How to use the series system reliability calculator
Find the reliability of a system that fails if any one of its components fails. Enter reliability of component 1, reliability of component 2, reliability of component 3 in the fields above; the system reliability (all must work), probability of failure are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “series system reliability”, “chain reliability”, “product of component reliabilities”, “calculate series system reliability”, “find system reliability”.
Formula
Variables
- r1 — Reliability of component 1
- r2 — Reliability of component 2
- r3 — Reliability of component 3
Worked example
With reliability of component 1 = 0.99, reliability of component 2 = 0.95, reliability of component 3 = 0.98, the calculator gives system reliability (all must work) ≈ 92.169 %; probability of failure ≈ 7.831 %.
Frequently asked questions
What is the series system reliability calculator used for?
Find the reliability of a system that fails if any one of its components fails. It helps with questions such as “series system reliability”, “chain reliability”, “product of component reliabilities”.
What is the formula for the series system reliability calculation?
System reliability (all must work) (%) = 100 × r1 × r2 × r3. Probability of failure (%) = 100-[System reliability (all must work)]. Here r1 is reliability of component 1, r2 is reliability of component 2, r3 is reliability of component 3.
What inputs do I need for the series system reliability calculator?
You need reliability of component 1, reliability of component 2, reliability of component 3. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the series system reliability calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the series system reliability result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.