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Bayesian reliability analysis for fuzzy lifetime data

机译：模糊寿命数据的贝叶斯可靠性分析

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摘要

Lifetime data are important in reliability analysis. Classical reliability estimation is based on precise lifetime data. It is usually assumed that observed lifetime data are precise real numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. Bayesian methods have proved to be very useful when the sample size is small. There is little study on Bayesian reliability estimation based on fuzzy lifetime data. Most of the reported works in this area is limited to single parameter lifetime distributions. In this paper, we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi-parameter lifetime distributions. An artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction. The genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level. This method can be used to determine the membership functions of the Bayesian estimates of multi-parameter distributions. The effectiveness of the proposed method is illustrated with normal and Weibull distributions.
机译：寿命数据在可靠性分析中很重要。经典的可靠性估算基于精确的寿命数据。通常假设观察到的寿命数据是精确的实数。但是，某些收集的寿命数据可能不准确，并以模糊数字的形式表示。因此，有必要将经典的统计估计方法从实数推广到模糊数。事实证明，当样本量较小时，贝叶斯方法非常有用。基于模糊寿命数据的贝叶斯可靠性估计研究很少。在该领域，大多数报道的工作仅限于单参数寿命分布。在本文中，我们提出了一种确定参数估计的隶属函数和多参数寿命分布可靠性函数的新方法。人工神经网络用于估计参数估计和可靠性预测的计算过程。遗传算法用于在任何切入水平下找到感兴趣的估计的隶属函数的边界值。该方法可用于确定多参数分布的贝叶斯估计的隶属函数。用正态分布和威布尔分布说明了该方法的有效性。

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