Enter reliability values, failure probabilities, MTBFs, or failure rates (depending on the tab) for up to 6 components to estimate system reliability.

System Reliability Calculator

Series/Parallel
k-out-of-n
Reliability vs Time
Availability
FIT/Rate Converter

System Reliability Formula

The following formula is used to calculate the system reliability of a series system (assuming independent component failures and that each value refers to the same mission time and operating conditions).

R = (1 - F1) * (1 - F2) * ... * (1 - Fn)
  • Where R is the system reliability (probability the system completes the mission without failure).
  • F1 to Fn are the failure probabilities (unreliabilities) of each component over the mission time, expressed as decimals in this formula (e.g., 50% = 0.50).

If you instead know constant failure rates (hazard rates) λi (e.g., failures per hour) and assume an exponential time-to-failure model, then each component has Ri(t) = e−λit and a series system has Rsys(t) = e−t(λ1+λ2+…+λn).

System Reliability Definition

What is system reliability?

System reliability is the probability that a system performs its intended function without failure for a specified period of time under stated conditions. (Availability, by contrast, is the fraction of time a repairable system is operational, accounting for downtime and repairs.)

The system reliability depends on each component when the system is set up in series. For example, if there are 3 components that all must work for the system to succeed, then (assuming independent failures) the system reliability is the product 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 probability of each component over the same mission time. In this problem, the failure probabilities are 25%, 30%, and 15%.

Finally, calculate the system reliability using the formula above:

R = (1 – F1) * (1 – F2) * (1 – F3)

R = (1 – .25) * (1 – .30) * (1 – .15)

R = .44625 = 44.625% reliability