Weibull Distribution Calculator
Calculate P(X < x) for the Weibull distribution.
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Enter the shape parameter k, the scale parameter lambda, and the x value. The calculator computes the CDF (failure probability), reliability (survival probability), and the hazard rate at x.
About This Calculator
The Weibull distribution is widely used in reliability engineering and survival analysis. When k < 1, the failure rate decreases over time (infant mortality). When k = 1, it becomes the exponential distribution (constant failure rate). When k > 1, the failure rate increases over time (wear-out). The scale parameter lambda determines the characteristic life.
Frequently Asked Questions
What does the shape parameter control?
The shape parameter k determines the failure behavior. k < 1: decreasing failure rate. k = 1: constant (exponential). k > 1: increasing failure rate. k = 2 gives the Rayleigh distribution.
What is the scale parameter?
Lambda is the characteristic life. At x = lambda, 63.2% of units will have failed regardless of the shape parameter.
How is Weibull used in reliability?
Engineers fit failure data to a Weibull distribution to predict product lifetime, warranty costs, and maintenance schedules.