The article presents an algorithm for fast and error-free determination of statistics such as the arithmetic mean and variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement data. Additionally, it shows that both floating-point and integer representation can be used to perform this kind of statistical calculations. The author proves a theorem on the number of bits of precision that an arithmetic type must have to guarantee error-free determination of the arithmetic mean and variance. The article also presents the extension of Welford’s formula for determining variance for the sliding window method—determining the variance of fixed-length contiguous subsequences. The section dedicated to implementation tests shows the running times of individual algorithms depending on the arithmetic type used. The research shows that the use of integers in calculations makes the determination of the aforementioned statistics much faster.

本文提出了一种用于快速，无错误地确定统计数据的算法，例如一系列工业测量数据序列的所有连续子序列和固定长度连续子序列的算术平均值和方差。此外，它表明浮点数和整数表示都可以用于执行这种统计计算。作者证明了关于算术类型必须保证精度无误确定算术平均值和方差所必须具有的精度位数的一个定理。本文还介绍了确定滑动窗口方法方差的Welford公式的扩展-确定固定长度连续子序列的方差。专门用于实现测试的部分显示了各个算法的运行时间，具体取决于所使用的算术类型。研究表明，在计算中使用整数可以更快地确定上述统计量。