Grey bootstrap method of evaluation of uncertainty in dynamic measurement

Abstract A method called the grey bootstrap method is proposed to resolve some problems about evaluation of the uncertainty in the process of dynamic measurement by developing four evaluating indicators, i.e. the estimated uncertainty, the estimated interval, the estimated true value and the mean uncertainty. The method can evaluate the uncertainty without any prior information about probability distribution of random variables, separating trends with known and unknown law. Computer simulation and experiment reveal that the fluctuant path of measured data series is perfectly enveloped in the estimated interval, that the law of trends is exactly traced by the estimated true value, that the variation domain of the random variables is availably assessed via the estimated uncertainty, and that statistical characteristic of dynamic measuring process is quantified with the mean uncertainty. Using the grey bootstrap method, the reliability of the estimated results can usually be up to 100% at the given confidence level.