Weibull Distribution Calculator
Compute Weibull distribution probabilities, failure rates, and reliability metrics with interactive survival and hazard visualization.
The Weibull distribution is the most widely used model in reliability engineering and survival analysis. Its shape parameter controls whether the failure rate is decreasing, constant, or increasing over time, making it versatile enough to model infant mortality, random failures, and wear-out mechanisms.
Use this calculator to compute survival probabilities, estimate component lifetimes, and visualize how the shape and scale parameters affect the hazard function and failure-time distribution.
Launch the Weibull Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhat does the shape parameter control in a Weibull distribution?
When shape < 1, the failure rate decreases over time (infant mortality). When shape = 1, it is constant (exponential). When shape > 1, the failure rate increases (wear-out). This single parameter makes Weibull extremely flexible for reliability modeling.
How is Weibull related to the exponential distribution?
The exponential distribution is a special case of the Weibull with shape parameter equal to 1, corresponding to a constant failure rate.
How do I interpret the scale parameter?
The scale parameter is the characteristic life: approximately 63.2% of units will have failed by this time, regardless of the shape parameter.