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.

The economic justification for a project is generally based on the lifetime cost of the project.  A major contribution to this cost involves an evaluation of the availability reliability and maintainability of the equipment..

The 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.

At its simplest level..

Availability = Uptime / (Downtime + Uptime)

The time units are generally hours and the time base is 1 year .  There are 8760 hours in one year.

From the design area of concern this equation translates to ..

Availability(Intrinsic) A _i = MTBF / (MTBF + MTTR)

MTBF = Mean time between failures..
MTTR = Mean time to repair / Mean time to replace.

Operational availability is defined differently

Availability (Operational) A _o = MTBM/(MTBM+MDT).

MTBM = Mean time between maintenance..
MDT = Mean Down Time

The ability of an item to perform a required function under given conditions for a given time interval.

The reliability is expressed as a probability (0-1 or 0 to 100%).  Thus the reliability of a component may be expressed as 99% that it will work successfully for one year. The reliability is essentially an indication of probability that a the item will not fail in the given time period.

A very generalised curve for the failure rates of components over time is the bathtub curve.   This shows that in the early period a number of failures result from manufacturing, assembly, commissioning, setting to work problems.  When all of the teething problems have been eliminated the remaining population has a useful life over which the items fail at a relatively low rate.  After a long operating time interval the items will fail at an increasing rate due to wear and other time related functions.   This curve applies mostly to electronic components which is why electronic products are operated continuously for set times (burn-in) prior to delivery to users..

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..

For systems with active items in parallel the resulting reliability is improved. For example if there are two items in parallel A (Reliability Ra) and B (Reliability Rb).  The overall reliability is = 1-(1-Ra)*(1-Rb)

The 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.

When a piece of equipment has failed it is important to get it back into an operating condition as soon as possible, this is known as maintainability.   To calculate the maintainability or Mean Time To Repair (MTTR) of an item, the time required to perform each anticipated repair task is multiplied by the relative frequency with which that task is performed(e.g. no. of times per year).    MTTR data supplied by manufacturers will be purely repair time which will assume the fault is correctly identified and the required spares and personnel are available.   The MTTR to the user will include the logistic delay as shown below.  The MTTR should also include factors such as the skill of the maintenance engineers

MTTR User factors...