基于贝叶斯方法的混凝土强度接收准则研究

Study on Acceptance Criterion of Concrete Strength Based on Bayesian Method

以一次计量抽样检验理论为依据,综合平衡生产方风险和使用方风险,并适当考虑保护生产方利益,提出无论对于标准差已知统计方法还是标准差未知统计方法,混凝土强度平均值的评定系数k均应对应于90%的等效保证率(0.9分位值);并以贝叶斯理论为依据确定了标准差未知统计方法的抽样方案。样本容量很小时,以平均质量标准差为依据建立了非统计方法的接收准则,并根据一次计数抽样检验理论提出最小值接收准则,并作为平均值接收准则的补充。采用贝叶斯方法,将前一检验周期内的样本和本次抽样样本合并,通过扩大样本容量,提高了标准差已知统计方法接收准则的检验功效;同时采用贝叶斯方法,综合考虑平均质量标准差和实测样本标准差,提高了非统计方法接收准则的检验功效。本文建议的接收准则具有更明确的统计学依据,通过采用统一的等效保证率使各种方法保持了较接近的检验功效,并用贝叶斯方法将各种方法统一于标准差未知统计方法。实例分析表明,本文建议的接收准则总体上略比GB/T 50107—2010严格,但变动幅度在可接受范围;采用合理的先验标准差后,本文建议的贝叶斯改进方法可以得到科学合理的评定结果。

Based on the theory of one-time sampling inspection,balancing the risks of the manufacturer and the user,and considering the protection of the interests of the manufacturer,it is proposed that the evaluation coefficient k for strength average value should be corresponded to 90%the equivalent assurance rate(0.9 Quantile value)for both the known standard deviation method and the unknown standard deviation method,and the sampling scheme when the standard deviation is unknown is determined based on Bayesian theory.When the sampling size is very small,the acceptance criteria of non-statistical method is established based on the average quality standard deviation,and the minimum value acceptance criterion is proposed according to the theory of one-time sampling inspection.Using the concept of Bayesian method,the samples in the previous inspection cycle and the current inspection cycle are combined to expand the sample size and improve the test efficacy of the acceptance criteria with known standard deviation.Bayesian method is adopted to comprehensively consider the average quality standard deviation and the standard deviation of measured samples to improve the test efficacy of acceptance criteria of non-statistical method.The acceptance criteria proposed in this paper have a more clearly statistical basis.The unified equivalent guarantee rate is used to keep the test efficacy close to each other,and the Bayesian theory is used to unify the various methods into the statistical method with unknown standard deviation.The case analysis shows that the acceptance criteria proposed in this paper are slightly stricter than those in GB/T 50107—2010,but the variation range is within the acceptable range;after adopting reasonable prior standard deviation,the Bayesian improved method proposed in this paper can obtain scientific and reasonable evaluation results.