改进的T-SPRT在电子商务产品质量检验中的应用

Application of Improved T-SPRT in E-Commerce Product Quality Inspection

摘要: 为保证消费者合法权益以及商家和企业的长久利益，本文对质量指标服从正态分布的电子商务产品在均值参数已知时，对标准差σ参数的截尾序贯检验方案进行了研究。给出了σ参数关于截尾序贯概率比检验(T-SPRT)的截尾序贯检验方案T的定义，方案犯两类错误的概率、平均试验样本量以及综合平均实验样本量等评价指标的计算表达式。并从截距项对T-SPRT方案T进行改进，给出了改进方案T^t的搜索步骤，并利用仿真实验验证方案T^t和评价指标的精确性。仿真结果表明，其仿真实验评价指标值与统计计算得到的评价指标值基本保持一致，表明本文建立的统计指标计算表达式和T^t方案是正确的。与T-SPRT方案T相比，改进方案T^t能更好的控制犯两类错误的概率，保证了实验双方的利益。同时，在样本量截尾值相等时，T^t方案拥有更少的综合平均实验样本量，其下降的比率在10%左右，使得实验成本得到了大幅度减少。

Abstract: In order to ensure the legitimate rights and interests of consumers and the long-term interests of merchants and enterprises, this paper studies the truncation sequential test scheme of the standard deviation σ parameter of e-commerce products whose quality indicators obey normal distribution when the mean parameter is known. The definition of the σ-parameter about the truncated sequential test plan of the truncated sequential probability ratio test (T-SPRT), the probability of the plan making two types of errors, the average test sample size, and the comprehensive average test sample size and other evaluation indicators are given. And the T-SPRT scheme T is improved from the intercept term, and the search steps for the improved scheme T^t are given. Simulation experiments are used to verify the accuracy of the scheme T^t and the evaluation index. The simulation results show that the evaluation index value of the simulation experiment is basically consistent with the evaluation index value obtained by statistical calculation, indicating that the statistical index calculation expression and T^t scheme established in this article are correct. Compared with T-SPRT scheme T, the scheme T^t can better control the probability of making two types of errors, ensuring the interests of both parties in the experiment. At the same time, when the sample size cut-off values are equal, the plan has a smaller comprehensive average experimental sample size, and the reduction rate is about 10%, which greatly reduces the experimental cost.