Measurement Uncertainty Evaluation And Control Based On Bayesian Theory

Dealing with the evaluation and control of uncertainty, the small samplessituation is very common, but the conventional evaluation method from the"Guidelines for Measurement Uncertainty Evaluation "(abbreviation: GUM) is oneof the statistical methods based on the law of large numbers, and these statisticalmethods rely on large sample size and the obedience of typical probabilitydistribution of measurement data. These formula applications are not applicableunder the small sample. Compared with other methods theory, Bayesian theory canbe seen as the most scientific system on uncertainty evaluation of the small sample.The Bayesian approach is an assumption based on the subjective experience, whichgives a huge risk on uncertainty evaluation and control; Therefore, this paperintroduces the Maximum Entropy principle and Monte Carlo methods on theframework of the Bayesian approach in order to avoid gross errors caused byassumptions, and effectively solve the posterior distribution.In using the maximum entropy method to solve the prior distribution, there is adifficulty of calculation of higher order moments. So quantile function is put forwardto get effectively their distribution function by dimension reduction; Through thestatistical analysis of the distribution function, the optimal estimation and itsuncertainty is obtained; Through Bootstrap of the distribution function, the containsinterval under a given probability is reliably determined no matter the distribution issymmetrical or not; In the process of evaluation of uncertainty, the difficulty ofcalculation on the Lagrange multiplier can be solved effectively in the view ofgenetic algorithm based on quantile. Through the simulation calculation, it isconcluded that the evaluation results that gets by using the new method foruncertainty evaluation is better than conventional method under the condition ofsmall samples.When using the prior distribution and likelihood function to determine the posterior distribution, because of the influence of prior distribution, parameterequation, and likelihood function, the structure of the posterior distribution is verycomplex. This makes it hard to deduce the distribution, and the distribution is difficultto conduct by statistics analysis. According to the above problems, this paper presentsmodel evaluation and control charts. Based on the method of Monte Carlo, the papergives the process of concrete steps on model evaluation and model control of themeasurement uncertainty. Through example comparison, it is obvious that usingMCM to evaluate and control uncertainty has several advantages: it is suitable for anymodel; it doesn‘t need to consider the influence of inputs‘distribution and correlationbetween them, and to estimate distribution of measurand. It can overcome thedrawback of uncertainty evaluation by general method, especially for unlinearalmodel, give more reliable measurement result.Under the small samples, the conventional method of uncertainty control based ona normal distribution is not applicable. Therefore, according to the uncertaintyassessment methods of Bayesian and Monte Carlo, the baseline and upper and lowercontrol limits of control charts are redefined. And its application in real-time onlinemonitoring ensures the stability of the uncertainty, the early warning if it isout-of-control and the analysis and remedy.