Abstract: The main difficulty in small-sample statistical evaluation is its few failures. The problem becomes more complicated when DOOF(Data only one eailures) occurs. It has received little attention in the existing literature. Bayesian method is applied to derive the failure probability under DOOF. The method takes beta distribution as the prior distribution. The scale parameter of beta distribution is not fixed, but follows a uniform distribution. Adopting the weighted least square estimate method, the formulas of reliability distribution parameter is obtained. Accordingly the reliability characteristic values are estimated. It is easy to apply and no complicated computation is involved in the formulas. Finally, the proposed method is applied to a DOOF problem in the following example. It is shown that the results agree with historical data. The validity of the above method in analyzing DOOF is proved.

Key words: DOOF data, Hierarchical Bayesian estimate, Reliability analysis