Abstract: When evaluating the fatigue life and reliability in the aerospace field, the locale test data sample size is usually extremely small (m=1 or 2) due to the cost and time limits. The compatibility test method can be used to expand the sample size. Conventional Wilcoxon rank sum test method and K-S (Kolmogorov-Smirnov) method are applicable for situation of small sample size. Less research has been conducted on the method for compatibility test of minimum sample size, and there is a lack of detailed explanation of the rationality of the method and comparison of actual effects of different methods. The fatigue life of aerospace products usually obeys the normal distribution, so normal distribution is analyzed in this paper. Two points x₁,x₂ are randomly selected from a normal distribution N(μ,σ²), and the mean μ₁ and standard deviation σ₁ are calculated to construct the new normal distribution N(μ₁,σ₁²). It is found using the Monte Carlo simulation that the probabilities that points placing at ±σ₁, ±2σ₁ and ±3σ₁ ranges of the new normal distribution N(μ₁,σ₁²) place at ±3σ range of the original normal distribution N(μ,σ²) are 99.80%,98.13% and 97.39% respectively. Aiming at the situation that the population follows normal distribution and the sample size is 2, this paper proposes to use the 3σ principle to test the prior information data and thus to expand the sample size. A comparison with other two methods shows that with the proposed method, the error rate is obviously lowered, and with the increase of prior information data, the method performs better.

Key words: compatibility test, 3σ principle, minimal samples, fatigue life test, reliability, normal distribution