gaussian) curve. The equation for the normal distribution is :
Both of these parameters are estimated from the data, i.e. the mean and standard deviation of the data.
From these parameters f(t) is fully defined enabling evaluation of f(t) from any value of t.
The Lognormal Distribution The lognormal distribution is commonly used for general reliability analysis, cycles
to failure in fatigue and material strengths and loading.
Weibull Distribution The Weibull distribution is a generalpurpose reliability distribution used to model material strength, timestofailure of electronic and mechanical components, equipment, or systems. In its most general case, the threeparameter Weibull pdf is defined by: with three parameters, where :
If the location parameter γ is assumed to be zero
then the distribution is known as the twoparameter Weibull distribution... The β = shape parameter gives indications on the prevalent failure modes.
The Exponential Distribution The exponential distribution is a commonly used distribution in reliability
engineering. Mathematically, it is a fairly simple distribution,
which sometimes leads to its use in inappropriate situations.
This distribution is used to model the behavior of units that have a
constant failure rate.
The mean time to failure of this distribution is If the location parameter γ is assumed to be zero then the distribution is called the one parameter exponential distribution. The mean time to failure and the reliability of this distribution is 