EWMS is defined as exponentially weighted mean square error. It is expressed as,\(S_i^2= ?(x_i-?)^2+(1-?) S_{i-1}^2\)

The value of lower cusum used in standardized scale cusum chart, used for monitoring process variability, is having negative value of what was used in normal cusum. This is written as,
\(S_i^-=max?\left\{0,-v_i-k+S_{i-1}^-\right\}\)

Woodall and Mahmoud (2005) recommended to always use a Shewhart control chart with a EWMA chart (especially when ? is small), as one way to counteract signal resistance?s high value.

The moving average is also a time weighted chart as EWMA charts and Cusum charts. The moving average chart uses Moving Average span w at time i, which is expressed as,
\(M_i=\frac{x_i+x_{i-1}+?x_{i-w+1}}{w}\)

The EWMA charts, which are also called Exponentially Weighted Moving Average charts, were first introduced in year of 1990 by Roberts. It was a revolutionary step towards process control.

The Shewhart control charts have signal resistance value equal to multiplier used to obtain control limit, which is constant. As a x chart is also a Shewhart control chart, so for this also, ? SR=constant?.

As pattern changes in cusums due to an assignable cause, changed pattern gets recorded in all next cusums. So, we can identify from which cusum, pattern changed, and hence assignable cause location can be known.

EWMA charts, when are in operation for a long period, term, 1-(1-?)²ⁱ becomes unity as i becomes large. So UCL can be written as,
UCL=\(?_0+L?\sqrt{\left\{\frac{?}{2-?}\right\}}\)

The value of upper cusum for cusum for normal variance has value of ?² replaced by sample variance S_i². It is expressed as,
\(C_i^+=max?(0,C_{i-1}^+ + S^2 + k)\)

As Combined Cusum-Shewhart procedure is used while using cusum charts to detect large process shifts while keeping process continued, this is called an on-line control.