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In statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique developed by E. S. Page of the University of Cambridge. It is typically used for monitoring change detection. [1] CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's sequential probability ratio test ...
A running total or rolling total is the summation of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total.
Control charts are classified into Shewhart individuals control chart (ISO 7870-2) [2] and CUSUM(CUsUM)(or cumulative sum control chart)(ISO 7870-4). [ 3 ] Control charts, also known as Shewhart charts (after Walter A. Shewhart ) or process-behavior charts , are a statistical process control tool used to determine if a manufacturing or business ...
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Thus each monomial is a constant times a product of cumulants in which the sum of the indices is n (e.g., in the term κ 3 κ 2 2 κ 1, the sum of the indices is 3 + 2 + 2 + 1 = 8; this appears in the polynomial that expresses the 8th moment as a function of the first eight cumulants).
An analogous computation can be done if we're testing if > using the summation of the range from to instead. Calculating a p {\displaystyle p} -value for a two-tailed test is slightly more complicated, since a binomial distribution isn't symmetric if π 0 ≠ 0.5 {\displaystyle \pi _{0}\neq 0.5} .