BIZOMAT MAKEOS · Maintenance
Weibull Reliability and B10 Life
What is the probability this component survives to a given time, and what are its B10 life and MTTF?
Reliability, probability of failure, hazard rate, B10 life and mean time to failure from Weibull shape and scale parameters, for a mission or maintenance interval.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shape parameter β | Shape from a Weibull analysis of failure data (below 1: early failures; 1: random; above 1: wear-out). | |
| Scale parameter η (characteristic life) | h | Characteristic life: the time by which 63.2% have failed. |
| Mission time or interval | h | Operating time or maintenance interval to evaluate. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Shape parameter β
- What it is
- The Weibull shape parameter from an analysis of failure data, which describes whether failures come early, at random or from wear-out.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from a Weibull analysis of relevant failure data, not from an assumed value.
What this means: Scale parameter η (characteristic life)
- What it is
- The Weibull scale parameter, the characteristic life: the time by which a fixed share of units has failed, from the same Weibull analysis.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer characteristic life raises reliability and lengthens B10 life and mean life.
- Get it right
- Use the same time unit for this and the mission time.
What this means: Mission time or interval
- What it is
- The operating time or maintenance interval at which you want the reliability and failure probability.
- Units and format
- Enter a number in h: hours. The form accepts 0 h or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer time lowers reliability.
- Get it right
- Use the same unit as the characteristic life; operating hours and calendar hours differ.
Method and formulas
- R(t) = exp(−(t ÷ η)^β); F = 1 − R.
- Hazard h(t) = (β ÷ η)(t ÷ η)^(β − 1).
- B10 = η (−ln 0.9)^(1/β); MTTF = η Γ(1 + 1/β).
- Example: β 2, η 10000 h: reliability at 2000 h is 96.079%, B10 life 3,245.9 h.
Limitations
- Two-parameter Weibull (no failure-free period); parameters must come from relevant failure data.
- Preventive replacement only helps when β > 1 (wear-out).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set preventive maintenance intervals from failure data
- Estimate spares demand
- Explain wear-out versus random failures
Who it is for
- Maintenance engineers
- Reliability engineers
- Maintenance technicians
What you get
- Reliability at time t
- Probability of failure
- Hazard rate
- B10 life and MTTF
Interpreting the result
- With β ≤ 1, scheduled replacement does not reduce failures; use condition monitoring instead.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Thermal ageing and insulation life
In Insulation Testing by the Numbers
What it covers: Thermal classes, the Arrhenius model and the ten-degree rule, hot spots, equivalent ageing hours for C-1, Weibull life of windings, and a summer of overheating judged with the wrong activation energy.
Method explained here · BIZOMAT original book
Surfaces, scatter and proof
In Metal Fatigue by the Numbers
What it covers: How surface finish is specified and inspected at fatigue-critical points, how Weibull analysis reads a fleet's failures, and how tests and field checks prove a design's life.
Method explained here · BIZOMAT original book
Reliability and life
In Thermoelectric Cooling by the Numbers
What it covers: How thermoelectric coolers wear out, Weibull and series-system reliability for a cooler, field MTBF with confidence bounds, spares, and a thermostat that cycled a module to death.
Method explained here · BIZOMAT original book
Drive life: capacitors, fans and power cycling
In Variable-Speed Drives by the Numbers
What it covers: How temperature sets the life of a drive's DC link capacitors and cooling fans, how power cycling wears out power modules, and how to combine the parts into a drive reliability and a maintenance plan.
Method explained here · BIZOMAT original book
Why vibration reveals condition
In Vibration Monitoring by the Numbers
What it covers: How faults change vibration, the P-F interval between first sign and failure, why time-based replacement fails for random failures, monitoring intervals, and a quarterly route that missed a bearing.
Useful alongside · BIZOMAT original book
Are the stops random? Poisson counts and memoryless clocks
In Breakdowns and Buffers by the Numbers
What it covers: Testing a stoppage log for the randomness a Markov model assumes: Poisson counts per shift, a c chart for special causes, exponential intervals, repair time spread and wear-out parts.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.