Calculator
Formula used
Series reliability: Rsystem = Π Ri
Failure-rate model: Ri = e-λiti
Adjusted component reliability: Ri,adj = Ri × di
System failure probability: Qsystem = 1 - Rsystem
Equivalent failure rate: λeq = -ln(Rsystem) / T, when mission time is consistent.
The calculator assumes statistically independent components in a pure series arrangement. Any component failure causes total system failure, so the product rule is appropriate for this model.
How to use this calculator
- Select Direct reliability or Failure rate and mission time.
- Set the common mission time, target reliability, and decimal precision.
- Enter one row for each component in the series chain.
- Use derating when you want a conservative adjustment.
- Leave mission time override blank to use the common mission time.
- Click Calculate reliability to show the result block above the form.
- Review the chart, cumulative values, weakest component, and target status.
- Export the summary using the CSV or PDF buttons.
Example data table
| Component | Direct Reliability | Derating Factor | Adjusted Reliability |
|---|---|---|---|
| Sensor Module | 0.9950 | 1.0000 | 0.9950 |
| Main Controller | 0.9920 | 1.0000 | 0.9920 |
| Power Supply | 0.9890 | 1.0000 | 0.9890 |
| Output Relay | 0.9970 | 1.0000 | 0.9970 |
Example series reliability = 0.9950 × 0.9920 × 0.9890 × 0.9970 = 0.973254. This shows how several strong components can still produce a noticeably lower system reliability in series.
FAQs
1) What does series system reliability mean?
It means every component must function for the full system to succeed. If one item fails, the complete series path fails, so system reliability is the product of component reliabilities.
2) When should I use direct reliability mode?
Use direct mode when you already know each component’s reliability over the mission period. It is faster and works well for vendor data sheets, test results, or previously calculated component values.
3) When should I use failure-rate mode?
Use failure-rate mode when you know λ and mission time. The calculator converts them into reliability with the exponential model, then applies the series product to find system performance.
4) What does the derating factor do?
Derating scales component reliability downward for conservative planning. A factor of 1 keeps the original value. A factor below 1 reduces it to reflect uncertainty, stress, or harsher operating assumptions.
5) Why is the system reliability lower than most components?
That is normal in series systems. Even very reliable parts multiply together, so the combined result drops as more components are added. Long chains usually need redundancy to improve total reliability.
6) What is the importance share percentage?
It estimates how much each adjusted component contributes to total reliability loss. Higher shares highlight components that deserve closer design review, quality improvement, or redundancy analysis.
7) Why might equivalent failure rate be hidden?
It is hidden when component mission times are inconsistent. A single equivalent rate is most meaningful when the system result corresponds to one common mission duration across all components.
8) Can I use this for parallel or mixed systems?
This page is designed for pure series systems only. Parallel, standby, and mixed architectures need different equations and should be modeled with a dedicated reliability block or fault-tree approach.