9 October 2008 Analysis for systematic stability using fuzzy-set theory
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For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.
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Xintao Xia, Xintao Xia, Zhongyu Wang, Zhongyu Wang, } "Analysis for systematic stability using fuzzy-set theory", Proc. SPIE 7128, Seventh International Symposium on Instrumentation and Control Technology: Measurement Theory and Systems and Aeronautical Equipment, 712805 (9 October 2008); doi: 10.1117/12.806345; https://doi.org/10.1117/12.806345

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