Tolerance analysis is a method to measure product quality. By measuring and comparing multiple samples of the same batch of products, the tolerance range of products is determined. The root mean square is the index used to calculate these tolerances. It is the square root of the average value of the square value of each tolerance deviation from the average value. Therefore, the root mean square can reflect the tolerance range and distribution of products.

Root mean square has important application value in product design and manufacturing. By analyzing the root mean square, the manufacturing accuracy and stability of products can be evaluated. The small root mean square means that the product has small tolerance and high consistency and quality stability. If the root mean square is large, it means that the tolerance of the product is large, the manufacturing accuracy and quality stability are not high, and the manufacturing process needs to be optimized and improved.

At the same time, root mean square is also widely used in quality control and process improvement. By monitoring the root mean square data of products, quality problems and production anomalies in production can be found in time to avoid large-scale quality problems in large-scale production. In addition, through root mean square analysis and comparison, we can find out the bad factors in the manufacturing process, further optimize the production process and improve the product quality and production efficiency.