Does a 10% percentile mean 10% survive?

No, it means the model predicts 10% have failed by that life. The surviving fraction is 90%.

Is characteristic life the average life?

No, characteristic life is the scale parameter. The mean depends on the shape, and the median is shown separately here.

Can I use a duty multiplier as the shape?

No, beta is a fitted Weibull shape parameter. An arbitrary duty multiplier does not describe a failure distribution.

Why is a 100% failed percentile unavailable?

The Weibull model reaches complete population failure only as time approaches infinity. A finite life requires a failed percentage below 100%.

Maintenance & Reliability calculator

Weibull Percentile Life Calculator

Estimate the life associated with a chosen failed-population percentile. Enter fitted Weibull scale and shape parameters, the failed percentage and your required percentile life.

What this calculator does

Estimate a failed-population life percentile from an accepted two-parameter Weibull model.

Formula used

Percentile life = eta × (−ln(1 − failed percentage ÷ 100))^(1 ÷ beta)
Median life = eta × ln(2)^(1 ÷ beta)
Surviving percentage = 100 − failed percentage
Life margin = percentile life − required percentile life

Inputs explained

Characteristic Life: Fitted Weibull scale parameter for the intended operating conditions.
Weibull Shape: Positive shape parameter from your fitted reliability model.
Failed Population Percentile: Population fraction expected to fail by the reported life.
Required Percentile Life: Your required life at this same failed-population percentile.

How to use the result

Best suited to fitted life model Review, percentile requirement comparison.
This calculation does not fit parameters or establish confidence bounds. A life percentile is a population statement, not an individual replacement deadline.

Current U.S. benchmarks

U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).

Common questions

Does a 10% percentile mean 10% survive? No, it means the model predicts 10% have failed by that life. The surviving fraction is 90%.
Is characteristic life the average life? No, characteristic life is the scale parameter. The mean depends on the shape, and the median is shown separately here.
Can I use a duty multiplier as the shape? No, beta is a fitted Weibull shape parameter. An arbitrary duty multiplier does not describe a failure distribution.
Why is a 100% failed percentile unavailable? The Weibull model reaches complete population failure only as time approaches infinity. A finite life requires a failed percentage below 100%.

Last reviewed 2026-10-06.