Discussion on A the CUSUM method statistical technique

CUSUM-chart is a statistical technique that is mainly used to find out the changes of means level from the sequenced series of the data points. According to the background noise definition, the arithmetical mean of the noise is constant and zero. On the other side, the “signal” can be explained as the deviation of the constant mean.

Most of the CUSUM is depend upon the running sample history of signal detection from background noise. The statistical measures used the dependent values on the estimated sum of the total noise and signals since from the starting of the data sample, which is shortly described in the definition of CUSUM. And the reason is its dependence on the origin time of the trial of the data. And CUSUM is the statistical measure that was used to discover the serial-dependence of the signals where the noise background has been presented.

A brief review of the CUSUM Method

In this method, just imagne that you have the set of discrete sequential points of data {x-n… , x0,x1, x2, …, xn,} whereas n is the positive integer. Without having any loss of generality, the sequel of the data points would be considered as a time-series. On the other side, n represents the time of occurrence of the data point. The estimated sum where the time t is given. The points to be noted that individually enhancing the function where xi is not negative(if xi 0), and the counting process is mainly the measurement of the region under the curve.

Null Hypothesis

In the special case, contain the selected data sequence, which is only noise,e.g.,  s null hypothesis.

In the given data segments regarding stationary noise, the constant value is the variance of the noise Var(n). Although, Var(n) can be used as a constant value for CUSUM-slop to detect changes and variance in the background noise. The time window used in CUSUM-slop calculation is inversely proportional to the criterion used for the detection of changes. Therefore, to calculate the threshold criterion the variance of the CUSUM-slope can be used in the statistical testing. While the "control" variable is a segment of contain noise data to determine SD and the empirical mean of the background noise. In quality control, a priori is determinant of noise whereas data sequences will have without defect components. While prior to the stimulus delivery the data required for neurophysiological experiment is collected which includes data sequences for background noise (without signal of interest). However, if sequences of data noise are not given then approximate values of average and SD can be used as an alternative. While the background noise level will be used as control statistic to determine variance and deviation.

Energy Criterion (EC) of A the CUSUM method statistical technique

In energy change, wavelet corresponds with the energy criterion algorithm basis. Unconventional PD location (6) and acoustics (5) used to measure and estimate arrival times of signals in sonic emission.

Delay in negative trend is caused by α and N (representing signal length)

 Akaike Information Criterion (AIC) of A the CUSUM method statistical technique

An auto-aggressive algorithm of time picking is used to detect signal arrival time. Here changes in the order and value (AR coefficients) are indicating the global minimum onset. AIC algorithm is determined with N elements

Here kth sample value is mentioned before and after the values of x(1,k), x(k+1,N), and var(x) . Although, results suggest that predefined window was required for highly sensitive AIC algorithm in filtered data.