The formula to calculate the system reliability (R) is:
\[ R = (1 - F1) \times (1 - F2) \times (1 - F3) \times \ldots \times (1 - FX) \]
Where:
System reliability is a measure of the percentage or ratio of time that a system is available to work, or has not undergone failure. The system reliability is dependent on each component in the system when the system is set up in series. For example, if there are 3 components that all need to work for the system to be available, then the reliability of the system is the product of each of the 3 components’ individual reliabilities.
Let's consider an example:
Using the formula to calculate System Reliability:
\[ R = (1 - 0.1) \times (1 - 0.2) \times (1 - 0.05) = 0.684 \]
This means that the system reliability for the given example is approximately 0.684 or 68.4%.