For costly and dangerous experiments, growing attention has been paid to the problem of the reliability of failure data with small sample sizes. The existing reliability theory relies on a given probability distribution, such as the Weibull distribution and the exponential distribution; thus it is ineffective if the probability distribution is unknown. This paper proposes the grey bootstrap method for the reliability analysis of very few failure data with a known or unknown probability distribution. The grey bootstrap method can be employed to generate many simulated data with few data outputted by a population, as well as to imitate the probability distribution of this population. The experimental investigation shows that the grey bootstrap method is effective in analyzing reliability with small sample sizes without any prior information of the probability distribution.
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