weibull distribution

简明释义

韦布尔分布

英英释义

例句

1.The failure rates of mechanical components can be effectively modeled using a weibull distribution (威布尔分布).

机械部件的故障率可以有效地使用weibull distribution (威布尔分布) 进行建模。

2.In survival analysis, researchers often use the weibull distribution (威布尔分布) to model time until an event occurs.

在生存分析中，研究人员经常使用weibull distribution (威布尔分布) 来建模事件发生的时间。

3.When analyzing wind speeds for turbine placement, a weibull distribution (威布尔分布) can provide insights into the expected energy output.

在分析风速以确定涡轮机位置时，weibull distribution (威布尔分布) 可以提供预期能量输出的见解。

4.The reliability analysis of the new product showed that it follows a weibull distribution (威布尔分布) with a shape parameter indicating increasing failure rates.

新产品的可靠性分析显示，它遵循一个weibull distribution (威布尔分布)，其形状参数表示故障率增加。

5.The software tool allows users to fit a weibull distribution (威布尔分布) to their data for better statistical analysis.

该软件工具允许用户将weibull distribution (威布尔分布) 拟合到他们的数据中，以便进行更好的统计分析。

作文

The concept of the weibull distribution is essential in the field of statistics and reliability engineering. It is a continuous probability distribution named after Wallodi Weibull, who described the distribution in detail in 1951. The weibull distribution is particularly useful for modeling life data, reliability data, and failure times of products. Its flexibility allows it to model various types of failure rates, which can either increase or decrease over time, making it a powerful tool for engineers and researchers.One of the significant features of the weibull distribution is its shape parameter, often denoted by beta (β). This parameter determines the shape of the distribution and consequently influences the behavior of the data being modeled. When β < 1, the distribution indicates that the failure rate decreases over time, which is typical for products that have a 'burn-in' period where early failures occur but are less likely as time goes on. Conversely, when β > 1, the failure rate increases with time, indicating aging effects or wear-out failures. When β = 1, the weibull distribution simplifies to the exponential distribution, suggesting a constant failure rate over time.Another important aspect of the weibull distribution is its scale parameter, often denoted by eta (η). This parameter stretches or compresses the distribution along the time axis. A larger η value indicates that the product has a longer life expectancy, while a smaller η value suggests a shorter lifespan. By adjusting these parameters, practitioners can fit the weibull distribution to a wide range of data sets, making it versatile for various applications.In practical applications, the weibull distribution is widely used in reliability analysis, where it helps predict product lifetimes and assess risks. For instance, a company manufacturing light bulbs may use the weibull distribution to estimate how long their bulbs will last under normal operating conditions. By analyzing historical failure data, they can determine the appropriate values for β and η, allowing them to make informed decisions about product design and quality control.Moreover, the weibull distribution plays a crucial role in survival analysis within medical research. Researchers can analyze patient survival times after treatment using this distribution. By fitting the weibull distribution to the data, they can identify factors affecting survival rates and improve treatment protocols based on statistical evidence.In conclusion, the weibull distribution is a fundamental concept in statistics, particularly in fields like reliability engineering and survival analysis. Its ability to model different failure rates through its shape and scale parameters makes it invaluable for predicting product lifetimes and understanding survival probabilities. As industries continue to seek ways to improve product reliability and optimize performance, the weibull distribution will undoubtedly remain a key analytical tool for engineers and researchers alike.

在统计学和可靠性工程领域，威布尔分布的概念至关重要。它是一种连续概率分布，以瓦洛迪·威布尔的名字命名，他在1951年详细描述了该分布。威布尔分布特别适用于建模生命数据、可靠性数据和产品的故障时间。它的灵活性使其能够建模各种类型的故障率，这些故障率可以随着时间的推移而增加或减少，从而成为工程师和研究人员的强大工具。威布尔分布的一个显著特征是其形状参数，通常用β表示。该参数决定了分布的形状，因此影响被建模数据的行为。当β < 1时，分布表明故障率随时间降低，这对于具有“老化”期的产品是典型的，此时早期故障发生，但随着时间的推移，故障的可能性较小。相反，当β > 1时，故障率随时间增加，表明老化效应或磨损故障。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。威布尔分布的另一个重要方面是其尺度参数，通常用η表示。该参数在时间轴上拉伸或压缩分布。较大的η值表明产品的预期寿命较长，而较小的η值则表明寿命较短。通过调整这些参数，实践者可以将威布尔分布拟合到各种数据集，使其在各种应用中都具有多样性。在实际应用中，威布尔分布广泛用于可靠性分析，帮助预测产品的使用寿命和评估风险。例如，一家制造灯泡的公司可以使用威布尔分布来估计其灯泡在正常操作条件下的使用寿命。通过分析历史故障数据，他们可以确定β和η的适当值，从而做出有关产品设计和质量控制的明智决策。此外，威布尔分布在医学研究中的生存分析中也发挥着关键作用。研究人员可以利用这种分布分析患者在治疗后的生存时间。通过将威布尔分布拟合到数据中，他们可以识别影响生存率的因素，并根据统计证据改善治疗方案。总之，威布尔分布是统计学中的一个基本概念，特别是在可靠性工程和生存分析等领域。它通过其形状和尺度参数建模不同的故障率，使其在预测产品寿命和理解生存概率方面具有重要价值。随着各行业继续寻求提高产品可靠性和优化性能的方法，威布尔分布无疑将继续成为工程师和研究人员的重要分析工具。