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A flexible distribution and its application in reliability engineering

机译：灵活分配及其在可靠性工程中的应用

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摘要

Probability distributions of random variables are necessary for reliability evaluation. Generally, probability distributions are determined using one or two parameters evaluated from the mean and standard deviation of statistical data. However, these distributions are not sufficiently flexible to represent the skewness and kurtosis of data. This study therefore proposes a probability distribution based on the cubic normal transformation, whose parameters are determined using the skewness and kurtosis, as well as the mean and standard deviation of available data. This distribution is categorized into six different types based on different combinations of skewness and kurtosis. The boundaries of each type are identified, and the completeness of each type is proved. The cubic normal distribution is demonstrated to provide significant flexibility, and its applicable range covers a large area in the skewness kurtosis plane, thus enabling it to approximate well-known distributions. The distribution is then applied in reliability engineering: simulating distributions of statistical data, calculating fourth-moment reliability index, finding optimal inspection intervals for condition-based maintenance system, and assessing the influence of input uncertainties on the whole output of a system. Several examples are presented to demonstrate the accuracy and efficacy of the distribution in the above-mentioned reliability engineering practices.
机译：随机变量的概率分布对于可靠性评估是必需的。通常，概率分布是根据统计数据的平均值和标准偏差评估的一个或两个参数确定的。但是，这些分布的灵活性不足以表示数据的偏度和峰度。因此，本研究提出了基于三次正态变换的概率分布，其三次方正态分布的参数是使用偏度和峰度以及可用数据的均值和标准差确定的。基于偏度和峰度的不同组合，此分布分为六种不同类型。确定每种类型的边界，并证明每种类型的完整性。立方正态分布被证明具有显着的灵活性，其适用范围覆盖了偏度峰度平面中的大面积区域，因此使它近似于众所周知的分布。然后将该分布应用于可靠性工程：模拟统计数据的分布，计算第四时刻的可靠性指标，找到基于状态的维护系统的最佳检查间隔以及评估输入不确定性对系统整体输出的影响。给出了几个示例，以证明上述可靠性工程实践中分布的准确性和有效性。

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