Reliability Equations

Failure rates of modules

(constant failure rates)

Failure ratesThe number of failures of an item per unit time. May be observed failure rate (e.g. from 'returns' data); assessed failure rate (from tests) or extrapolated (from tests at higher stress levels). are a little like electrical resistances, there is a serial configuration (when the moduleA collection of hardware components that are more or less permanently connected. If a component in the module fails the complete module is replaced. fails if one of the component fails) and a parallel configuration (when all the members of some set of components have to fail for the module to fail).

The overall failure rate (Fm) for serial components is given by:

where Fci are the failure rates of the components and ni are the numbers of components.

The failure rate (Fm) for parallel components is given by:

where Rc is the repair rateThe number of corrective maintenance actions that can be carried out in unit time. Corrective action should also include logistic allowance, diagnosis time, and time needed to bring the equipment fully back on line, unless some of these activities are considered elsewhere in calculations. of the components.

Note: there are many formulae for parallel redundancy depending on how/when failed components are repaired and how many working components are needed. The formulae above is the most optimistic and is the case when failed components are immediately repaired and only one is required.

Repair rates of modules

The overall repair rate (Rm) for serial components is given as a weighted average by:

The overall repair rate (Rm) for n parallel components is given by:

The reason for this slightly surprising result is that repair of the first failed component has already started when the last fails.

Availability of modules

The availabilityThe proportion of time that an item is capable of operating to specification within a large time interval. of a module or component is given by:

The unavailabilityThe propourtion of time that an item is incapable of operating to specification within a large time interval. Equals 1 - Availability. is simply 1-A.

The equations given on this page provide a first estimate of module and system reliability parameters, but contain a numerous approximations and assumptions.

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