Weibull distribution

简明释义

韦布尔分布

英英释义

例句

1.The researchers applied the Weibull distribution 韦布尔分布 to model the time until failure for mechanical systems.

研究人员应用韦布尔分布 Weibull distribution来模拟机械系统的故障时间。

2.Using the Weibull distribution 韦布尔分布, they were able to predict when maintenance should be performed.

通过使用韦布尔分布 Weibull distribution，他们能够预测何时应该进行维护。

3.In their study, they found that the life span of the components followed a Weibull distribution 韦布尔分布 pattern.

在他们的研究中，他们发现组件的寿命遵循了韦布尔分布 Weibull distribution模式。

4.They plotted the survival function using the Weibull distribution 韦布尔分布 to visualize the reliability of the system.

他们使用韦布尔分布 Weibull distribution绘制生存函数，以可视化系统的可靠性。

5.The reliability engineers used the Weibull distribution 韦布尔分布 to analyze the failure rates of the new product.

可靠性工程师使用韦布尔分布 Weibull distribution来分析新产品的故障率。

作文

The Weibull distribution is a continuous probability distribution named after Wallodi Weibull, who described the distribution in 1951. It has gained significant importance in reliability engineering and failure analysis due to its versatility in modeling various types of data. The Weibull distribution can be used to model life data, which makes it invaluable for predicting product life cycles and understanding failure rates. Its flexibility allows it to represent different types of failure rates, making it applicable in various fields such as engineering, finance, and environmental studies.One of the key features of the Weibull distribution is its shape parameter, often denoted as beta (β). This parameter influences the shape of the distribution and the behavior of the failure rate. When β < 1, the distribution indicates that the failure rate decreases over time, suggesting that products are 'burning in' and becoming more reliable as they age. When β = 1, the Weibull distribution simplifies to the exponential distribution, indicating a constant failure rate over time. Conversely, when β > 1, the failure rate increases with time, suggesting that products are aging and more likely to fail as they reach the end of their life cycle.The scale parameter, denoted as eta (η), stretches or compresses the distribution along the time axis. This means that by adjusting η, one can model the life span of products more accurately. For instance, if we want to analyze the life expectancy of a specific type of machinery, we can use the Weibull distribution to fit the data collected from past failures. By estimating the parameters β and η, we can gain insights into how long we can expect the machinery to operate before failure occurs.In practical applications, the Weibull distribution is widely used in reliability testing and risk assessment. Engineers often employ this distribution to determine the reliability of products under various conditions. For example, in the automotive industry, manufacturers may use the Weibull distribution to analyze the failure rates of different components, allowing them to improve design and manufacturing processes to enhance product reliability.Moreover, the Weibull distribution is not limited to engineering alone; it also finds applications in finance where it can model the time until an event occurs, such as the default on a loan or the failure of a financial asset. In environmental studies, the Weibull distribution can help model the time between natural disasters or the lifespan of ecological systems.In conclusion, the Weibull distribution is a powerful statistical tool that provides valuable insights across various domains. Its ability to model different failure rates through the adjustment of its parameters makes it an essential method for engineers, financial analysts, and researchers alike. Understanding the Weibull distribution empowers professionals to make informed decisions based on the likelihood of failure and the expected lifespan of products and systems, ultimately leading to improved designs and better risk management strategies.

威布尔分布是一种连续概率分布，以Wallodi Weibull的名字命名，他在1951年描述了该分布。由于其在可靠性工程和故障分析中的重要性，威布尔分布被广泛应用于建模各种类型的数据。威布尔分布可用于建模寿命数据，这使它在预测产品生命周期和理解故障率方面具有不可或缺的价值。它的灵活性使其能够表示不同类型的故障率，因此在工程、金融和环境研究等多个领域都有应用。威布尔分布的一个关键特征是其形状参数，通常用β（beta）表示。该参数影响分布的形状和故障率的行为。当β < 1时，分布表明故障率随时间减少，暗示产品正在“磨合”，随着使用时间的增加变得更加可靠。当β = 1时，威布尔分布简化为指数分布，表明故障率在时间上保持不变。相反，当β > 1时，故障率随时间增加，暗示产品在老化，随着使用时间的增加更可能发生故障。规模参数η（eta）则沿时间轴拉伸或压缩分布。这意味着通过调整η，可以更准确地建模产品的寿命。例如，如果我们想分析某种机械设备的预期寿命，我们可以使用威布尔分布来拟合从过去故障中收集的数据。通过估计参数β和η，我们可以深入了解在发生故障之前，我们可以期望机械设备运行多长时间。在实际应用中，威布尔分布被广泛用于可靠性测试和风险评估。工程师经常使用该分布来确定在各种条件下产品的可靠性。例如，在汽车工业中，制造商可能会使用威布尔分布来分析不同部件的故障率，从而改进设计和制造过程，提高产品的可靠性。此外，威布尔分布不仅限于工程领域；它还在金融领域找到了应用，可以建模事件发生的时间，例如贷款违约或金融资产的失败。在环境研究中，威布尔分布可以帮助建模自然灾害之间的时间或生态系统的寿命。总之，威布尔分布是一种强大的统计工具，为各个领域提供了宝贵的见解。通过调整其参数建模不同的故障率，使其成为工程师、金融分析师和研究人员的重要方法。理解威布尔分布使专业人士能够根据故障的可能性和产品及系统的预期寿命做出明智的决策，最终导致更好的设计和更有效的风险管理策略。