Maintainability

Maintainability is defined as the probability of performing a successful repair action within a given time. In other words, maintainability measures the ease and speed with which a system can be restored to operational status after a failure occurs. For example, if it is said that a particular component has a 90% maintainability in one hour, this means that there is a 90% probability that the component will be repaired within an hour. In maintainability, the random variable is time-to-repair, in the same manner as time-to-failure is the random variable in reliability. As an example, consider the maintainability equation for a system in which the repair times are distributed exponentially. Its maintainability M(t) is given by:

Where μ = repair rate.

Note the similarity between this equation and the equation for the reliability of a system with exponentially distributed failure times. However, since the maintainability represents the probability of an event occurring (repairing the system) while the reliability represents the probability of an event not occurring (failure), the maintainability expression is the equivalent of the unreliability expression, (1 - R). Furthermore, the single model parameter μ is now referred to as the repair rate, which is analogous to the failure rate, λ, used in reliability for an exponential distribution.

Similarly, the mean of the distribution can be obtained by:

This now becomes the mean time to repair (MTTR) instead of the mean time to failure (MTTF).

The same concept can be expanded to other distributions. In the case of the Weibull distribution, maintainability, M(t), is given by:

While the mean time to repair (MTTR) is given by:

And the Weibull repair rate is given by:

As a last example, if a lognormal distribution is chosen, then:

Where:

mean of the natural logarithms of the times-to-repair.
standard deviation of the natural logarithms of the times-to-repair.

It should be clear by now that any distribution can be used, as well as related concepts and methods used in life data analysis. The only difference being that instead of times-to-failure we are using times-to-repair. What one chooses to include in the time-to-repair varies but can include:

The time it takes to successfully diagnose the cause of the failure.
The time it takes to procure or deliver the parts necessary to perform the repair.
The time it takes to gain access to the failed part or parts.
The time it takes to remove the failed components and replace them with functioning ones.
The time involved with bringing the system back to operating status.
The time it takes to verify that the system is functioning within specifications.
The time associated with "closing up" a system and returning it to normal operation.

In the interest of being fair and accurate, one should disclose (document) what was and was not included in determining the repair distribution.

Go to weibull.com
Go to ReliaSoft.com