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`Mathematical Problems in EngineeringVolume 2017, Article ID 1594898, 11 pageshttps://doi.org/10.1155/2017/1594898`
Research Article

## Calculation of Misjudgment Probability for Product Inspection Based on Measurement Uncertainty

1School of Instrument Science and Optoelectronic Engineering, Hefei University of Technology, Hefei 230009, China
2Shenzhen Engineering Laboratory of Geometry Measurement Technology, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China
3Fujian Province Institute of Metrology, Fuzhou 350003, China

Correspondence should be addressed to Yin-bao Cheng; nc.ude.tufh.liam@oabniygnehc and Hou-de Liu; nc.ude.auhgnist.zs@dh.uil

Received 14 March 2017; Revised 28 October 2017; Accepted 13 November 2017; Published 7 December 2017

Academic Editor: Ludovic Chamoin

Copyright © 2017 Xiao-huai Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.