In the traditional industrial verification process, when the aim is the compliance to assigned specifications, it is difficult to find an affordable statistical method for the purpose. Most data tables in industrial procedures and standards deal with tolerance limits neglecting the potential needs to verify assigned specification limits. A two-sided tolerance interval, combined with a bivariate statistical hypothesis test can be used to address this problem. The proposed risk-based approach leads to the determination of the minimum sample size with preestablished probabilities of Type I and Type II errors, that are essential elements for estimating the safety and reliability risk. A novel method is proposed for determination of the tolerance interval testing factors. This approach calculates the testing factors based on the deviation of the mean and the variance from the null hypothesis when a specified value of Type II error is found. The deviations of the mean and variance are determined in such a way that an assigned proportion of the population falls within the specification limits. Additional studies are provided to assess the robustness of the method for nonnormal environments and to compare it with other methods.

中文翻译：

---

用公差区间确定规格限验证的样本量

在传统的工业验证过程中，当目标是符合指定的规范时，很难找到一种经济实惠的统计方法。工业程序和标准中的大多数数据表都涉及公差限制，而忽略了验证指定规格限制的潜在需求。可以使用两侧容差区间与双变量统计假设检验相结合来解决此问题。建议的基于风险的方法导致确定最小样本量，并预先确定 I 类和 II 类错误的概率，这是估计安全性和可靠性风险的基本要素。提出了一种确定公差区间测试因子的新方法。当找到指定的类型 II 错误值时，此方法根据均值和方差与原假设的偏差来计算检验因子。均值和方差的偏差以这样一种方式确定，即指定的总体比例落在规格限内。提供了额外的研究来评估该方法对非正常环境的稳健性，并将其与其他方法进行比较。