keisoku

Weibull Distribution Percent Point (Quantile) Calculator

Find the Weibull percent point x=λ(−ln(1−p))^(1/k) from probability p, shape k and scale λ, with B10/B50 life and reliability.

Input

Enter the probability p, the method, the shape parameter k and the scale parameter λ to compute the Weibull percent point (quantile) x=λ(−ln(1−p))^(1/k).

Probability for the percent point. Enter a value greater than 0 and less than 1.

Method

Choose whether the input p is treated as cumulative failure probability or as reliability.

Weibull shape parameter. Enter a positive value (k=1 gives the exponential distribution).

Weibull scale parameter (characteristic life). Enter a positive value.

Result

Percent point x for p = 0.1, k = 2, λ = 1,000

324.59284597

B10 life (F = 0.1)

324.59284597

B50 life (median)

832.55461116

Cumulative F(x)

0.1

Reliability R(x)

0.9

Density f(x)

0.00058427

Mean life

886.22692545

Variance

214,601.83660255

Probability density function (PDF)

Cumulative distribution function (CDF)

How it works

  • The percent point is the inverse of the CDF F(x)=1−exp(−(x/λ)^k) and is given by the closed form x(p)=λ(−ln(1−p))^(1/k).
  • Choosing cumulative failure treats the input p as the cumulative failure probability, while choosing reliability treats p as reliability R and uses 1−R as the cumulative failure probability before computing the quantile.
  • B10 life is the time at which 10 percent cumulative failure is reached (quantile at p=0.1), and B50 life is the median (quantile at p=0.5).
  • The mean is λ·Γ(1+1/k) and the variance is λ²·[Γ(1+2/k)−Γ(1+1/k)²], with the gamma function evaluated by the Lanczos approximation.
  • Shape k=1 gives the exponential distribution and k=2 the Rayleigh distribution. Larger k means less spread in failure times.

Reviews

Tell us what you think of this calculator.

Write a review

  1. Home

  2. Weibull Distribution Percent Point (Quantile) Calculator