基于小批量制造过程的动态质量控制限及其简便计算方法

讨论了一种基于t分布动态控制限的小批量生产质量控制方法，并给出了该控制限的简便计算过程。控制方法通过分析抽样样本数量与控制图虚发警报概率之间的函数对应关系，得到一组能使虚发警报概率保持相对稳定的动态控制限，建立了基于t分布的控制界限值随样本数量变化的数学模型，并利用上侧分位数的初等数学表达式近似表示t分布，从而简化计算过程。实际计算结果表明，当样本组数小于5时，控制方法的计算误差仅为正态逼近法的20％。控制方法形式简单，不需使用正态分布函数，适合小批量生产过程的质量控制。

Research on Dynamic Quality Control Limits and Its Convenient Calculation Method under Small Batch Production Conditions

A new quality control approach to the small batch production, which used dynamic control limits based on t-distribution, was presented, and the simple and convenient algorithm was also addressed. First, by analyzing the function relationship between the number of samples and the probability of the first type of errors, a group of dynamic control limits was attained, by which the probability of the first type of errors was reliably regardless of the number of observations. Then a model based on t--distribution was set up, in which the control limits changed with the number of samples. Finally, a simplified calculation method was thus proposed using the approximate expression for the t --distribution on upper percentile. The results of calculation show that the error of proposed approach is only 20% of that by the traditional approach, while the sample groups are less than 5. In conclusion, the proposed approach has a simple form without Gauss distribution and is in a large application to the quality control of small batch production.