Measuring instruments are intended to be intelligent, precise, multi-functional and developing multidirectionally, scientific, and reasonable; the reliable evaluation of measurement uncertainty of precision instruments is also becoming more and more difficult, and the evaluation of the Coordinate Measuring Machines (CMM) measurement uncertainty is among the typical problems. Based on Geometric Product Specification (GPS), this paper has systematically studied the CMM uncertainty for evaluating the size and geometrical errors oriented toward measurement tasks, and thus has realized the rapid and reliable evaluation of the CMM uncertainty for task-oriented measurement. For overestimation of the CMM uncertainty for task-oriented measurements in the initial evaluation, a systematic optimization solution has been proposed. Finally, the feasibility and validity of the evaluation model and the optimization method have been verified by three different types of measurement examples of diameter, flatness and perpendicularity. It is typical and representative to systematically solve the problem of the CMM uncertainty for evaluating the measurement tasks targeted at dimensions and geometric errors, and the research contents can be effectively applied to solve the uncertainty evaluation problems of other precision instruments, which are of great practical significance not only for promoting the combination of modern uncertainty theory and practical applications but also for improving the application values of precision measurement instruments.
Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the noninformative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.
It is important to research into the misjudgment probability of product inspection based on measurement uncertainty, which is of great significance to improve the reliability of inspection results. This paper mainly focused on total inspection and sampling inspection methods and regarded the misjudgment probability as the index to provide quantitative misjudgment risk results for both producer and consumer sides. Through the absolute probability and the conditional probability model, the estimation formula of the total inspection misjudgment rate is deduced, respectively, and the calculation methods of qualification determination and misjudgment rate of the full inspection results are studied. According to the total inspection misjudgment rate, the methods of misjudgment rate of sampling inspection and qualification determination of measurement results are researched. The misjudgment rate of measurement results is calculated based on the exhaustive method and the Monte-Carlo simulation. The estimation results show that the misjudgment probabilities calculated by absolute probability models can be used as the basis for the selection of the measurement plan for product inspection. The misjudgment probability calculated by conditional probability models is more directly to reflect the risks for both producer and consumer sides, and it prompts inspectors to make decisions more carefully.
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