The Weibull distribution is a continuous probability distribution commonly used in reliability analysis and failure time modeling. It is characterized by its shape parameter, which determines the distribution's form, allowing it to model various types of failure rates. Depending on the value of this parameter, the distribution can represent increasing, constant, or decreasing failure rates. This distribution is particularly useful in fields like engineering and survival analysis, where it helps predict the lifespan of products or systems. The Weibull distribution can also be applied in various industries, including manufacturing and healthcare, to assess risks and improve reliability.