Syntax
WEIBULL(x, alpha, beta, cumulative)
| Parameter | Description |
|---|---|
| x | Parameter of the WEIBULL function. |
| alpha | Parameter of the WEIBULL function. |
| beta | Parameter of the WEIBULL function. |
| cumulative | Parameter of the WEIBULL function. |
Examples
Probability of failure within 2 years
Formula
=WEIBULL(2, 1.5, 5, TRUE)
Returns ~0.1647. With shape=1.5 (increasing failure rate) and scale=5 years, about 16.5% of units fail within the first 2 years.
Survival probability
Formula
=1-WEIBULL(10000, 2, 8000, TRUE)
Returns ~0.2096. About 21% of components survive past 10,000 hours when the Weibull shape is 2 (linearly increasing failure rate) and scale is 8,000 hours.
PDF for failure rate analysis
Formula
=WEIBULL(3, 2, 4, FALSE)
Returns ~0.1902. The probability density at t=3 with shape=2 (Rayleigh distribution) and scale=4.
Common Errors
#NUM!
x must be non-negative, and both alpha (shape) and beta (scale) must be positive.
#VALUE!
Occurs when arguments are non-numeric.
Tips
Shape parameter interpretation
alpha < 1: decreasing failure rate (infant mortality). alpha = 1: constant failure rate (exponential distribution). alpha > 1: increasing failure rate (wear-out).
Scale is the characteristic life
The scale parameter (beta) is the time at which 63.2% of units have failed, regardless of the shape parameter. It is also called the characteristic life in reliability.
Reliability function
The reliability (survival) function is simply =1 - WEIBULL(t, alpha, beta, TRUE). This gives the probability of surviving past time t.
Try WEIBULL in Viztab
Import your data and use WEIBULL with 370+ other formulas. No signup required.
Open Viztab