通过双假设检验控制生产与采购中的误判风险。
Acceptance or Rejection of Lots while Minimizing and Controlling Type I and Type II Errors
- 采用双假设检验同时控制生产者与消费者误差。
- 结合失败次数极限提升检验效能，可精准识别缺陷率区间。
- 支持多种分布模型与模糊逻辑，适合工业质量控制场景。
双假设检验（DHT）可同时控制第一类错误（生产者风险）和第二类错误（消费者风险）。该方法能判断一批产品缺陷率p是否位于1.5%至2%、2%至5%、5%至10%等区间，直至满足特定概率要求。通过并列使用下界分布的Ⅰ类错误与上界分布的Ⅱ类错误，两者均可被控制并最小化。适用于组件生产或采购环节，当缺陷率未知时，结合现有技术和工艺进行判定。检验功效通过引入与更新理论相关的连续失效极限（LSF）得到增强。针对不同应用场景，提出四种伯努利事件序列分布模型：二项分布、泊松近似二项分布、高斯近似二项分布（含两种变体），并评估其计算开销。同时引入模糊逻辑规则以辅助决策。
原文摘要 · Abstract (English)
The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%, and so on, until finding a required value for this probability. Using the two probabilities side by side, the Type I error for the lower probability distribution and the Type II error for the higher probability distribution, both can be controlled and minimized. It can be applied in the development or manufacturing process of a batch of components, or in the case of purchasing from a supplier, when the percentage of defects (p) is unknown, considering the technology and/or process available to obtain them. The power of the test is amplified by the joint application of the Limit of Successive Failures (LSF) related to the Renewal Theory. To enable the choice of the most appropriate algorithm for each application. Four distributions are proposed for the Bernoulli event sequence, including their computational efforts: Binomial, Binomial approximated by Poisson, and Binomial approximated by Gaussian (with two variants). Fuzzy logic rules are also applied to facilitate decision-making.
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