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威布尔分布是航空装备中较为典型的故障数据分布。为了验证航空装备故障数据在威布尔分布和随机右删失情形下其描述性统计量对客观贝叶斯可靠性评估的影响程度,设计多重马尔可夫链仿真算法,以删失比、样本量为主要因变量,对客观贝叶斯方法进行了敏感性分析。考虑在两参数威布尔分布情形下,以方差较大的伽马分布作为其无信息先验分布,在不同删失比、样本量的驱动下,对威布尔分布的尺度参数和形状参数进行点估计。以分布参数估计均值和变异系数来衡量其估计误差,并将平均故障间隔时间估计误差作为重要的评判依据。数值模拟结果表明,对于故障数据服从威布尔分布时,当样本量在10以上,或者删失比在0.5以下时,客观贝叶斯估计精度较好;当样本量为10以下时,该方法在删失比为0.5以上时估计偏差过大,应该探索更好的小子样条件下高删失比的可靠性评估方法。
Weibull distribution is more typical of aviation equipment fault data distribution. In order to verify the influence degree of descriptive statistics on objective Bayesian reliability evaluation in aviation equipment fault data under Weibull distribution and random right censoring, a multi-Markov chain simulation algorithm is designed. Based on censored data, sample size As the main dependent variable, the objective Bayesian method was analyzed. Considering the two-parameter Weibull distribution, we use the gamma distribution with large variance as the priori distribution with no information. Under the different censoring rates and sample sizes, the dimension and shape parameters of Weibull distribution are considered estimate. The estimation error is measured by the mean of distribution parameter estimation and coefficient of variation, and the estimation error of mean time between failures (MTBF) is taken as the important criterion. The numerical simulation results show that the objective Bayesian estimation accuracy is better when the fault data obeys Weibull distribution when the sample size is above 10, or the censoring ratio is below 0.5. When the sample size is below 10, When the censoring ratio is 0.5 or more, the estimated deviation is too large, and a better method for evaluating the reliability of a high censoring ratio under a small sample condition should be explored.