As process variability shifts can be monitored using a Shewhart R chart or an s-chart, if re is a chance of shifting of process variability, y can be used in conjunction with modified control charts.

Farnum was first person to present generalized approach to DNOM procedure. He defined coefficient of variation as ?/?.

The ARL(2)₀ close form expression could not be evaluated. So Nelson and Stephenson give a lower bound on ARL(2)₀ which is written as,
\(ARL(2)_0=\frac{s^r-1}{2(r-1)}\)

When GCC are used to control process, we plot only largest and smallest of s means observed at any time period on x? chart. If y lie inside control limits, so will ors do.

The Upper control limit of acceptance control chart, when sample size n, and fraction nonconforming for 1-? probability rejection are specified, is expressed as,
\(UCL=USL-\left(Z_?+\frac{Z_?}{\sqrt{n}}\right)\)

The term M_i is average of original mean measurements. It is used in expression of standard variable used in standardized x bar charts for short production runs.

The modified control charts are effective when spread of process is quite less than limits used. So 2-sigma limits are recommended for modified control charts.

The number nonconforming chart is called np chart too. It plots number of nonconforming samples in total samples. The target value for number nonconforming chart is np.

The above process can have different set of data from different streams at any instant of time, so it is an example of Multiple Stream Process.

The one sided in-control ARL for any GCC of any MSP was first explained by Nelson (1986). He expressed it as,
\(ARL(1)_0=\frac{s^r-1}{s-1}\)