Abstract: A hierarchical bootstrap maximum entropy evaluation model is proposed to analyze the life reliability of mechanical products under the condition of small samples without any prior information. Adequate sample data is obtained by using bootstrap method to re-sample the current zero-failure data samples. Based on maximum entropy method, the different Lagrange multipliers can be obtained by changing the number of samples. In order to get the interval estimation values of Lagrange multipliers, the bootstrap method is used again to re-sample the small sample data of Lagrange multipliers. The probability density functions and reliability functions are achieved by carrying on permutation and combination for the upper and lower limit values of each Lagrange multiplier, so the interval estimation values of reliability functions can be gained using minimum uncertainty principle. Experimental investigation shows that the hierarchical bootstrap maximum entropy evaluation model can effectively solve the reliability evaluation problem for zero-failure data of small samples with known or unknown probability distributions.

Key words: system assessment and feasibility analysis, reliability evaluation, hierarchical bootstrap maximum entropy method, poor information, zero-failure data, Lagrange multipliers