Reliability

The reliability module will compute the reliability of simple systems. If it is used repeatedly, then complex systems can be developed. This module can easily be used to determine the appropriate number of backup (standby) pieces of equipment/components.

Data

The general framework for reliability is given by the number of simple systems which are in series and the maximum number of components in any simple system. By a simple system we mean that it is a set of parallel components without any series. In the example below we are setting up for a system with 4 simple systems in series. The largest number of components in any of these four simple systems is 6. There is only one type data which needs to be entered.

Component reliability. The required information is the reliability of each component. It is used for computing the reliability of the simple parallel series represented by the column.

Note: This is a module where using the option to not display zeroes will make the data display more readable.

Solution

A sample solution screen that also contains the data is given below. Notice that the row in which the probability is entered does not matter as exemplified by the fact that systems 1 and 2 each have the same reliability of 99%.

Simple system reliability. Below each parallel system (column) its reliability is presented. The reliability, r, of n components in parallel is given by:

r=1-(1-r₁)(1-r₂)...(1-r_n)

where r_j is the reliability of the j^th individual component. In the example, the first parallel set has a reliability of its one component which is .99, the same is true for the second set, the third has an overall reliability of .999856 as listed at the bottom of the third column and the fourth has a reliability of .999872.

System reliability. The overall system reliability is given at the bottom. The overall reliability is the product of the individual parallel series reliabilities. The example has a system reliability of .979834.

Example 2 - Determining the number of backups

It is possible to compute the number of backups required in order to ensure a specified system reliability for a parallel system. For example, suppose that the reliability of an individual component is 50% and the desired system reliability is 99%. Then, by creating a table with no backups, 1 backup, 2 backups, etc. the appropriate number of backups can be found. (This is an enumeration method). For the reliabilities specified as 50% and 99% we see from below that the appropriate number of components is 7 (6 backups).

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