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This document presents the study of a one‐dimensional thermal inclinometer based on free convection.

A micromachined one is used. The sensitivity of the sensor is optimized in a close chamber containing CO2 gas under pressure.

By using this type of sensor in a close chamber containing CO2 gas under pressure, the sensitivity increase and the response time decrease when the pressure increase. High resolution will be achieved.

High shock reliability.

Measuring μg acceleration.

Low cost production.

The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve.

Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution.

By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method.

The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.