KEVOS® MAKEOS · Maintenance
System Reliability from Weibull Components (Series and Redundancy)
What is the chance this machine runs a mission without failure when its components wear out on Weibull curves, and does redundancy on one item get it to target?
Reliability of a system of up to four component blocks in series, each with its own Weibull shape and characteristic life (as the Weibull reliability tool) and a number of identical units in active redundancy: component and block reliability at the mission time, system reliability, the weakest block, and the system mean time to failure by numerical integration of the system reliability curve.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Mission time | h | Operating time the system must survive. |
| Target system reliability | % | Reliability the system must reach over the mission. |
| Block 1 | ||
| Block 1 Weibull shape β | Weibull shape of the units in block 1 (below 1 early failures, 1 random, above 1 wear-out). | |
| Block 1 characteristic life η (0 = not used) | h | Characteristic life of the units in block 1, where 63.2% have failed; 0 if the block is not used. |
| Block 1 identical units in parallel | Number of identical units sharing the job in block 1 (1 for a single unit; 2 for a duty/standby pair running together). | |
| Block 2 | ||
| Block 2 Weibull shape β | Weibull shape of the units in block 2 (below 1 early failures, 1 random, above 1 wear-out). | |
| Block 2 characteristic life η (0 = not used) | h | Characteristic life of the units in block 2, where 63.2% have failed; 0 if the block is not used. |
| Block 2 identical units in parallel | Number of identical units sharing the job in block 2 (1 for a single unit; 2 for a duty/standby pair running together). | |
| Block 3 | ||
| Block 3 Weibull shape β | Weibull shape of the units in block 3 (below 1 early failures, 1 random, above 1 wear-out). | |
| Block 3 characteristic life η (0 = not used) | h | Characteristic life of the units in block 3, where 63.2% have failed; 0 if the block is not used. |
| Block 3 identical units in parallel | Number of identical units sharing the job in block 3 (1 for a single unit; 2 for a duty/standby pair running together). | |
| Block 4 | ||
| Block 4 Weibull shape β | Weibull shape of the units in block 4 (below 1 early failures, 1 random, above 1 wear-out). | |
| Block 4 characteristic life η (0 = not used) | h | Characteristic life of the units in block 4, where 63.2% have failed; 0 if the block is not used. |
| Block 4 identical units in parallel | Number of identical units sharing the job in block 4 (1 for a single unit; 2 for a duty/standby pair running together). | |
Method and formulas
- Unit reliability R = exp[−(t ÷ η)^β] (as the Weibull reliability tool).
- Block with k units in active redundancy R_b = 1 − (1 − R)^k; system in series R_s = Π R_b.
- System MTTF = ∫ R_s(t) dt, integrated numerically.
- Example: over 2000 h the system reliability is 92.945%; block 1 is the weakest; MTTF about 7,426.2 h.
Limitations
- Independent failures; common-cause failures defeat redundancy.
- Active redundancy with perfect switching; standby units need a different model.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a machine against a reliability target
- See whether a redundant pump or fan is worth it
- Find the component that limits reliability
Who it is for
- Reliability engineers
- Maintenance engineers
- Design engineers
What you get
- Unit and block reliability at the mission time
- System reliability and the weakest block
- System mean time to failure
Interpreting the result
- Redundancy helps most on the weakest block; doubling an already reliable block adds little.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
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Open the System Reliability from Weibull Components (Series and Redundancy) calculator
