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Abstract.A novel method using a fuzzy practicable interval to characterize non-statistical uncertainty in dynamic measurement is proposed. The method permits the uncertainty being estimated under the conditions that the number of measurements is very small and the probability distribution unknown. The feasibility of the method is validated by computer-simulation experiments.

For costly and dangerous experiments, growing attention has been paid to the problem of the reliability analysis of zerofailure data, with many new findings in world countries, especially in China. The existing reliability theory relies on the known lifetime distribution, such as the Weibull distribution and the gamma distribution. Thus, it is ineffective if the lifetime probability distribution is unknown. For this end, this article proposes the grey bootstrap method in the information poor theory for the reliability analysis of zero-failure data under the condition of a known or unknown probability distribution of lifetime. The grey bootstrap method is able to generate many simulated zero-failure data with the help of few zero-failure data and to estimate the lifetime probability distribution by means of an empirical failure probability function defined in this article. The experimental investigation presents that the grey bootstrap method is effective in the reliability analysis only with the few zero-failure data and without any prior information of the lifetime probability distribution.

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