Enter the failure rates of up to 5 components in series into the calculator to determine the system reliability.

## System Reliability Formula

The following formula is used to calculate the system reliability of a series system.

R = (1-F1) * (1-F2) * (1-F3) * (1-FX)….

• Where R is the reliability of the system
• F1 to FX are the failure rates of each component in the system. These failure rates are expressed as decimals in this formula. i.e, a failure rate of 50% = .50.

## System Reliability Definition

What is system reliability?

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.

## Example Problem

How to calculate system reliability?

The following example outlines how to calculate the system reliability of a system with multiple components in series.

First, determine the number of components in the system that can fail. For this example, there are 3 components.

Next, determine the failure rates of each component. In this problem, the failure rates are 25%, 30%, and 15%.

Finally, calculate the system reliability using the formula above:

R = (1-F1) * (1-F2) * (1-F3) * (1-FX)….

R = (1-.25) * (1-.30) * (1-.15)

R = .44625 = 44.625% reliability