无失效数据下ZZ分布的可靠性分析

Reliability Analysis of ZZ Distribution Under Zero Failure Data

有些产品的寿命用常见的分布去刻画与实际偏差较大,而ZZ分布能够较好地描述这一类产品的寿命分布,为了在无失效数据条件下对ZZ分布进行可靠性分析,通过对该分布可靠度函数进行变换,并利用其凹凸性得到产品在各检测时刻可靠度之间更为精确地关系,进一步在先验分布为均匀分布和更一般的分布下,给出了各个时刻可靠度的贝叶斯估计。同时依据无失效数据场合下,已知函数的置信水平为1-α的最优置信下限公式,给出了ZZ分布可靠度函数的最优置信下限表达式,并且在几种特殊场合得到了便于使用的简化形式。

It is a deviation reality that lifespan of some products is described by common distributions. However,the ZZ distribution can better describe the lifespan distribution of this type of product. In order tostudy the reliability of the ZZ distribution under the condition of no failure data, and the reliability function is transformed, and the concavity and convexity is used to obtain a more precise relationship between the reliability of the products at each detection time. Further, under the prior distribution is the uniform distribution or more general distribution, Bayesian Estimation of the reliability at each moment is given. Meanwhile, according to the optimal confidence lower limit formula of known function with confidence level of 1-α in the case of no failure data, the optimal confidence lower limit expression of the reliability function is given, and the simplified form that is convenient to use is obtained in several special cases.